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count="10"/>0<sp count="11"/>q3<sp count="11"/>0<sp count="10"/>0 </text> </region> <region region-id="420" left="264" top="488.25" width="57.75" height="13.5" align-x="306.75" align-y="498" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">ORIGIN</ml:id> <ml:real>1</ml:real> </ml:define> </math> <rendering item-idref="5"/> </region> <region region-id="691" left="24" top="626.25" width="412.5" height="39" align-x="24" align-y="636" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Výchozí poloha - pro výchozí polohu a výpočet inverzní úlohy jsou na místě kloubových proměnných použity proměnné s1, s2, a s3. 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<ml:real>0.14112000805986721</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>1</ml:real> <ml:real>0</ml:real> <ml:real>0.14112000805986721</ml:real> <ml:real>0.98999249660044542</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0.04854649416886482</ml:real> <ml:real>0.80116679780424771</ml:real> <ml:real>1.154</ml:real> <ml:real>1</ml:real> </ml:matrix> </result> </ml:eval> </math> <rendering item-idref="25"/> </region> <region region-id="414" left="36" top="1292.25" width="494.25" height="24" align-x="36" align-y="1302" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial CE" charset="238"> <inlineAttr line-through="false">Řešení soustavy transcendentních rovnic je provedeno jako kontrolní řešení správnosti výpočtu pomocí Taylorova rozvoje transformační matice</inlineAttr> </f> 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push-down="false" lock-width="false"> Řešení metodou Taylorova rozvoje transformační matice </text> </region> <region region-id="53" left="24" top="1634.25" width="108" height="12" align-x="24" align-y="1644" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Diferenciální operátory </text> </region> <region region-id="43" left="18" top="1688.25" width="62.25" height="12" align-x="18" align-y="1698" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> rotační kloub </text> </region> <region region-id="44" left="120" top="1661.25" width="97.5" height="67.5" align-x="139.5" align-y="1698" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> 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use-page-width="false" push-down="false" lock-width="true"> Je vypočtena transformační matice Tb3 ve výchozí poloze a je uložena jako matice TV, matice TD - žádaná poloha zústává konstantní </text> </region> <region region-id="512" left="30" top="2033.25" width="131.25" height="67.5" align-x="50.25" align-y="2070" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">TV</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="4" cols="4"> <ml:real>-1</ml:real> <ml:real>1.2246063538223773E-16</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>1</ml:real> <ml:real>0</ml:real> <ml:real>1.2246063538223773E-16</ml:real> <ml:real>1</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> 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<ml:real>0</ml:real> <ml:real>0.04854649416886482</ml:real> <ml:real>0.80116679780424771</ml:real> <ml:real>1.154</ml:real> <ml:real>1</ml:real> </ml:matrix> </result> </ml:eval> </math> <rendering item-idref="44"/> </region> <region region-id="70" left="18" top="2120.25" width="287.25" height="12" align-x="18" align-y="2130" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Jednotlivé parciální derivace do rozvoje transformační matice </text> </region> <region region-id="838" left="30" top="2174.25" width="140.25" height="17.25" align-x="56.25" align-y="2184" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="31">U</ml:id> <ml:apply> <ml:mult/> <ml:apply> 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<ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>-1</ml:real> <ml:real>1.2246063538223773E-16</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>-1.01</ml:real> <ml:real>-0.064999999999999877</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> </ml:matrix> </result> </ml:eval> </math> <rendering item-idref="46"/> </region> <region region-id="840" left="30" top="2198.25" width="138.75" height="17.25" align-x="56.25" align-y="2208" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="32">U</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="b0">A</ml:id> <ml:id xml:space="preserve" subscript="01">A</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="t">D</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="12">A</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="23">A</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="47"/> </region> <region region-id="860" left="372" top="2171.25" width="103.5" height="67.5" align-x="397.5" align-y="2208" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="32">U</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="4" cols="4"> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>1</ml:real> <ml:real>0</ml:real> </ml:matrix> </result> </ml:eval> </math> <rendering item-idref="48"/> </region> <region region-id="841" left="30" top="2222.25" width="138.75" height="17.25" align-x="56.25" align-y="2232" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="33">U</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="b0">A</ml:id> <ml:id xml:space="preserve" subscript="01">A</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="12">A</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="t">D</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="23">A</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="49"/> </region> <region region-id="873" left="492" top="2195.25" width="103.5" height="67.5" align-x="517.5" align-y="2232" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="33">U</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="4" cols="4"> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>1.2246063538223773E-16</ml:real> <ml:real>1</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> </ml:matrix> </result> </ml:eval> </math> <rendering item-idref="50"/> </region> <region region-id="77" left="12" top="2270.25" width="432" height="12" align-x="12" align-y="2280" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Sestavená soustava rovnic (obrázek z učebního textu) bude řešena maticově </text> </region> <region region-id="880" left="30" top="2304" width="248.25" height="85.5" align-x="30" align-y="2304" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <picture> <png item-idref="51" display-width="246.75" display-height="84"/> </picture> <rendering item-idref="52"/> </region> <region region-id="81" left="18" top="2420.25" width="156.75" height="12" align-x="18" align-y="2430" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Matice koeficientů u proměnných </text> </region> <region region-id="1297" left="222" top="2420.25" width="123" height="12" align-x="238.5" align-y="2430" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Inverze matice koeficientů </text> </region> <region region-id="1300" left="378" top="2420.25" width="98.25" height="12" align-x="378" align-y="2430" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Matice pravých stran </text> </region> <region region-id="82" left="6" top="2444.25" width="160.5" height="74.25" align-x="21" align-y="2484" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIUnit" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">C</ml:id> <ml:matrix rows="3" cols="3"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve" subscript="31">U</ml:id> <ml:sequence> <ml:real>1</ml:real> <ml:real>4</ml:real> </ml:sequence> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve" subscript="31">U</ml:id> <ml:sequence> <ml:real>2</ml:real> <ml:real>4</ml:real> </ml:sequence> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve" subscript="31">U</ml:id> <ml:sequence> <ml:real>3</ml:real> <ml:real>4</ml:real> </ml:sequence> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve" subscript="32">U</ml:id> <ml:sequence> <ml:real>1</ml:real> <ml:real>4</ml:real> </ml:sequence> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve" subscript="32">U</ml:id> <ml:sequence> <ml:real>2</ml:real> <ml:real>4</ml:real> </ml:sequence> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve" subscript="32">U</ml:id> <ml:sequence> <ml:real>3</ml:real> <ml:real>4</ml:real> </ml:sequence> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve" subscript="33">U</ml:id> <ml:sequence> <ml:real>1</ml:real> <ml:real>4</ml:real> </ml:sequence> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve" subscript="33">U</ml:id> <ml:sequence> <ml:real>2</ml:real> <ml:real>4</ml:real> </ml:sequence> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve" subscript="33">U</ml:id> <ml:sequence> <ml:real>3</ml:real> <ml:real>4</ml:real> </ml:sequence> </ml:apply> </ml:matrix> </ml:define> </math> <rendering item-idref="53"/> </region> <region region-id="899" left="192" top="2456.25" width="129.75" height="49.5" align-x="219" align-y="2484" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">C</ml:id> <ml:real>-1</ml:real> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="3" cols="3"> <ml:real>-0.99009900990099009</ml:real> <ml:real>0</ml:real> <ml:real>-0.064356435643564233</ml:real> <ml:real>1.2124815384379974E-16</ml:real> <ml:real>0</ml:real> <ml:real>1</ml:real> <ml:real>0</ml:real> <ml:real>1</ml:real> <ml:real>0</ml:real> </ml:matrix> </result> </ml:eval> </math> <rendering item-idref="54"/> </region> <region region-id="910" left="348" top="2447.25" width="111" height="67.5" align-x="362.25" align-y="2484" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">B</ml:id> <ml:matrix rows="3" cols="1"> <ml:apply> <ml:minus/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">TD</ml:id> <ml:sequence> <ml:real>1</ml:real> <ml:real>4</ml:real> </ml:sequence> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">TV</ml:id> <ml:sequence> <ml:real>1</ml:real> <ml:real>4</ml:real> </ml:sequence> </ml:apply> </ml:apply> <ml:apply> <ml:minus/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">TD</ml:id> <ml:sequence> <ml:real>2</ml:real> <ml:real>4</ml:real> </ml:sequence> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">TV</ml:id> <ml:sequence> <ml:real>2</ml:real> <ml:real>4</ml:real> </ml:sequence> </ml:apply> </ml:apply> <ml:apply> <ml:minus/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">TD</ml:id> <ml:sequence> <ml:real>3</ml:real> <ml:real>4</ml:real> </ml:sequence> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">TV</ml:id> <ml:sequence> <ml:real>3</ml:real> <ml:real>4</ml:real> </ml:sequence> </ml:apply> </ml:apply> </ml:matrix> </ml:define> </math> <rendering item-idref="55"/> </region> <region region-id="913" left="486" top="2456.25" width="87.75" height="49.5" align-x="499.5" align-y="2484" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">B</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="3" cols="1"> <ml:real>0.1135464941688647</ml:real> <ml:real>-0.2088332021957523</ml:real> <ml:real>-0.30000000000000027</ml:real> </ml:matrix> </result> </ml:eval> </math> <rendering item-idref="56"/> </region> <region region-id="371" left="30" top="2558.25" width="172.5" height="12" align-x="30" align-y="2568" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Řešením soustavy rovnic je matice D </text> </region> <region region-id="517" left="30" top="2588.25" width="54.75" height="19.5" align-x="45" align-y="2604" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">D</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">C</ml:id> <ml:real>-1</ml:real> </ml:apply> <ml:id xml:space="preserve">B</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="57"/> </region> <region region-id="518" left="156" top="2576.25" width="88.5" height="49.5" align-x="170.25" align-y="2604" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">D</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="3" cols="1"> <ml:real>-0.11242227145432152</ml:real> <ml:real>-0.30000000000000027</ml:real> <ml:real>-0.21614064984028319</ml:real> </ml:matrix> </result> </ml:eval> </math> <rendering item-idref="58"/> </region> <region region-id="931" left="24" top="2642.25" width="333.75" height="12" align-x="34.5" align-y="2652" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> Krok, který je potřeba udělat z výchozí polohy směrem k řešení je tedy </text> </region> <region region-id="919" left="42" top="2666.25" width="61.5" height="19.5" align-x="70.5" align-y="2676" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="1">Δs</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">D</ml:id> <ml:sequence> <ml:real>1</ml:real> <ml:real>1</ml:real> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="59"/> </region> <region region-id="922" left="42" top="2684.25" width="61.5" height="19.5" align-x="70.5" align-y="2694" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="2">Δs</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">D</ml:id> <ml:sequence> <ml:real>2</ml:real> <ml:real>1</ml:real> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="60"/> </region> <region region-id="926" left="42" top="2702.25" width="61.5" height="19.5" align-x="70.5" align-y="2712" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="3">Δs</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">D</ml:id> <ml:sequence> <ml:real>3</ml:real> <ml:real>1</ml:real> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="61"/> </region> <region region-id="933" left="24" top="2732.25" width="145.5" height="12" align-x="47.25" align-y="2742" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> Vypočtení nové výchozí polohy </text> </region> <region region-id="133" left="36" top="2762.25" width="72.75" height="17.25" align-x="54.75" align-y="2772" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="1">s</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve" subscript="1">s</ml:id> <ml:id xml:space="preserve" subscript="1">Δs</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="62"/> </region> <region region-id="134" left="36" top="2780.25" width="72.75" height="17.25" align-x="54.75" align-y="2790" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="2">s</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve" subscript="2">s</ml:id> <ml:id xml:space="preserve" subscript="2">Δs</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="63"/> </region> <region region-id="135" left="36" top="2798.25" width="72.75" height="17.25" align-x="54.75" align-y="2808" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="3">s</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve" subscript="3">s</ml:id> <ml:id xml:space="preserve" subscript="3">Δs</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="64"/> </region> <region region-id="116" left="240" top="2798.25" width="207.75" height="24" align-x="240" align-y="2808" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Pro kontrolu porovnání s již předem vypočtenými referenčními hodnotami </text> </region> <region region-id="136" left="36" top="2834.25" width="72" height="17.25" align-x="54" align-y="2844" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="1">s</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>3.0291703821354714</ml:real> </result> </ml:eval> </math> <rendering item-idref="65"/> </region> <region region-id="271" left="234" top="2834.25" width="39.75" height="17.25" align-x="252.75" align-y="2844" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="1">q</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>3</ml:real> </result> </ml:eval> </math> <rendering item-idref="66"/> </region> <region region-id="137" left="36" top="2852.25" width="48" height="17.25" align-x="54" align-y="2862" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="2">s</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>0.59999999999999976</ml:real> </result> </ml:eval> </math> <rendering item-idref="67"/> </region> <region region-id="272" left="234" top="2852.25" width="48.75" height="17.25" align-x="252.75" align-y="2862" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="2">q</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>0.6</ml:real> </result> </ml:eval> </math> <rendering item-idref="68"/> </region> <region region-id="138" left="36" top="2870.25" width="72" height="17.25" align-x="54" align-y="2880" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="3">s</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>0.79385935015971687</ml:real> </result> </ml:eval> </math> <rendering item-idref="69"/> </region> <region region-id="273" left="234" top="2870.25" width="48.75" height="17.25" align-x="252.75" align-y="2880" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="3">q</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>0.8</ml:real> </result> </ml:eval> </math> <rendering item-idref="70"/> </region> <region region-id="1335" left="30" top="2906.25" width="424.5" height="66" align-x="36" align-y="2916" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Při pohledu na vypočtené kloubové proměnné vidíme, že s1 se liší o 29 tisícin radiánu, s2 je již vypočtena přesně ( je nastaveno zobrazování na 5 desetinných míst), s3 se liší zhruba o 7 mm. Je tedy nutná další iterace. Je to způsobeno poměrně velkým rozdílem mezi výchozí a žádanou polohou. Pokud bude tento rozdíl malý, řešení je nalezeno již po jedné iteraci. </text> </region> <region region-id="1336" left="30" top="3008.25" width="281.25" height="12" align-x="30" align-y="3018" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Druhá iterace - výrazy jsou zkopírovány z předchozí iterace </text> </region> <region region-id="954" left="30" top="3032.25" width="137.25" height="12" align-x="30" align-y="3042" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> Matice v nové výchozí poloze </text> </region> <region region-id="1105" left="24" top="3065.25" width="120" height="67.5" align-x="51" align-y="3102" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math 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background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Je vypočtena transformační matice Tb3 ve výchozí poloze a je uložena jako matice TV, matice TD - žádaná poloha zústává konstantní </text> </region> <region region-id="1112" left="54" top="3239.25" width="203.25" height="67.5" align-x="74.25" align-y="3276" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">TV</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="4" cols="4"> <ml:real>-0.99368726940523</ml:real> <ml:real>0.11218560790929398</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>1</ml:real> <ml:real>0</ml:real> <ml:real>0.11218560790929398</ml:real> <ml:real>0.99368726940523</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0.024469921280804954</ml:real> <ml:real>0.79613999446612349</ml:real> <ml:real>1.154</ml:real> <ml:real>1</ml:real> </ml:matrix> </result> </ml:eval> </math> <rendering item-idref="77"/> </region> <region region-id="1186" left="288" top="3239.25" width="204" height="67.5" align-x="309" align-y="3276" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">TD</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="4" cols="4"> <ml:real>-0.98999249660044542</ml:real> <ml:real>0.14112000805986721</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>1</ml:real> <ml:real>0</ml:real> <ml:real>0.14112000805986721</ml:real> <ml:real>0.98999249660044542</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0.04854649416886482</ml:real> <ml:real>0.80116679780424771</ml:real> <ml:real>1.154</ml:real> <ml:real>1</ml:real> </ml:matrix> </result> </ml:eval> </math> <rendering item-idref="78"/> </region> <region region-id="1114" left="42" top="3326.25" width="287.25" height="12" align-x="42" align-y="3336" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Jednotlivé parciální derivace do rozvoje transformační matice </text> </region> <region region-id="1115" left="54" top="3380.25" width="140.25" height="17.25" align-x="80.25" align-y="3390" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" 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<ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>1</ml:real> <ml:real>0</ml:real> </ml:matrix> </result> </ml:eval> </math> <rendering item-idref="82"/> </region> <region region-id="1119" left="54" top="3428.25" width="138.75" height="17.25" align-x="80.25" align-y="3438" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="33">U</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="b0">A</ml:id> <ml:id xml:space="preserve" subscript="01">A</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="12">A</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="t">D</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="23">A</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="83"/> </region> <region region-id="1171" left="588" top="3401.25" width="136.5" height="67.5" align-x="613.5" align-y="3438" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="33">U</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="4" cols="4"> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0.11218560790929398</ml:real> <ml:real>0.99368726940523</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> </ml:matrix> </result> </ml:eval> </math> <rendering item-idref="84"/> </region> <region region-id="1304" left="48" top="3476.25" width="156.75" height="12" align-x="48" align-y="3486" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Matice koeficientů u proměnných </text> </region> <region region-id="1305" left="252" top="3476.25" width="123" height="12" align-x="268.5" align-y="3486" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Inverze matice koeficientů </text> </region> <region region-id="1306" left="408" top="3476.25" width="98.25" height="12" align-x="408" align-y="3486" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Matice pravých stran </text> </region> <region region-id="1125" left="30" top="3500.25" width="160.5" height="74.25" align-x="45" align-y="3540" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">C</ml:id> <ml:matrix rows="3" cols="3"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve" subscript="31">U</ml:id> <ml:sequence> <ml:real>1</ml:real> <ml:real>4</ml:real> </ml:sequence> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve" subscript="31">U</ml:id> <ml:sequence> <ml:real>2</ml:real> <ml:real>4</ml:real> </ml:sequence> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve" subscript="31">U</ml:id> <ml:sequence> <ml:real>3</ml:real> <ml:real>4</ml:real> </ml:sequence> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve" subscript="32">U</ml:id> <ml:sequence> <ml:real>1</ml:real> <ml:real>4</ml:real> </ml:sequence> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve" subscript="32">U</ml:id> <ml:sequence> <ml:real>2</ml:real> <ml:real>4</ml:real> </ml:sequence> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve" subscript="32">U</ml:id> <ml:sequence> <ml:real>3</ml:real> <ml:real>4</ml:real> </ml:sequence> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve" subscript="33">U</ml:id> <ml:sequence> <ml:real>1</ml:real> <ml:real>4</ml:real> </ml:sequence> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve" subscript="33">U</ml:id> <ml:sequence> <ml:real>2</ml:real> <ml:real>4</ml:real> </ml:sequence> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve" subscript="33">U</ml:id> <ml:sequence> <ml:real>3</ml:real> <ml:real>4</ml:real> </ml:sequence> </ml:apply> </ml:matrix> </ml:define> </math> <rendering item-idref="85"/> </region> <region region-id="1126" left="216" top="3512.25" width="162.75" height="49.5" align-x="243" align-y="3540" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">C</ml:id> <ml:real>-1</ml:real> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="3" cols="3"> <ml:real>-1.2517170317453712</ml:real> <ml:real>0</ml:real> <ml:real>0.030824000845844853</ml:real> <ml:real>0.14131673058549138</ml:real> <ml:real>0</ml:real> <ml:real>1.002872856893287</ml:real> <ml:real>0</ml:real> <ml:real>1</ml:real> <ml:real>0</ml:real> </ml:matrix> </result> </ml:eval> </math> <rendering item-idref="86"/> </region> <region region-id="1191" left="390" top="3503.25" width="111" height="67.5" align-x="404.25" align-y="3540" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">B</ml:id> <ml:matrix rows="3" cols="1"> <ml:apply> <ml:minus/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">TD</ml:id> <ml:sequence> <ml:real>1</ml:real> <ml:real>4</ml:real> </ml:sequence> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">TV</ml:id> <ml:sequence> <ml:real>1</ml:real> <ml:real>4</ml:real> </ml:sequence> </ml:apply> </ml:apply> <ml:apply> <ml:minus/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">TD</ml:id> <ml:sequence> <ml:real>2</ml:real> <ml:real>4</ml:real> </ml:sequence> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">TV</ml:id> <ml:sequence> <ml:real>2</ml:real> <ml:real>4</ml:real> </ml:sequence> </ml:apply> </ml:apply> <ml:apply> <ml:minus/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">TD</ml:id> <ml:sequence> <ml:real>3</ml:real> <ml:real>4</ml:real> </ml:sequence> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">TV</ml:id> <ml:sequence> <ml:real>3</ml:real> <ml:real>4</ml:real> </ml:sequence> </ml:apply> </ml:apply> </ml:matrix> </ml:define> </math> <rendering item-idref="87"/> </region> <region region-id="1192" left="528" top="3509.25" width="111.75" height="55.5" align-x="541.5" align-y="3540" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">B</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="3" cols="1"> <ml:real>0.024076572888059866</ml:real> <ml:real>0.0050268033381242194</ml:real> <ml:real>0</ml:real> </ml:matrix> </result> </ml:eval> </math> <rendering item-idref="88"/> </region> <region region-id="1129" left="54" top="3614.25" width="172.5" height="12" align-x="54" align-y="3624" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Řešením soustavy rovnic je matice D </text> </region> <region region-id="1130" left="54" top="3644.25" width="54.75" height="19.5" align-x="69" align-y="3660" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">D</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">C</ml:id> <ml:real>-1</ml:real> </ml:apply> <ml:id xml:space="preserve">B</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="89"/> </region> <region region-id="1131" left="180" top="3629.25" width="118.5" height="55.5" align-x="194.25" align-y="3660" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">D</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="3" cols="1"> <ml:real>-0.029426684937003428</ml:real> <ml:real>0</ml:real> <ml:real>0.00578338092781195</ml:real> </ml:matrix> </result> </ml:eval> </math> <rendering item-idref="90"/> </region> <region region-id="1132" left="48" top="3698.25" width="333.75" height="12" align-x="58.5" align-y="3708" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Krok, který je potřeba udělat z výchozí polohy směrem k řešení je tedy </text> </region> <region region-id="1133" left="66" top="3722.25" width="61.5" height="19.5" align-x="94.5" align-y="3732" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="1">Δs</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">D</ml:id> <ml:sequence> <ml:real>1</ml:real> <ml:real>1</ml:real> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="91"/> </region> <region region-id="1134" left="66" top="3740.25" width="61.5" height="19.5" align-x="94.5" align-y="3750" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="2">Δs</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">D</ml:id> <ml:sequence> <ml:real>2</ml:real> <ml:real>1</ml:real> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="92"/> </region> <region region-id="1135" left="66" top="3758.25" width="61.5" height="19.5" align-x="94.5" align-y="3768" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="3">Δs</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">D</ml:id> <ml:sequence> <ml:real>3</ml:real> <ml:real>1</ml:real> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="93"/> </region> <region region-id="1136" left="48" top="3788.25" width="145.5" height="12" align-x="71.25" align-y="3798" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Vypočtení nové výchozí polohy </text> </region> <region region-id="1137" left="60" top="3818.25" width="72.75" height="17.25" align-x="78.75" align-y="3828" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="1">s</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve" subscript="1">s</ml:id> <ml:id xml:space="preserve" subscript="1">Δs</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="94"/> </region> <region region-id="1138" left="60" top="3836.25" width="72.75" height="17.25" align-x="78.75" align-y="3846" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="2">s</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve" subscript="2">s</ml:id> <ml:id xml:space="preserve" subscript="2">Δs</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="95"/> </region> <region region-id="1139" left="60" top="3854.25" width="72.75" height="17.25" align-x="78.75" align-y="3864" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="3">s</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve" subscript="3">s</ml:id> <ml:id xml:space="preserve" subscript="3">Δs</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="96"/> </region> <region region-id="1140" left="264" top="3854.25" width="207.75" height="24" align-x="264" align-y="3864" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Pro kontrolu porovnání s již předem vypočtenými referenčními hodnotami </text> </region> <region region-id="1141" left="60" top="3890.25" width="72" height="17.25" align-x="78" align-y="3900" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="1">s</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>2.9997436971984679</ml:real> </result> </ml:eval> </math> <rendering item-idref="97"/> </region> <region region-id="1142" left="258" top="3890.25" width="39.75" height="17.25" align-x="276.75" align-y="3900" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="1">q</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>3</ml:real> </result> </ml:eval> </math> <rendering item-idref="98"/> </region> <region region-id="1143" left="60" top="3908.25" width="48" height="17.25" align-x="78" align-y="3918" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="2">s</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>0.59999999999999976</ml:real> </result> </ml:eval> </math> <rendering item-idref="99"/> </region> <region region-id="1144" left="258" top="3908.25" width="48.75" height="17.25" align-x="276.75" align-y="3918" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="2">q</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>0.6</ml:real> </result> </ml:eval> </math> <rendering item-idref="100"/> </region> <region region-id="1145" left="60" top="3926.25" width="72" height="17.25" align-x="78" align-y="3936" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="3">s</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>0.79964273108752881</ml:real> </result> </ml:eval> </math> <rendering item-idref="101"/> </region> <region region-id="1146" left="258" top="3926.25" width="48.75" height="17.25" align-x="276.75" align-y="3936" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="3">q</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>0.8</ml:real> </result> </ml:eval> </math> <rendering item-idref="102"/> </region> <region region-id="1346" left="54" top="3968.25" width="424.5" height="54" align-x="60" align-y="3978" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Při pohledu na vypočtené kloubové proměnné vidíme, že s1 se liší o necelou tisícinu radiánu, s2 je vypočtena přesně ( je nastaveno zobrazování na 5 desetinných míst), s3 se liší zhruba o 4 desetitisíciny mm. To by pro běžnou přesnost v robotice již stačilo. Pro ještě přesnější výpočet je provedena ještě další iterace. </text> </region> <region region-id="1147" left="60" top="4052.25" width="274.5" height="12" align-x="60" align-y="4062" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Třetí iterace - výrazy jsou zkopírovány z předchozí iterace </text> </region> <region region-id="1193" left="42" top="4091.25" width="120" height="67.5" align-x="69" align-y="4128" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="b0">A</ml:id> <ml:matrix rows="4" cols="4"> <ml:real>1</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>1</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>1</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0.554</ml:real> <ml:real>1</ml:real> </ml:matrix> </ml:define> </math> <rendering item-idref="103"/> </region> <region region-id="1194" left="180" top="4087.5" width="162" height="75" align-x="207" align-y="4128" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="01">A</ml:id> <ml:matrix rows="4" cols="4"> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:id xml:space="preserve" subscript="1">s</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:id xml:space="preserve" subscript="1">s</ml:id> </ml:apply> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:apply> <ml:neg/> <ml:apply> <ml:id 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region-id="1198" left="216" top="4184.25" width="48.75" height="17.25" align-x="237" align-y="4194" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">TV</ml:id> <ml:id xml:space="preserve" subscript="b3">T</ml:id> </ml:define> </math> <rendering item-idref="108"/> </region> <region region-id="1199" left="66" top="4220.25" width="525" height="24" align-x="70.5" align-y="4230" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Je vypočtena transformační matice Tb3 ve výchozí poloze a je uložena jako matice TV, matice TD - žádaná poloha zústává konstantní </text> </region> <region region-id="1200" left="72" top="4265.25" width="197.25" height="67.5" align-x="92.25" align-y="4302" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">TV</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="4" cols="4"> <ml:real>-0.98995629463056267</ml:real> <ml:real>0.14137374127229754</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>1</ml:real> <ml:real>0</ml:real> <ml:real>0.14137374127229754</ml:real> <ml:real>0.98995629463056267</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0.048701325424055128</ml:real> <ml:real>0.80080064827837283</ml:real> <ml:real>1.154</ml:real> <ml:real>1</ml:real> </ml:matrix> </result> </ml:eval> </math> <rendering item-idref="109"/> </region> <region region-id="1201" left="216" top="4265.25" width="204" height="67.5" align-x="237" align-y="4302" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">TD</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="4" cols="4"> <ml:real>-0.98999249660044542</ml:real> <ml:real>0.14112000805986721</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>1</ml:real> <ml:real>0</ml:real> <ml:real>0.14112000805986721</ml:real> <ml:real>0.98999249660044542</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0.04854649416886482</ml:real> <ml:real>0.80116679780424771</ml:real> <ml:real>1.154</ml:real> <ml:real>1</ml:real> </ml:matrix> </result> </ml:eval> </math> <rendering item-idref="110"/> </region> <region region-id="1202" left="60" top="4352.25" width="287.25" height="12" align-x="60" align-y="4362" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Jednotlivé parciální derivace do rozvoje transformační matice </text> </region> <region region-id="1203" left="72" top="4406.25" width="140.25" height="17.25" align-x="98.25" align-y="4416" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="31">U</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="b0">A</ml:id> <ml:id xml:space="preserve" subscript="r">D</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="01">A</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="12">A</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="23">A</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="111"/> </region> <region region-id="1204" left="258" top="4379.25" width="214.5" height="67.5" align-x="283.5" align-y="4416" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="31">U</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="4" cols="4"> <ml:real>-0.14137374127229754</ml:real> <ml:real>-0.98995629463056267</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>-0.98995629463056267</ml:real> <ml:real>0.14137374127229754</ml:real> 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xml:space="preserve" subscript="23">A</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="113"/> </region> <region region-id="1256" left="480" top="4403.25" width="103.5" height="67.5" align-x="505.5" align-y="4440" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="32">U</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="4" cols="4"> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>1</ml:real> <ml:real>0</ml:real> </ml:matrix> </result> </ml:eval> </math> <rendering item-idref="114"/> </region> <region region-id="1207" left="72" top="4454.25" width="138.75" height="17.25" align-x="98.25" align-y="4464" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="33">U</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="b0">A</ml:id> <ml:id xml:space="preserve" subscript="01">A</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="12">A</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="t">D</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="23">A</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="115"/> </region> <region region-id="1257" left="600" top="4427.25" width="136.5" height="67.5" align-x="625.5" align-y="4464" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="33">U</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="4" cols="4"> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0.14137374127229754</ml:real> <ml:real>0.98995629463056267</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> </ml:matrix> </result> </ml:eval> </math> <rendering item-idref="116"/> </region> <region region-id="1310" left="54" top="4496.25" width="156.75" height="12" align-x="54" align-y="4506" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Matice koeficientů u proměnných </text> </region> <region region-id="1311" left="258" top="4496.25" width="123" height="12" align-x="274.5" align-y="4506" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Inverze matice koeficientů </text> </region> <region region-id="1312" left="414" top="4496.25" width="98.25" height="12" align-x="414" align-y="4506" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Matice pravých stran </text> </region> <region region-id="1213" left="48" top="4526.25" width="160.5" height="74.25" align-x="63" align-y="4566" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">C</ml:id> <ml:matrix rows="3" cols="3"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve" subscript="31">U</ml:id> <ml:sequence> <ml:real>1</ml:real> <ml:real>4</ml:real> </ml:sequence> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve" subscript="31">U</ml:id> <ml:sequence> <ml:real>2</ml:real> <ml:real>4</ml:real> </ml:sequence> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve" subscript="31">U</ml:id> <ml:sequence> <ml:real>3</ml:real> <ml:real>4</ml:real> </ml:sequence> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve" subscript="32">U</ml:id> <ml:sequence> <ml:real>1</ml:real> <ml:real>4</ml:real> </ml:sequence> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve" subscript="32">U</ml:id> <ml:sequence> <ml:real>2</ml:real> <ml:real>4</ml:real> </ml:sequence> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve" subscript="32">U</ml:id> <ml:sequence> <ml:real>3</ml:real> <ml:real>4</ml:real> </ml:sequence> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve" subscript="33">U</ml:id> <ml:sequence> <ml:real>1</ml:real> <ml:real>4</ml:real> </ml:sequence> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve" subscript="33">U</ml:id> <ml:sequence> <ml:real>2</ml:real> <ml:real>4</ml:real> </ml:sequence> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve" subscript="33">U</ml:id> <ml:sequence> <ml:real>3</ml:real> <ml:real>4</ml:real> </ml:sequence> </ml:apply> </ml:matrix> </ml:define> </math> <rendering item-idref="117"/> </region> <region region-id="1214" left="234" top="4538.25" width="150.75" height="49.5" align-x="261" align-y="4566" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">C</ml:id> <ml:real>-1</ml:real> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="3" cols="3"> <ml:real>-1.2379982411447721</ml:real> <ml:real>0</ml:real> <ml:real>0.060903855597887364</ml:real> <ml:real>0.17679613129231683</ml:real> <ml:real>0</ml:real> <ml:real>1.0014480431645634</ml:real> <ml:real>0</ml:real> <ml:real>1</ml:real> <ml:real>0</ml:real> </ml:matrix> </result> </ml:eval> </math> <rendering item-idref="118"/> </region> <region region-id="1215" left="390" top="4529.25" width="111" height="67.5" align-x="404.25" align-y="4566" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">B</ml:id> <ml:matrix rows="3" cols="1"> <ml:apply> <ml:minus/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">TD</ml:id> <ml:sequence> <ml:real>1</ml:real> <ml:real>4</ml:real> </ml:sequence> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">TV</ml:id> <ml:sequence> <ml:real>1</ml:real> <ml:real>4</ml:real> </ml:sequence> </ml:apply> </ml:apply> <ml:apply> <ml:minus/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">TD</ml:id> <ml:sequence> <ml:real>2</ml:real> <ml:real>4</ml:real> </ml:sequence> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">TV</ml:id> <ml:sequence> <ml:real>2</ml:real> <ml:real>4</ml:real> </ml:sequence> </ml:apply> </ml:apply> <ml:apply> <ml:minus/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">TD</ml:id> <ml:sequence> <ml:real>3</ml:real> <ml:real>4</ml:real> </ml:sequence> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">TV</ml:id> <ml:sequence> <ml:real>3</ml:real> <ml:real>4</ml:real> </ml:sequence> </ml:apply> </ml:apply> </ml:matrix> </ml:define> </math> <rendering item-idref="119"/> </region> <region region-id="1216" left="528" top="4532.25" width="123.75" height="61.5" align-x="541.5" align-y="4566" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">B</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="3" cols="1"> <ml:real>-0.00015483125519030749</ml:real> <ml:real>0.00036614952587488148</ml:real> <ml:real>0</ml:real> </ml:matrix> </result> </ml:eval> </math> <rendering item-idref="120"/> </region> <region region-id="1217" left="72" top="4640.25" width="172.5" height="12" align-x="72" align-y="4650" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Řešením soustavy rovnic je matice D </text> </region> <region region-id="1218" left="72" top="4670.25" width="54.75" height="19.5" align-x="87" align-y="4686" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">D</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">C</ml:id> <ml:real>-1</ml:real> </ml:apply> <ml:id xml:space="preserve">B</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="121"/> </region> <region region-id="1219" left="198" top="4652.25" width="118.5" height="61.5" align-x="212.25" align-y="4686" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">D</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="3" cols="1"> <ml:real>0.00025641464124903315</ml:real> <ml:real>0</ml:real> <ml:real>0.00035724990578488256</ml:real> </ml:matrix> </result> </ml:eval> </math> <rendering item-idref="122"/> </region> <region region-id="1220" left="66" top="4724.25" width="333.75" height="12" align-x="76.5" align-y="4734" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Krok, který je potřeba udělat z výchozí polohy směrem k řešení je tedy </text> </region> <region region-id="1221" left="84" top="4748.25" width="61.5" height="19.5" align-x="112.5" align-y="4758" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="1">Δs</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">D</ml:id> <ml:sequence> <ml:real>1</ml:real> <ml:real>1</ml:real> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="123"/> </region> <region region-id="1222" left="84" top="4766.25" width="61.5" height="19.5" align-x="112.5" align-y="4776" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="2">Δs</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">D</ml:id> <ml:sequence> <ml:real>2</ml:real> <ml:real>1</ml:real> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="124"/> </region> <region region-id="1223" left="84" top="4784.25" width="61.5" height="19.5" align-x="112.5" align-y="4794" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="3">Δs</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">D</ml:id> <ml:sequence> <ml:real>3</ml:real> <ml:real>1</ml:real> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="125"/> </region> <region region-id="1224" left="66" top="4814.25" width="145.5" height="12" align-x="89.25" align-y="4824" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Vypočtení nové výchozí polohy </text> </region> <region region-id="1225" left="78" top="4844.25" width="72.75" height="17.25" align-x="96.75" align-y="4854" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="1">s</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve" subscript="1">s</ml:id> <ml:id xml:space="preserve" subscript="1">Δs</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="126"/> </region> <region region-id="1226" left="78" top="4862.25" width="72.75" height="17.25" align-x="96.75" align-y="4872" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="2">s</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve" subscript="2">s</ml:id> <ml:id xml:space="preserve" subscript="2">Δs</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="127"/> </region> <region region-id="1227" left="78" top="4880.25" width="72.75" height="17.25" align-x="96.75" align-y="4890" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="3">s</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve" subscript="3">s</ml:id> <ml:id xml:space="preserve" subscript="3">Δs</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="128"/> </region> <region region-id="1228" left="282" top="4880.25" width="207.75" height="24" align-x="282" align-y="4890" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Pro kontrolu porovnání s již předem vypočtenými referenčními hodnotami </text> </region> <region region-id="1229" left="78" top="4916.25" width="39" height="17.25" align-x="96" align-y="4926" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="1">s</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>3.000000111839717</ml:real> </result> </ml:eval> </math> <rendering item-idref="129"/> </region> <region region-id="1230" left="276" top="4916.25" width="39.75" height="17.25" align-x="294.75" align-y="4926" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="1">q</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>3</ml:real> </result> </ml:eval> </math> <rendering item-idref="130"/> </region> <region region-id="1231" left="78" top="4934.25" width="48" height="17.25" align-x="96" align-y="4944" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="2">s</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>0.59999999999999976</ml:real> </result> </ml:eval> </math> <rendering item-idref="131"/> </region> <region region-id="1232" left="276" top="4934.25" width="48.75" height="17.25" align-x="294.75" align-y="4944" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="2">q</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>0.6</ml:real> </result> </ml:eval> </math> <rendering item-idref="132"/> </region> <region region-id="1233" left="78" top="4952.25" width="48" height="17.25" align-x="96" align-y="4962" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="3">s</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>0.79999998099331371</ml:real> </result> </ml:eval> </math> <rendering item-idref="133"/> </region> <region region-id="1234" left="276" top="4952.25" width="48.75" height="17.25" align-x="294.75" align-y="4962" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="3">q</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>0.8</ml:real> </result> </ml:eval> </math> <rendering item-idref="134"/> </region> <region region-id="1321" left="24" top="4988.25" width="418.5" height="36" align-x="24" align-y="4998" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Po třetí iteraci jsou již hodnoty hledaných kloubových proměnných vypočteny naprosto správně (zobrazení výsledku je nastaveno na pět desetinných míst), odpovídají referenčním hodnotám a výpočet může skončit </text> </region> <region region-id="1323" left="30" top="5102.25" width="163.5" height="12" align-x="63" align-y="5112" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> Programování v prostředí Mathcad </text> </region> <region region-id="1325" left="30" top="5126.25" width="354.75" height="12" align-x="48" align-y="5136" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> Výchozí poloha, pro kterou jsou v programu vyčísleny transformační matice </text> </region> <region region-id="1274" left="66" top="5150.25" width="35.25" height="17.25" align-x="84.75" align-y="5160" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="1">s</ml:id> <ml:id xml:space="preserve">π</ml:id> </ml:define> </math> <rendering item-idref="135"/> </region> <region region-id="1275" left="132" top="5150.25" width="42.75" height="17.25" align-x="150.75" align-y="5160" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="3">s</ml:id> <ml:real>0.9</ml:real> </ml:define> </math> <rendering item-idref="136"/> </region> <region region-id="1276" left="198" top="5150.25" width="42.75" height="17.25" align-x="216.75" align-y="5160" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="2">s</ml:id> <ml:real>0.8</ml:real> </ml:define> </math> <rendering item-idref="137"/> </region> <region region-id="1327" left="36" top="5180.25" width="72" height="12" align-x="53.25" align-y="5190" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> Žádaná poloha </text> </region> <region region-id="1328" left="30" top="5207.25" width="204" height="67.5" align-x="51" align-y="5244" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">TD</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="4" cols="4"> <ml:real>-0.98999249660044542</ml:real> <ml:real>0.14112000805986721</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>1</ml:real> <ml:real>0</ml:real> <ml:real>0.14112000805986721</ml:real> <ml:real>0.98999249660044542</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0.04854649416886482</ml:real> <ml:real>0.80116679780424771</ml:real> <ml:real>1.154</ml:real> <ml:real>1</ml:real> </ml:matrix> </result> </ml:eval> </math> <rendering item-idref="138"/> </region> <region region-id="1277" left="6" top="5306.25" width="412.5" height="24" align-x="6" align-y="5316" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Program v Mathcadu definuje funkci inverze(ε), kde ε je požadovaná přesnost výpočtu - zde součet kroků </text> </region> <region region-id="1259" left="66" top="5342.25" width="255" height="757.5" align-x="122.25" align-y="5352" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve">inverze</ml:id> <ml:boundVars> <ml:id xml:space="preserve">ε</ml:id> </ml:boundVars> </ml:function> <ml:program> <ml:localDefine> <ml:id xml:space="preserve">ds</ml:id> <ml:real>100</ml:real> </ml:localDefine> <ml:while> <ml:apply> <ml:greaterThan/> <ml:id xml:space="preserve">ds</ml:id> <ml:id xml:space="preserve">ε</ml:id> </ml:apply> <ml:program> <ml:localDefine> <ml:id xml:space="preserve" subscript="b0">A</ml:id> <ml:matrix rows="4" cols="4"> <ml:real>1</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>1</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> 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<ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>1</ml:real> </ml:matrix> </ml:localDefine> <ml:localDefine> <ml:id xml:space="preserve" subscript="12">A</ml:id> <ml:matrix rows="4" cols="4"> <ml:real>1</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>1</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>-1</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0.065</ml:real> <ml:real>0</ml:real> <ml:id xml:space="preserve" subscript="2">s</ml:id> <ml:real>1</ml:real> </ml:matrix> </ml:localDefine> <ml:localDefine> <ml:id xml:space="preserve" subscript="23">A</ml:id> <ml:matrix rows="4" cols="4"> <ml:real>1</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>1</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>1</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:id xml:space="preserve" subscript="3">s</ml:id> <ml:real>1</ml:real> </ml:matrix> </ml:localDefine> <ml:localDefine> <ml:id xml:space="preserve">TV</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="b0">A</ml:id> <ml:id xml:space="preserve" subscript="01">A</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="12">A</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="23">A</ml:id> </ml:apply> </ml:localDefine> <ml:localDefine> <ml:id xml:space="preserve" subscript="1">U</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="b0">A</ml:id> <ml:id xml:space="preserve" subscript="r">D</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="01">A</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="12">A</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="23">A</ml:id> </ml:apply> </ml:localDefine> <ml:localDefine> <ml:id 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count="3"/>Pi/2 3<sp count="10"/>0<sp count="11"/>q3<sp count="11"/>0<sp count="10"/>0 </text> </region> <region region-id="420" left="264" top="488.25" width="57.75" height="13.5" align-x="306.75" align-y="498" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">ORIGIN</ml:id> <ml:real>1</ml:real> </ml:define> </math> <rendering item-idref="5"/> </region> <region region-id="691" left="24" top="626.25" width="412.5" height="39" align-x="24" align-y="636" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Výchozí poloha - pro výchozí polohu a výpočet inverzní úlohy jsou na místě kloubových proměnných použity proměnné s1, s2, a s3. 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<ml:real>0.14112000805986721</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>1</ml:real> <ml:real>0</ml:real> <ml:real>0.14112000805986721</ml:real> <ml:real>0.98999249660044542</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0.04854649416886482</ml:real> <ml:real>0.80116679780424771</ml:real> <ml:real>1.154</ml:real> <ml:real>1</ml:real> </ml:matrix> </result> </ml:eval> </math> <rendering item-idref="25"/> </region> <region region-id="414" left="36" top="1292.25" width="494.25" height="24" align-x="36" align-y="1302" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial CE" charset="238"> <inlineAttr line-through="false">Řešení soustavy transcendentních rovnic je provedeno jako kontrolní řešení správnosti výpočtu pomocí Taylorova rozvoje transformační matice</inlineAttr> </f> 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push-down="false" lock-width="false"> Řešení metodou Taylorova rozvoje transformační matice </text> </region> <region region-id="53" left="24" top="1634.25" width="108" height="12" align-x="24" align-y="1644" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Diferenciální operátory </text> </region> <region region-id="43" left="18" top="1688.25" width="62.25" height="12" align-x="18" align-y="1698" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> rotační kloub </text> </region> <region region-id="44" left="120" top="1661.25" width="97.5" height="67.5" align-x="139.5" align-y="1698" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> 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<ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>1</ml:real> <ml:real>0</ml:real> </ml:matrix> </result> </ml:eval> </math> <rendering item-idref="48"/> </region> <region region-id="841" left="30" top="2222.25" width="138.75" height="17.25" align-x="56.25" align-y="2232" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="33">U</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="b0">A</ml:id> <ml:id xml:space="preserve" subscript="01">A</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="12">A</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="t">D</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="23">A</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="49"/> </region> <region region-id="873" left="492" top="2195.25" width="103.5" height="67.5" align-x="517.5" align-y="2232" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="33">U</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="4" cols="4"> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>1.2246063538223773E-16</ml:real> <ml:real>1</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> </ml:matrix> </result> </ml:eval> </math> <rendering item-idref="50"/> </region> <region region-id="77" left="12" top="2270.25" width="432" height="12" align-x="12" align-y="2280" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Sestavená soustava rovnic (obrázek z učebního textu) bude řešena maticově </text> </region> <region region-id="880" left="30" top="2304" width="248.25" height="85.5" align-x="30" align-y="2304" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <picture> <png item-idref="51" display-width="246.75" display-height="84"/> </picture> <rendering item-idref="52"/> </region> <region region-id="81" left="18" top="2420.25" width="156.75" height="12" align-x="18" align-y="2430" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Matice koeficientů u proměnných </text> </region> <region region-id="1297" left="222" top="2420.25" width="123" height="12" align-x="238.5" align-y="2430" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Inverze matice koeficientů </text> </region> <region region-id="1300" left="378" top="2420.25" width="98.25" height="12" align-x="378" align-y="2430" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Matice pravých stran </text> </region> <region region-id="82" left="6" top="2444.25" width="160.5" height="74.25" align-x="21" align-y="2484" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIUnit" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">C</ml:id> <ml:matrix rows="3" cols="3"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve" subscript="31">U</ml:id> <ml:sequence> <ml:real>1</ml:real> <ml:real>4</ml:real> </ml:sequence> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve" subscript="31">U</ml:id> <ml:sequence> <ml:real>2</ml:real> <ml:real>4</ml:real> </ml:sequence> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve" subscript="31">U</ml:id> <ml:sequence> <ml:real>3</ml:real> <ml:real>4</ml:real> </ml:sequence> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve" subscript="32">U</ml:id> <ml:sequence> <ml:real>1</ml:real> <ml:real>4</ml:real> </ml:sequence> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve" subscript="32">U</ml:id> <ml:sequence> <ml:real>2</ml:real> <ml:real>4</ml:real> </ml:sequence> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve" subscript="32">U</ml:id> <ml:sequence> <ml:real>3</ml:real> <ml:real>4</ml:real> </ml:sequence> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve" subscript="33">U</ml:id> <ml:sequence> <ml:real>1</ml:real> <ml:real>4</ml:real> </ml:sequence> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve" subscript="33">U</ml:id> <ml:sequence> <ml:real>2</ml:real> <ml:real>4</ml:real> </ml:sequence> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve" subscript="33">U</ml:id> <ml:sequence> <ml:real>3</ml:real> <ml:real>4</ml:real> </ml:sequence> </ml:apply> </ml:matrix> </ml:define> </math> <rendering item-idref="53"/> </region> <region region-id="899" left="192" top="2456.25" width="129.75" height="49.5" align-x="219" align-y="2484" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">C</ml:id> <ml:real>-1</ml:real> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="3" cols="3"> <ml:real>-0.99009900990099009</ml:real> <ml:real>0</ml:real> <ml:real>-0.064356435643564233</ml:real> <ml:real>1.2124815384379974E-16</ml:real> <ml:real>0</ml:real> <ml:real>1</ml:real> <ml:real>0</ml:real> <ml:real>1</ml:real> <ml:real>0</ml:real> </ml:matrix> </result> </ml:eval> </math> <rendering item-idref="54"/> </region> <region region-id="910" left="348" top="2447.25" width="111" height="67.5" align-x="362.25" align-y="2484" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">B</ml:id> <ml:matrix rows="3" cols="1"> <ml:apply> <ml:minus/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">TD</ml:id> <ml:sequence> <ml:real>1</ml:real> <ml:real>4</ml:real> </ml:sequence> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">TV</ml:id> <ml:sequence> <ml:real>1</ml:real> <ml:real>4</ml:real> </ml:sequence> </ml:apply> </ml:apply> <ml:apply> <ml:minus/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">TD</ml:id> <ml:sequence> <ml:real>2</ml:real> <ml:real>4</ml:real> </ml:sequence> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">TV</ml:id> <ml:sequence> <ml:real>2</ml:real> <ml:real>4</ml:real> </ml:sequence> </ml:apply> </ml:apply> <ml:apply> <ml:minus/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">TD</ml:id> <ml:sequence> <ml:real>3</ml:real> <ml:real>4</ml:real> </ml:sequence> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">TV</ml:id> <ml:sequence> <ml:real>3</ml:real> <ml:real>4</ml:real> </ml:sequence> </ml:apply> </ml:apply> </ml:matrix> </ml:define> </math> <rendering item-idref="55"/> </region> <region region-id="913" left="486" top="2456.25" width="87.75" height="49.5" align-x="499.5" align-y="2484" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">B</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="3" cols="1"> <ml:real>0.1135464941688647</ml:real> <ml:real>-0.2088332021957523</ml:real> <ml:real>-0.30000000000000027</ml:real> </ml:matrix> </result> </ml:eval> </math> <rendering item-idref="56"/> </region> <region region-id="371" left="30" top="2558.25" width="172.5" height="12" align-x="30" align-y="2568" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Řešením soustavy rovnic je matice D </text> </region> <region region-id="517" left="30" top="2588.25" width="54.75" height="19.5" align-x="45" align-y="2604" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">D</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">C</ml:id> <ml:real>-1</ml:real> </ml:apply> <ml:id xml:space="preserve">B</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="57"/> </region> <region region-id="518" left="156" top="2576.25" width="88.5" height="49.5" align-x="170.25" align-y="2604" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">D</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="3" cols="1"> <ml:real>-0.11242227145432152</ml:real> <ml:real>-0.30000000000000027</ml:real> <ml:real>-0.21614064984028319</ml:real> </ml:matrix> </result> </ml:eval> </math> <rendering item-idref="58"/> </region> <region region-id="931" left="24" top="2642.25" width="333.75" height="12" align-x="34.5" align-y="2652" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> Krok, který je potřeba udělat z výchozí polohy směrem k řešení je tedy </text> </region> <region region-id="919" left="42" top="2666.25" width="61.5" height="19.5" align-x="70.5" align-y="2676" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="1">Δs</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">D</ml:id> <ml:sequence> <ml:real>1</ml:real> <ml:real>1</ml:real> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="59"/> </region> <region region-id="922" left="42" top="2684.25" width="61.5" height="19.5" align-x="70.5" align-y="2694" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="2">Δs</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">D</ml:id> <ml:sequence> <ml:real>2</ml:real> <ml:real>1</ml:real> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="60"/> </region> <region region-id="926" left="42" top="2702.25" width="61.5" height="19.5" align-x="70.5" align-y="2712" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="3">Δs</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">D</ml:id> <ml:sequence> <ml:real>3</ml:real> <ml:real>1</ml:real> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="61"/> </region> <region region-id="933" left="24" top="2732.25" width="145.5" height="12" align-x="47.25" align-y="2742" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> Vypočtení nové výchozí polohy </text> </region> <region region-id="133" left="36" top="2762.25" width="72.75" height="17.25" align-x="54.75" align-y="2772" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="1">s</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve" subscript="1">s</ml:id> <ml:id xml:space="preserve" subscript="1">Δs</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="62"/> </region> <region region-id="134" left="36" top="2780.25" width="72.75" height="17.25" align-x="54.75" align-y="2790" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="2">s</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve" subscript="2">s</ml:id> <ml:id xml:space="preserve" subscript="2">Δs</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="63"/> </region> <region region-id="135" left="36" top="2798.25" width="72.75" height="17.25" align-x="54.75" align-y="2808" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="3">s</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve" subscript="3">s</ml:id> <ml:id xml:space="preserve" subscript="3">Δs</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="64"/> </region> <region region-id="116" left="240" top="2798.25" width="207.75" height="24" align-x="240" align-y="2808" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Pro kontrolu porovnání s již předem vypočtenými referenčními hodnotami </text> </region> <region region-id="136" left="36" top="2834.25" width="72" height="17.25" align-x="54" align-y="2844" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="1">s</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>3.0291703821354714</ml:real> </result> </ml:eval> </math> <rendering item-idref="65"/> </region> <region region-id="271" left="234" top="2834.25" width="39.75" height="17.25" align-x="252.75" align-y="2844" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="1">q</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>3</ml:real> </result> </ml:eval> </math> <rendering item-idref="66"/> </region> <region region-id="137" left="36" top="2852.25" width="48" height="17.25" align-x="54" align-y="2862" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="2">s</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>0.59999999999999976</ml:real> </result> </ml:eval> </math> <rendering item-idref="67"/> </region> <region region-id="272" left="234" top="2852.25" width="48.75" height="17.25" align-x="252.75" align-y="2862" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="2">q</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>0.6</ml:real> </result> </ml:eval> </math> <rendering item-idref="68"/> </region> <region region-id="138" left="36" top="2870.25" width="72" height="17.25" align-x="54" align-y="2880" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="3">s</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>0.79385935015971687</ml:real> </result> </ml:eval> </math> <rendering item-idref="69"/> </region> <region region-id="273" left="234" top="2870.25" width="48.75" height="17.25" align-x="252.75" align-y="2880" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="3">q</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>0.8</ml:real> </result> </ml:eval> </math> <rendering item-idref="70"/> </region> <region region-id="1335" left="30" top="2906.25" width="424.5" height="66" align-x="36" align-y="2916" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Při pohledu na vypočtené kloubové proměnné vidíme, že s1 se liší o 29 tisícin radiánu, s2 je již vypočtena přesně ( je nastaveno zobrazování na 5 desetinných míst), s3 se liší zhruba o 7 mm. Je tedy nutná další iterace. Je to způsobeno poměrně velkým rozdílem mezi výchozí a žádanou polohou. Pokud bude tento rozdíl malý, řešení je nalezeno již po jedné iteraci. </text> </region> <region region-id="1336" left="30" top="3008.25" width="281.25" height="12" align-x="30" align-y="3018" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Druhá iterace - výrazy jsou zkopírovány z předchozí iterace </text> </region> <region region-id="954" left="30" top="3032.25" width="137.25" height="12" align-x="30" align-y="3042" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> Matice v nové výchozí poloze </text> </region> <region region-id="1105" left="24" top="3065.25" width="120" height="67.5" align-x="51" align-y="3102" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math 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background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Je vypočtena transformační matice Tb3 ve výchozí poloze a je uložena jako matice TV, matice TD - žádaná poloha zústává konstantní </text> </region> <region region-id="1112" left="54" top="3239.25" width="203.25" height="67.5" align-x="74.25" align-y="3276" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">TV</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="4" cols="4"> <ml:real>-0.99368726940523</ml:real> <ml:real>0.11218560790929398</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>1</ml:real> <ml:real>0</ml:real> <ml:real>0.11218560790929398</ml:real> <ml:real>0.99368726940523</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0.024469921280804954</ml:real> <ml:real>0.79613999446612349</ml:real> <ml:real>1.154</ml:real> <ml:real>1</ml:real> </ml:matrix> </result> </ml:eval> </math> <rendering item-idref="77"/> </region> <region region-id="1186" left="288" top="3239.25" width="204" height="67.5" align-x="309" align-y="3276" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">TD</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="4" cols="4"> <ml:real>-0.98999249660044542</ml:real> <ml:real>0.14112000805986721</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>1</ml:real> <ml:real>0</ml:real> <ml:real>0.14112000805986721</ml:real> <ml:real>0.98999249660044542</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0.04854649416886482</ml:real> <ml:real>0.80116679780424771</ml:real> <ml:real>1.154</ml:real> <ml:real>1</ml:real> </ml:matrix> </result> </ml:eval> </math> <rendering item-idref="78"/> </region> <region region-id="1114" left="42" top="3326.25" width="287.25" height="12" align-x="42" align-y="3336" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Jednotlivé parciální derivace do rozvoje transformační matice </text> </region> <region region-id="1115" left="54" top="3380.25" width="140.25" height="17.25" align-x="80.25" align-y="3390" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" 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<ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>1</ml:real> <ml:real>0</ml:real> </ml:matrix> </result> </ml:eval> </math> <rendering item-idref="82"/> </region> <region region-id="1119" left="54" top="3428.25" width="138.75" height="17.25" align-x="80.25" align-y="3438" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="33">U</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="b0">A</ml:id> <ml:id xml:space="preserve" subscript="01">A</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="12">A</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="t">D</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="23">A</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="83"/> </region> <region region-id="1171" left="588" top="3401.25" width="136.5" height="67.5" align-x="613.5" align-y="3438" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="33">U</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="4" cols="4"> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0.11218560790929398</ml:real> <ml:real>0.99368726940523</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> </ml:matrix> </result> </ml:eval> </math> <rendering item-idref="84"/> </region> <region region-id="1304" left="48" top="3476.25" width="156.75" height="12" align-x="48" align-y="3486" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Matice koeficientů u proměnných </text> </region> <region region-id="1305" left="252" top="3476.25" width="123" height="12" align-x="268.5" align-y="3486" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Inverze matice koeficientů </text> </region> <region region-id="1306" left="408" top="3476.25" width="98.25" height="12" align-x="408" align-y="3486" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Matice pravých stran </text> </region> <region region-id="1125" left="30" top="3500.25" width="160.5" height="74.25" align-x="45" align-y="3540" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">C</ml:id> <ml:matrix rows="3" cols="3"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve" subscript="31">U</ml:id> <ml:sequence> <ml:real>1</ml:real> <ml:real>4</ml:real> </ml:sequence> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve" subscript="31">U</ml:id> <ml:sequence> <ml:real>2</ml:real> <ml:real>4</ml:real> </ml:sequence> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve" 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<ml:sequence> <ml:real>3</ml:real> <ml:real>4</ml:real> </ml:sequence> </ml:apply> </ml:matrix> </ml:define> </math> <rendering item-idref="85"/> </region> <region region-id="1126" left="216" top="3512.25" width="162.75" height="49.5" align-x="243" align-y="3540" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">C</ml:id> <ml:real>-1</ml:real> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="3" cols="3"> <ml:real>-1.2517170317453712</ml:real> <ml:real>0</ml:real> <ml:real>0.030824000845844853</ml:real> <ml:real>0.14131673058549138</ml:real> <ml:real>0</ml:real> <ml:real>1.002872856893287</ml:real> <ml:real>0</ml:real> <ml:real>1</ml:real> <ml:real>0</ml:real> </ml:matrix> </result> </ml:eval> </math> 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<ml:sequence> <ml:real>2</ml:real> <ml:real>4</ml:real> </ml:sequence> </ml:apply> </ml:apply> <ml:apply> <ml:minus/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">TD</ml:id> <ml:sequence> <ml:real>3</ml:real> <ml:real>4</ml:real> </ml:sequence> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">TV</ml:id> <ml:sequence> <ml:real>3</ml:real> <ml:real>4</ml:real> </ml:sequence> </ml:apply> </ml:apply> </ml:matrix> </ml:define> </math> <rendering item-idref="87"/> </region> <region region-id="1192" left="528" top="3509.25" width="111.75" height="55.5" align-x="541.5" align-y="3540" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">B</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="3" cols="1"> <ml:real>0.024076572888059866</ml:real> <ml:real>0.0050268033381242194</ml:real> <ml:real>0</ml:real> </ml:matrix> </result> </ml:eval> </math> <rendering item-idref="88"/> </region> <region region-id="1129" left="54" top="3614.25" width="172.5" height="12" align-x="54" align-y="3624" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Řešením soustavy rovnic je matice D </text> </region> <region region-id="1130" left="54" top="3644.25" width="54.75" height="19.5" align-x="69" align-y="3660" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">D</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">C</ml:id> 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background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Krok, který je potřeba udělat z výchozí polohy směrem k řešení je tedy </text> </region> <region region-id="1133" left="66" top="3722.25" width="61.5" height="19.5" align-x="94.5" align-y="3732" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="1">Δs</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">D</ml:id> <ml:sequence> <ml:real>1</ml:real> <ml:real>1</ml:real> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="91"/> </region> <region region-id="1134" left="66" top="3740.25" width="61.5" height="19.5" align-x="94.5" align-y="3750" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="2">Δs</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">D</ml:id> <ml:sequence> <ml:real>2</ml:real> <ml:real>1</ml:real> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="92"/> </region> <region region-id="1135" left="66" top="3758.25" width="61.5" height="19.5" align-x="94.5" align-y="3768" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="3">Δs</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">D</ml:id> <ml:sequence> <ml:real>3</ml:real> <ml:real>1</ml:real> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="93"/> </region> <region region-id="1136" left="48" top="3788.25" width="145.5" height="12" align-x="71.25" align-y="3798" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Vypočtení nové výchozí polohy </text> </region> <region region-id="1137" left="60" top="3818.25" width="72.75" height="17.25" align-x="78.75" align-y="3828" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="1">s</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve" subscript="1">s</ml:id> <ml:id xml:space="preserve" subscript="1">Δs</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="94"/> </region> <region region-id="1138" left="60" top="3836.25" width="72.75" height="17.25" align-x="78.75" align-y="3846" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="2">s</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve" subscript="2">s</ml:id> <ml:id xml:space="preserve" subscript="2">Δs</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="95"/> </region> <region region-id="1139" left="60" top="3854.25" width="72.75" height="17.25" align-x="78.75" align-y="3864" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="3">s</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve" subscript="3">s</ml:id> <ml:id xml:space="preserve" subscript="3">Δs</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="96"/> </region> <region region-id="1140" left="264" top="3854.25" width="207.75" height="24" align-x="264" align-y="3864" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Pro kontrolu porovnání s již předem vypočtenými referenčními hodnotami </text> </region> <region region-id="1141" left="60" top="3890.25" width="72" height="17.25" align-x="78" align-y="3900" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="1">s</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>2.9997436971984679</ml:real> </result> </ml:eval> </math> <rendering item-idref="97"/> </region> <region region-id="1142" left="258" top="3890.25" width="39.75" height="17.25" align-x="276.75" align-y="3900" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="1">q</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>3</ml:real> </result> </ml:eval> </math> <rendering item-idref="98"/> </region> <region region-id="1143" left="60" top="3908.25" width="48" height="17.25" align-x="78" align-y="3918" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval 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</region> <region region-id="1346" left="54" top="3968.25" width="424.5" height="54" align-x="60" align-y="3978" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Při pohledu na vypočtené kloubové proměnné vidíme, že s1 se liší o necelou tisícinu radiánu, s2 je vypočtena přesně ( je nastaveno zobrazování na 5 desetinných míst), s3 se liší zhruba o 4 desetitisíciny mm. To by pro běžnou přesnost v robotice již stačilo. Pro ještě přesnější výpočet je provedena ještě další iterace. </text> </region> <region region-id="1147" left="60" top="4052.25" width="274.5" height="12" align-x="60" align-y="4062" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Třetí iterace - výrazy jsou zkopírovány z předchozí iterace </text> </region> <region region-id="1193" left="42" top="4091.25" width="120" height="67.5" align-x="69" align-y="4128" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="b0">A</ml:id> <ml:matrix rows="4" cols="4"> <ml:real>1</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>1</ml:real> <ml:real>0</ml:real> 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region-id="1198" left="216" top="4184.25" width="48.75" height="17.25" align-x="237" align-y="4194" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">TV</ml:id> <ml:id xml:space="preserve" subscript="b3">T</ml:id> </ml:define> </math> <rendering item-idref="108"/> </region> <region region-id="1199" left="66" top="4220.25" width="525" height="24" align-x="70.5" align-y="4230" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Je vypočtena transformační matice Tb3 ve výchozí poloze a je uložena jako matice TV, matice TD - žádaná poloha zústává konstantní </text> </region> <region region-id="1200" left="72" top="4265.25" width="197.25" height="67.5" align-x="92.25" align-y="4302" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">TV</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="4" cols="4"> <ml:real>-0.98995629463056267</ml:real> <ml:real>0.14137374127229754</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>1</ml:real> <ml:real>0</ml:real> <ml:real>0.14137374127229754</ml:real> <ml:real>0.98995629463056267</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0.048701325424055128</ml:real> <ml:real>0.80080064827837283</ml:real> <ml:real>1.154</ml:real> <ml:real>1</ml:real> </ml:matrix> </result> </ml:eval> </math> <rendering item-idref="109"/> </region> <region region-id="1201" left="216" top="4265.25" width="204" height="67.5" align-x="237" align-y="4302" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">TD</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="4" cols="4"> <ml:real>-0.98999249660044542</ml:real> <ml:real>0.14112000805986721</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>1</ml:real> <ml:real>0</ml:real> <ml:real>0.14112000805986721</ml:real> <ml:real>0.98999249660044542</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0.04854649416886482</ml:real> <ml:real>0.80116679780424771</ml:real> <ml:real>1.154</ml:real> <ml:real>1</ml:real> </ml:matrix> </result> </ml:eval> </math> <rendering item-idref="110"/> </region> <region region-id="1202" left="60" top="4352.25" width="287.25" height="12" align-x="60" align-y="4362" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Jednotlivé parciální derivace do rozvoje transformační matice </text> </region> <region region-id="1203" left="72" top="4406.25" width="140.25" height="17.25" align-x="98.25" align-y="4416" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="31">U</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="b0">A</ml:id> <ml:id xml:space="preserve" subscript="r">D</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="01">A</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="12">A</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="23">A</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="111"/> </region> <region region-id="1204" left="258" top="4379.25" width="214.5" height="67.5" align-x="283.5" align-y="4416" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="31">U</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="4" cols="4"> <ml:real>-0.14137374127229754</ml:real> <ml:real>-0.98995629463056267</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>-0.98995629463056267</ml:real> <ml:real>0.14137374127229754</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>-0.80080064827837283</ml:real> <ml:real>0.048701325424055128</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> </ml:matrix> </result> </ml:eval> </math> <rendering item-idref="112"/> </region> <region region-id="1205" left="72" top="4430.25" width="138.75" height="17.25" align-x="98.25" align-y="4440" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="32">U</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="b0">A</ml:id> <ml:id xml:space="preserve" subscript="01">A</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="t">D</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="12">A</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="23">A</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="113"/> </region> <region region-id="1256" left="480" top="4403.25" width="103.5" height="67.5" align-x="505.5" align-y="4440" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="32">U</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="4" cols="4"> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>1</ml:real> <ml:real>0</ml:real> </ml:matrix> </result> </ml:eval> </math> <rendering item-idref="114"/> </region> <region region-id="1207" left="72" top="4454.25" width="138.75" height="17.25" align-x="98.25" align-y="4464" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="33">U</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="b0">A</ml:id> <ml:id xml:space="preserve" subscript="01">A</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="12">A</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="t">D</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="23">A</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="115"/> </region> <region region-id="1257" left="600" top="4427.25" width="136.5" height="67.5" align-x="625.5" align-y="4464" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="33">U</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="4" cols="4"> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0.14137374127229754</ml:real> <ml:real>0.98995629463056267</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> </ml:matrix> </result> </ml:eval> </math> <rendering item-idref="116"/> </region> <region region-id="1310" left="54" top="4496.25" width="156.75" height="12" align-x="54" align-y="4506" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Matice koeficientů u proměnných </text> </region> <region region-id="1311" left="258" top="4496.25" width="123" height="12" align-x="274.5" align-y="4506" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Inverze matice koeficientů </text> </region> <region region-id="1312" left="414" top="4496.25" width="98.25" height="12" align-x="414" align-y="4506" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Matice pravých stran </text> </region> <region region-id="1213" left="48" top="4526.25" width="160.5" height="74.25" align-x="63" align-y="4566" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">C</ml:id> <ml:matrix rows="3" cols="3"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve" subscript="31">U</ml:id> <ml:sequence> <ml:real>1</ml:real> <ml:real>4</ml:real> </ml:sequence> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve" subscript="31">U</ml:id> <ml:sequence> <ml:real>2</ml:real> <ml:real>4</ml:real> </ml:sequence> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve" subscript="31">U</ml:id> <ml:sequence> <ml:real>3</ml:real> <ml:real>4</ml:real> </ml:sequence> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve" subscript="32">U</ml:id> <ml:sequence> <ml:real>1</ml:real> <ml:real>4</ml:real> </ml:sequence> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve" subscript="32">U</ml:id> <ml:sequence> <ml:real>2</ml:real> <ml:real>4</ml:real> </ml:sequence> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve" subscript="32">U</ml:id> <ml:sequence> <ml:real>3</ml:real> <ml:real>4</ml:real> </ml:sequence> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve" subscript="33">U</ml:id> <ml:sequence> <ml:real>1</ml:real> <ml:real>4</ml:real> </ml:sequence> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve" subscript="33">U</ml:id> <ml:sequence> <ml:real>2</ml:real> <ml:real>4</ml:real> </ml:sequence> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve" subscript="33">U</ml:id> <ml:sequence> <ml:real>3</ml:real> <ml:real>4</ml:real> </ml:sequence> </ml:apply> </ml:matrix> </ml:define> </math> <rendering item-idref="117"/> </region> <region region-id="1214" left="234" top="4538.25" width="150.75" height="49.5" align-x="261" align-y="4566" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math 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xml:space="preserve">B</ml:id> <ml:matrix rows="3" cols="1"> <ml:apply> <ml:minus/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">TD</ml:id> <ml:sequence> <ml:real>1</ml:real> <ml:real>4</ml:real> </ml:sequence> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">TV</ml:id> <ml:sequence> <ml:real>1</ml:real> <ml:real>4</ml:real> </ml:sequence> </ml:apply> </ml:apply> <ml:apply> <ml:minus/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">TD</ml:id> <ml:sequence> <ml:real>2</ml:real> <ml:real>4</ml:real> </ml:sequence> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">TV</ml:id> <ml:sequence> <ml:real>2</ml:real> <ml:real>4</ml:real> </ml:sequence> </ml:apply> </ml:apply> <ml:apply> <ml:minus/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">TD</ml:id> <ml:sequence> <ml:real>3</ml:real> <ml:real>4</ml:real> </ml:sequence> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">TV</ml:id> <ml:sequence> <ml:real>3</ml:real> <ml:real>4</ml:real> </ml:sequence> </ml:apply> </ml:apply> </ml:matrix> </ml:define> </math> <rendering item-idref="119"/> </region> <region region-id="1216" left="528" top="4532.25" width="123.75" height="61.5" align-x="541.5" align-y="4566" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">B</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="3" cols="1"> <ml:real>-0.00015483125519030749</ml:real> <ml:real>0.00036614952587488148</ml:real> <ml:real>0</ml:real> </ml:matrix> </result> </ml:eval> </math> <rendering item-idref="120"/> </region> <region region-id="1217" left="72" top="4640.25" width="172.5" height="12" align-x="72" align-y="4650" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Řešením soustavy rovnic je matice D </text> </region> <region region-id="1218" left="72" top="4670.25" width="54.75" height="19.5" align-x="87" align-y="4686" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">D</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">C</ml:id> <ml:real>-1</ml:real> </ml:apply> <ml:id xml:space="preserve">B</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="121"/> </region> <region region-id="1219" left="198" top="4652.25" width="118.5" height="61.5" align-x="212.25" align-y="4686" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math 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background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="1">Δs</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">D</ml:id> <ml:sequence> <ml:real>1</ml:real> <ml:real>1</ml:real> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="123"/> </region> <region region-id="1222" left="84" top="4766.25" width="61.5" height="19.5" align-x="112.5" align-y="4776" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="2">Δs</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">D</ml:id> <ml:sequence> <ml:real>2</ml:real> <ml:real>1</ml:real> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="124"/> </region> <region region-id="1223" left="84" top="4784.25" width="61.5" height="19.5" align-x="112.5" align-y="4794" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="3">Δs</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">D</ml:id> <ml:sequence> <ml:real>3</ml:real> <ml:real>1</ml:real> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="125"/> </region> <region region-id="1224" left="66" top="4814.25" width="145.5" height="12" align-x="89.25" align-y="4824" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Vypočtení nové výchozí polohy </text> </region> <region 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subscript="2">s</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve" subscript="2">s</ml:id> <ml:id xml:space="preserve" subscript="2">Δs</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="127"/> </region> <region region-id="1227" left="78" top="4880.25" width="72.75" height="17.25" align-x="96.75" align-y="4890" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="3">s</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve" subscript="3">s</ml:id> <ml:id xml:space="preserve" subscript="3">Δs</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="128"/> </region> <region region-id="1228" left="282" top="4880.25" width="207.75" height="24" align-x="282" align-y="4890" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Pro kontrolu porovnání s již předem vypočtenými referenčními hodnotami </text> </region> <region region-id="1229" left="78" top="4916.25" width="39" height="17.25" align-x="96" align-y="4926" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="1">s</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>3.000000111839717</ml:real> </result> </ml:eval> </math> <rendering item-idref="129"/> </region> <region region-id="1230" left="276" top="4916.25" width="39.75" height="17.25" align-x="294.75" align-y="4926" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="1">q</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>3</ml:real> </result> </ml:eval> </math> <rendering item-idref="130"/> </region> <region region-id="1231" left="78" top="4934.25" width="48" height="17.25" align-x="96" align-y="4944" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="2">s</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>0.59999999999999976</ml:real> </result> </ml:eval> </math> <rendering item-idref="131"/> </region> <region region-id="1232" left="276" top="4934.25" width="48.75" height="17.25" align-x="294.75" align-y="4944" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="2">q</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>0.6</ml:real> </result> </ml:eval> </math> <rendering item-idref="132"/> </region> <region region-id="1233" left="78" top="4952.25" width="48" height="17.25" align-x="96" align-y="4962" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="3">s</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>0.79999998099331371</ml:real> </result> </ml:eval> </math> <rendering item-idref="133"/> </region> <region region-id="1234" left="276" top="4952.25" width="48.75" height="17.25" align-x="294.75" align-y="4962" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="3">q</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>0.8</ml:real> </result> </ml:eval> </math> <rendering item-idref="134"/> </region> <region region-id="1321" left="24" top="4988.25" width="418.5" height="36" align-x="24" align-y="4998" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Po třetí iteraci jsou již hodnoty hledaných kloubových proměnných vypočteny naprosto správně (zobrazení výsledku je nastaveno na pět desetinných míst), odpovídají referenčním hodnotám a výpočet může skončit </text> </region> <region region-id="1323" left="30" top="5102.25" width="163.5" height="12" align-x="63" align-y="5112" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> Programování v prostředí Mathcad </text> </region> <region region-id="1325" left="30" top="5126.25" width="354.75" height="12" align-x="48" align-y="5136" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> Výchozí poloha, pro kterou jsou v programu vyčísleny transformační matice </text> </region> <region region-id="1274" left="66" top="5150.25" width="35.25" height="17.25" align-x="84.75" align-y="5160" show-border="false" show-highlight="false" is-protected="true" z-order="0" 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tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="2">s</ml:id> <ml:real>0.8</ml:real> </ml:define> </math> <rendering item-idref="137"/> </region> <region region-id="1327" left="36" top="5180.25" width="72" height="12" align-x="53.25" align-y="5190" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> Žádaná poloha </text> </region> <region region-id="1328" left="30" top="5207.25" width="204" height="67.5" align-x="51" align-y="5244" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">TD</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="4" cols="4"> <ml:real>-0.98999249660044542</ml:real> <ml:real>0.14112000805986721</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>1</ml:real> <ml:real>0</ml:real> <ml:real>0.14112000805986721</ml:real> <ml:real>0.98999249660044542</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0.04854649416886482</ml:real> <ml:real>0.80116679780424771</ml:real> <ml:real>1.154</ml:real> <ml:real>1</ml:real> </ml:matrix> </result> </ml:eval> </math> <rendering item-idref="138"/> </region> <region region-id="1277" left="6" top="5306.25" width="412.5" height="24" align-x="6" align-y="5316" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Program v Mathcadu definuje funkci inverze(ε), kde ε je požadovaná přesnost výpočtu - zde součet kroků </text> 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