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unit="revolution"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="24"/> </region> <region region-id="412" left="654" top="190.2" width="106.2" height="21" align-x="694.2" align-y="204" 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="encoder">J</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>11.13</ml:real> <ml:id xml:space="preserve">gm</ml:id> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">mm</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="25"/> </region> <region region-id="413" left="792" top="190.2" width="129.6" height="21" align-x="831" align-y="204" 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="encoder">J</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>1.1130000000000001E-08</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="kilogram"/> <unitReference unit="meter" power-numerator="2"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="26"/> </region> <region region-id="158" left="18" top="255" width="151.2" height="10.8" align-x="25.2" align-y="264" 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"> Vici 10 port valve motor sizing calcs </text> </region> <region region-id="159" left="192" top="255" width="75" height="16.2" align-x="229.8" align-y="264" 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="friction">T</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>4</ml:real> <ml:id xml:space="preserve">in</ml:id> </ml:apply> <ml:id xml:space="preserve">lbf</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="27"/> </region> <region region-id="160" left="300" top="255" width="127.2" height="10.8" align-x="318" align-y="264" 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"> Measured with torque wrench </text> </region> <region region-id="414" left="492" top="255" width="70.8" height="10.8" align-x="501.6" align-y="264" 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"> Total Load Inertia </text> </region> <region region-id="499" left="264" top="267" width="85.2" height="16.2" align-x="300.6" align-y="276" 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="friction">T</ml:id> <ml:unitOverride> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">N</ml:id> <ml:id xml:space="preserve">m</ml:id> </ml:apply> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>0.45193931611046673</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="meter"/> <unitReference unit="newton"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="28"/> </region> <region region-id="415" left="552" top="279" width="177" height="16.2" align-x="579" align-y="288" 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="load">J</ml:id> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:id xml:space="preserve" subscript="rotor">J</ml:id> <ml:id xml:space="preserve" subscript="shaft">J</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="coupling">J</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="encoder">J</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="29"/> </region> <region region-id="416" left="780" top="274.2" width="116.4" height="21" align-x="805.8" align-y="288" 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="load">J</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>2.011596380863672E-06</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="kilogram"/> <unitReference unit="meter" power-numerator="2"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="30"/> </region> <region region-id="417" left="36" top="285" width="209.4" height="10.8" align-x="45" align-y="294" 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"> Load inertia reflected through gearhead to motor </text> </region> <region region-id="418" left="102" top="316.8" width="117" height="39" align-x="163.2" align-y="336" 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="loadReflected">J</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="load">J</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="gearhead">N</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="31"/> </region> <region region-id="419" left="258" top="322.2" width="154.8" height="21" align-x="318" align-y="336" 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="loadReflected">J</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>7.9569494120630988E-11</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="kilogram"/> <unitReference unit="meter" power-numerator="2"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="32"/> </region> <region region-id="458" left="468" top="332.4" width="139.8" height="27" align-x="561" align-y="348" 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="2232_12">noLoadSpeed</ml:id> <ml:apply> <ml:mult/> <ml:real>7100</ml:real> <ml:apply> <ml:div/> <ml:id xml:space="preserve">rev</ml:id> <ml:id xml:space="preserve">min</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="33"/> </region> <region region-id="459" left="654" top="334.2" width="150.6" height="21" align-x="735" align-y="348" 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="2232_12">stallTorque</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>46.8</ml:real> <ml:apply> <ml:pow/> <ml:real>10</ml:real> <ml:real>-3</ml:real> </ml:apply> </ml:apply> <ml:id xml:space="preserve">N</ml:id> </ml:apply> <ml:id xml:space="preserve">m</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="34"/> </region> <region region-id="420" left="126" top="364.2" width="97.8" height="21" align-x="170.4" align-y="378" 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="gearhead">J</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>0.4</ml:real> <ml:id xml:space="preserve">gm</ml:id> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">cm</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="35"/> </region> <region region-id="421" left="282" top="364.2" width="117" height="21" align-x="325.2" align-y="378" 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="gearhead">J</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>4E-08</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="kilogram"/> <unitReference unit="meter" power-numerator="2"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="36"/> </region> <region region-id="460" left="480" top="375" width="142.2" height="16.2" align-x="577.2" align-y="384" 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="2232_12">noLoadCurrent</ml:id> <ml:apply> <ml:mult/> <ml:real>0.0175</ml:real> <ml:id xml:space="preserve">A</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="37"/> </region> <region region-id="461" left="672" top="368.4" width="168.6" height="27" align-x="768.6" align-y="384" 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="2232_12">torqueConstant</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>16.0</ml:real> <ml:apply> <ml:pow/> <ml:real>10</ml:real> <ml:real>-3</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">N</ml:id> <ml:id xml:space="preserve">m</ml:id> </ml:apply> <ml:id xml:space="preserve">A</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="38"/> </region> <region region-id="422" left="108" top="393" width="137.4" height="16.2" align-x="135" align-y="402" 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="total">J</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve" subscript="loadReflected">J</ml:id> <ml:id xml:space="preserve" subscript="gearhead">J</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="39"/> </region> <region region-id="423" left="282" top="394.2" width="116.4" height="21" align-x="307.8" align-y="408" 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="total">J</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>4.0079569494120631E-08</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="kilogram"/> <unitReference unit="meter" power-numerator="2"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="40"/> </region> <region region-id="462" left="492" top="398.4" width="150.6" height="39" align-x="570.6" align-y="414" 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="2232_12">backEMF</ml:id> <ml:apply> <ml:mult style="auto-select"/> <ml:apply> <ml:mult/> <ml:real>1.68</ml:real> <ml:apply> <ml:pow/> <ml:real>10</ml:real> <ml:real>-3</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:id xml:space="preserve">V</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">rev</ml:id> <ml:id xml:space="preserve">min</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="41"/> </region> <region region-id="463" left="702" top="405" width="86.4" height="16.2" align-x="748.8" align-y="414" 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="2232_12">R</ml:id> <ml:apply> <ml:mult/> <ml:real>4.2</ml:real> <ml:id xml:space="preserve">ohm</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="42"/> </region> <region region-id="424" left="120" top="424.2" width="85.8" height="21" align-x="152.4" align-y="438" 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="motor">J</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>3.8</ml:real> <ml:id xml:space="preserve">gm</ml:id> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">cm</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="43"/> </region> <region region-id="425" left="264" top="430.2" width="112.2" height="21" align-x="295.2" align-y="444" 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="motor">J</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>3.8E-07</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="kilogram"/> <unitReference unit="meter" power-numerator="2"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="44"/> </region> <region region-id="464" left="474" top="441" width="154.2" height="16.2" align-x="534" align-y="450" 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">noLoadSpeed</ml:id> <ml:id xml:space="preserve" subscript="2232_12">noLoadSpeed</ml:id> </ml:define> </math> <rendering item-idref="45"/> </region> <region region-id="465" left="678" top="441" width="129.6" height="16.2" align-x="725.4" align-y="450" 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">stallTorque</ml:id> <ml:id xml:space="preserve" subscript="2232_12">stallTorque</ml:id> </ml:define> </math> <rendering item-idref="46"/> </region> <region region-id="466" left="696" top="465" width="161.4" height="16.2" align-x="759.6" align-y="474" 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">torqueConstant</ml:id> <ml:id xml:space="preserve" subscript="2232_12">torqueConstant</ml:id> </ml:define> </math> <rendering item-idref="47"/> </region> <region region-id="467" left="480" top="471" width="162.6" height="16.2" align-x="544.2" align-y="480" 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">noLoadCurrent</ml:id> <ml:id xml:space="preserve" subscript="2232_12">noLoadCurrent</ml:id> </ml:define> </math> <rendering item-idref="48"/> </region> <region region-id="468" left="702" top="495" width="82.8" height="16.2" align-x="736.8" align-y="504" 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="motor">R</ml:id> <ml:id xml:space="preserve" subscript="2232_12">R</ml:id> </ml:define> </math> <rendering item-idref="49"/> </region> <region region-id="469" left="486" top="501" width="124.8" height="16.2" align-x="531" align-y="510" 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">backEMF</ml:id> <ml:id xml:space="preserve" subscript="2232_12">backEMF</ml:id> </ml:define> </math> <rendering item-idref="50"/> </region> <region region-id="431" left="24" top="597" width="146.4" height="10.8" align-x="42.6" align-y="606" 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"> Maximum Torque required by motor </text> </region> <region region-id="426" left="60" top="471" width="141" height="10.8" align-x="69" align-y="480" 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"> Load inertia to motor inertia ratio </text> </region> <region region-id="427" left="228" top="460.8" width="63" height="34.2" align-x="255" align-y="480" 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="ratio">J</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="total">J</ml:id> <ml:id xml:space="preserve" subscript="motor">J</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="51"/> </region> <region region-id="428" left="342" top="471" width="60.6" height="16.2" align-x="367.8" align-y="480" 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="ratio">J</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>0.10547255130031745</ml:real> </result> </ml:eval> </math> <rendering item-idref="52"/> </region> <region region-id="249" left="30" top="513" width="133.2" height="10.8" align-x="48.6" align-y="522" 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"> Maximum required acceleration </text> </region> <region region-id="283" left="18" top="550.8" width="118.2" height="34.2" align-x="67.2" align-y="570" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define 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region-id="159" left="192" top="255" width="75" height="16.2" align-x="229.8" align-y="264" 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="friction">T</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>4</ml:real> <ml:id xml:space="preserve">in</ml:id> </ml:apply> <ml:id xml:space="preserve">lbf</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="27"/> </region> <region region-id="160" left="300" top="255" width="127.2" height="10.8" align-x="318" align-y="264" 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"> Measured with torque wrench </text> </region> <region region-id="414" left="492" top="255" width="70.8" height="10.8" align-x="501.6" align-y="264" 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"> Total Load Inertia </text> </region> <region region-id="499" left="264" top="267" width="85.2" height="16.2" align-x="300.6" align-y="276" 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="friction">T</ml:id> <ml:unitOverride> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">N</ml:id> <ml:id xml:space="preserve">m</ml:id> </ml:apply> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>0.45193931611046673</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="meter"/> <unitReference unit="newton"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="28"/> </region> <region region-id="415" left="552" top="279" width="177" height="16.2" align-x="579" align-y="288" 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="load">J</ml:id> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:id xml:space="preserve" subscript="rotor">J</ml:id> <ml:id xml:space="preserve" subscript="shaft">J</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="coupling">J</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="encoder">J</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="29"/> </region> <region region-id="416" left="780" top="274.2" width="116.4" height="21" align-x="805.8" align-y="288" 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="load">J</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>2.011596380863672E-06</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="kilogram"/> <unitReference unit="meter" power-numerator="2"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="30"/> </region> <region region-id="417" left="36" top="285" width="209.4" height="10.8" align-x="45" align-y="294" 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"> Load inertia reflected through gearhead to motor </text> </region> <region region-id="418" left="102" top="316.8" width="117" height="39" align-x="163.2" align-y="336" 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="loadReflected">J</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="load">J</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="gearhead">N</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="31"/> </region> <region region-id="419" left="258" top="322.2" width="154.8" height="21" align-x="318" align-y="336" 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="loadReflected">J</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>7.9569494120630988E-11</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="kilogram"/> <unitReference unit="meter" power-numerator="2"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="32"/> </region> <region region-id="458" left="468" top="332.4" width="139.8" height="27" align-x="561" align-y="348" 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="2232_12">noLoadSpeed</ml:id> <ml:apply> <ml:mult/> <ml:real>7100</ml:real> <ml:apply> <ml:div/> <ml:id xml:space="preserve">rev</ml:id> <ml:id xml:space="preserve">min</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="33"/> </region> <region region-id="459" left="654" top="334.2" width="150.6" height="21" align-x="735" align-y="348" 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="2232_12">stallTorque</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>46.8</ml:real> <ml:apply> <ml:pow/> <ml:real>10</ml:real> <ml:real>-3</ml:real> </ml:apply> </ml:apply> <ml:id xml:space="preserve">N</ml:id> </ml:apply> <ml:id xml:space="preserve">m</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="34"/> </region> <region region-id="420" left="126" top="364.2" width="97.8" height="21" align-x="170.4" align-y="378" 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="gearhead">J</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>0.4</ml:real> <ml:id xml:space="preserve">gm</ml:id> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">cm</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="35"/> </region> <region region-id="421" left="282" top="364.2" width="117" height="21" align-x="325.2" align-y="378" 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="gearhead">J</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>4E-08</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="kilogram"/> <unitReference unit="meter" power-numerator="2"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="36"/> </region> <region region-id="460" left="480" top="375" width="142.2" height="16.2" align-x="577.2" align-y="384" 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="2232_12">noLoadCurrent</ml:id> <ml:apply> <ml:mult/> <ml:real>0.0175</ml:real> <ml:id xml:space="preserve">A</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="37"/> </region> <region region-id="461" left="672" top="368.4" width="168.6" height="27" align-x="768.6" align-y="384" 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="2232_12">torqueConstant</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>16.0</ml:real> <ml:apply> <ml:pow/> <ml:real>10</ml:real> <ml:real>-3</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">N</ml:id> <ml:id xml:space="preserve">m</ml:id> </ml:apply> <ml:id xml:space="preserve">A</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="38"/> </region> <region region-id="422" left="108" top="393" width="137.4" height="16.2" align-x="135" align-y="402" 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="total">J</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve" subscript="loadReflected">J</ml:id> <ml:id xml:space="preserve" subscript="gearhead">J</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="39"/> </region> <region region-id="423" left="282" top="394.2" width="116.4" height="21" align-x="307.8" align-y="408" 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="total">J</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>4.0079569494120631E-08</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="kilogram"/> <unitReference unit="meter" power-numerator="2"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="40"/> </region> <region region-id="462" left="492" top="398.4" width="150.6" height="39" align-x="570.6" align-y="414" 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="2232_12">backEMF</ml:id> <ml:apply> <ml:mult style="auto-select"/> <ml:apply> <ml:mult/> <ml:real>1.68</ml:real> <ml:apply> <ml:pow/> <ml:real>10</ml:real> <ml:real>-3</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:id xml:space="preserve">V</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">rev</ml:id> <ml:id xml:space="preserve">min</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="41"/> </region> <region region-id="463" left="702" top="405" width="86.4" height="16.2" align-x="748.8" align-y="414" 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="2232_12">R</ml:id> <ml:apply> <ml:mult/> <ml:real>4.2</ml:real> <ml:id xml:space="preserve">ohm</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="42"/> </region> <region region-id="424" left="120" top="424.2" width="85.8" height="21" align-x="152.4" align-y="438" 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="motor">J</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>3.8</ml:real> <ml:id xml:space="preserve">gm</ml:id> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">cm</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="43"/> </region> <region region-id="425" left="264" top="430.2" width="112.2" height="21" align-x="295.2" align-y="444" 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="motor">J</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>3.8E-07</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="kilogram"/> <unitReference unit="meter" power-numerator="2"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="44"/> </region> <region region-id="464" left="474" top="441" width="154.2" height="16.2" align-x="534" align-y="450" 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">noLoadSpeed</ml:id> <ml:id xml:space="preserve" subscript="2232_12">noLoadSpeed</ml:id> </ml:define> </math> <rendering item-idref="45"/> </region> <region region-id="465" left="678" top="441" width="129.6" height="16.2" align-x="725.4" align-y="450" 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">stallTorque</ml:id> <ml:id xml:space="preserve" subscript="2232_12">stallTorque</ml:id> </ml:define> </math> <rendering item-idref="46"/> </region> <region region-id="466" left="696" top="465" width="161.4" height="16.2" align-x="759.6" align-y="474" 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">torqueConstant</ml:id> <ml:id xml:space="preserve" subscript="2232_12">torqueConstant</ml:id> </ml:define> </math> <rendering item-idref="47"/> </region> <region region-id="467" left="480" top="471" width="162.6" height="16.2" align-x="544.2" align-y="480" 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">noLoadCurrent</ml:id> <ml:id xml:space="preserve" subscript="2232_12">noLoadCurrent</ml:id> </ml:define> </math> <rendering item-idref="48"/> </region> <region region-id="468" left="702" top="495" width="82.8" height="16.2" align-x="736.8" align-y="504" 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="motor">R</ml:id> <ml:id xml:space="preserve" subscript="2232_12">R</ml:id> </ml:define> </math> <rendering item-idref="49"/> </region> <region region-id="469" left="486" top="501" width="124.8" height="16.2" align-x="531" align-y="510" 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">backEMF</ml:id> <ml:id xml:space="preserve" subscript="2232_12">backEMF</ml:id> </ml:define> </math> <rendering item-idref="50"/> </region> <region region-id="431" left="24" top="597" width="146.4" height="10.8" align-x="42.6" align-y="606" 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"> Maximum Torque required by motor </text> </region> <region region-id="426" left="60" top="471" width="141" height="10.8" align-x="69" align-y="480" 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"> Load inertia to motor inertia ratio </text> </region> <region region-id="427" left="228" top="460.8" width="63" height="34.2" align-x="255" align-y="480" 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="ratio">J</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="total">J</ml:id> <ml:id xml:space="preserve" subscript="motor">J</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="51"/> </region> <region region-id="428" left="342" top="471" width="60.6" height="16.2" align-x="367.8" align-y="480" 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="ratio">J</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>0.10547255130031745</ml:real> </result> </ml:eval> </math> <rendering item-idref="52"/> </region> <region region-id="249" left="30" top="513" width="133.2" height="10.8" align-x="48.6" align-y="522" 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"> Maximum required acceleration </text> </region> <region region-id="283" left="18" top="550.8" width="118.2" height="34.2" align-x="67.2" align-y="570" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" 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