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mcd:eqproperties=""
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mcd:alignx="449" mcd:aligny="240"
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J.1f is the rolling matrix

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C1 is the sliding matrix

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mcd:eqproperties=""
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mcd:alignx="69" mcd:aligny="536"
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want to know the max rpm for 25 cm/sec speed in X or Y direction:

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Motors need to be capable of rpm from -40 to +40



With g = 45

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mcd:alignx="209" mcd:aligny="984"
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l = length wheels are from center

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mcd:alignx="425" mcd:aligny="1040"
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J.1f is the rolling matrix

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mcd:alignx="390" mcd:aligny="1120"
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C1 is the sliding matrix

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mcd:eqproperties=""
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mcd:eqproperties=""
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mcd:eqproperties=""
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mcd:properties=""
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mcd:alignx="77" mcd:aligny="1392"
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want to know the max rpm for 25 cm/sec speed in X or Y direction:

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mcd:eqproperties=""
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mcd:eqproperties=""
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mcd:eqproperties=""
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mcd:properties=""
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mcd:alignx="251" mcd:aligny="1568"
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Motors need to be capable of rpm from -35 to +35



With omnidirectional wheels g = 0

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Torque requirements:

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table weight = TW



table radius = Tr



Fine Sand Density = rho.sand



Sandstone density = rho.stone



Avg depth of medium = d



Aluminum density = rho alum



Table aluminum thickness = Tt

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MA = F = torque

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mcd:eqproperties=""
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Worst case rotational torque needed:

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Max speed 25 cm/sec

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mcd:alignx="374" mcd:aligny="2672"
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Component of V perp to center rot

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mcd:alignx="366" mcd:aligny="2752"
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Rotation around center

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mcd:eqproperties=""
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mcd:eqproperties=""
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mcd:eqproperties=""
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mcd:eqproperties=""
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mcd:properties=""
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mcd:alignx="437" mcd:aligny="2968"
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units are screwed up due to



mathcad not letting me put



in differing units in one matrix

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The values for w for worst case spinning are within the max for worst case linear motion.

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What about torque for worst case: Where table is all the way to one side and it is spinning with w = .5 rad/sec