Quote:
Originally Posted by GeeTwo
The system I analyzed was simply the wheel with the attached gear and axle
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Ah ok. Let me revise my list of interactions then:
- the strafing module arm -> the wheel. You label the radial (relative to the drive axle) component of this B, and I think the tangent component L (though this isn't defined clearly in the paper)
- the driving gear -> the wheel gear. You label this D
- the ground -> the wheel (contact force). You label this N
- the ground -> the wheel (frictional force). You label this F
The part that I was missing was fully understanding why L = 0.
I think I've discovered the divergence in reasonings: I analyzed the normal force under the condition where the wheel is locked to the strafing module arm, which implies that there are additional torques(forces) in the system than there actually are.
A nice way to see this (if there was anyone else who was confused) is to imagine that you have a wheel mounted on the end of an arm, kind of like a
pinwheel, and you support the stick near where the wheel is attached. 1) If the wheel were fixed rotationally to the arm, then if you try to spin the wheel, a torque would be induced on the arm, cause it to spin as well. 2) However, if the wheel is free to spin, then spinning the wheel does not induce this torque on the arm.
The other half of the issue is to see that there is no torque induced directly on the strafing module arm by the motor. Thus, the only forces that could generate L are reaction forces. If it weren't for the meshed gears, the strafing module would be free to rotate about the drive axle, so there isn't any resistance in the tangential direction, thus nowhere for a reaction force to come from.
tl;dr I think I agree with your (Gus's) reasoning now.
I spent far more time thinking about this than I would have hoped to.