paper: Analysis of “a torque-actuated module” used for strafing in an H-drive.

[RyanCahoon]

Originally Posted by GeeTwo

The system I analyzed was simply the wheel with the attached gear and axle

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.

[GeeTwo]

Ryan,
I think I understand your reasoning, and based on that, only disagree on one minor point:

Thus, the only forces that could generate L are reaction forces.

There is also the weight of the module, which is applied at the CoG, presumably a bit below the drive bearing when the module is horizontal, and thus will provide a slight torque about the drive bearing, and produce a bit of L in the upward/right direction. However, I have already argued that this force is negligible compared to the drive forces.

[RyanCahoon]

Originally Posted by GeeTwo

There is also the weight of the module

Agreed; I've been concerned with the idealized analysis of the system - massless and frictionless (except for the wheel/ground interaction) - so I've been ignoring the weight forces.

A full analysis of this system would also incorporate the weight of the robot. This would have place an upper bound on the normal force produced, and thus inform the choice of final gear ratio.

[GeeTwo]

Originally Posted by RyanCahoon

A full analysis of this system would also incorporate the weight of the robot. This would have place an upper bound on the normal force produced, and thus inform the choice of final gear ratio.

Also agreed. This analysis would be fairly typical for FRC, though focused on acceleration much more than top speed. If the robot were anticipated to be strafing at anything close to top speed, a less isotropic holonomic drive (mecanum, kiwi, or killough) or a crab or swerve drive would be in order.