about the torque calculation of a mecanum wheel

[Ether]

Originally Posted by GeeTwo

While Matsinos does decompose the "driving force" F_i into F_i,p and F_i,t improperly because he assumes that it is transverse to the wheel axis (it is not), this error is inconsequential

His error is fundamental.

He takes a component of force (F_i), breaks it into 2 new components (F_i,p and F_i,t), throws away one of those components (F_i,t), and then breaks the remaining component (F_i,p) into yet two new components (F_i,y and F_i,x).

This is a common high-school physics error.

The proper way to analyze the wheel is to start with the net force (of the floor acting on the bottom of the wheel, in the plane of the floor). This net force F_i,net has a known direction: parallel to the axis of the roller touching the floor.

Then break that net force F_i,net into forward F_i,y and sideways F_i,x components.

The forward force F_i,y will be equal to tau/r, where tau is the driving torque on the wheel and r is the wheel radius. This known value of F_i,y can then be used to compute the magnitude of F_i,x and F_i,net.