Kinematic Analysis of Mecanum wheel
 

I've posted a paper here on kinematic analysis of 4-wheel mecanum robot:

http://www.chiefdelphi.com/media/papers/2390

Please pardon any typos, this was put together rather quickly (and late at night).

I realize I may have left out some details, but I will gladly answer questions that anyone has.

Note that the analysis shows that, for equal wheel angular speeds, the fwd/rev speed of the robot is equal to the strafe speed (for 45 degree rollers).

For example, consider wheel 4 (the front starboard wheel):

omega_4 = (1/r)(Vx + Vy +K*omega_v)

for pure forward motion, Vy=0 and omega_v=0, so omega_4 = (1/r)(Vx)

for pure strafe left, Vx=0 and omega_v=0m so omega_4 = (1/r)(Vy)

... so you get the same strafe speed (Vy) as forward speed (Vx) for the same wheel speed (omega_4)


The reason that strafe often seems slower in real life is because, with open-loop (voltage control) of the drive motors, the wheel speeds are somewhat slower when strafing than when going fwd/rev. Force vector analysis shows that roller bearing friction affects strafing motion differently than it affects fwd/rev motion: Friction in the roller bearings actually improves traction in the fwd/rev direction, and reduces traction and available torque in the strafing direction. So theory does agree well with observation.


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