# Mecanum wheels "circumference" wheels at less than 45 degrees?

Re: Mecanum wheels “circumference” wheels at less than 45 degrees?

Sorry if this has been answered (somewhere) - I’m a complete newbie to “non-traditional wheels” and anything CAD beyond the ancient Mac Super3D.

I’ve googled and not managed to hit the correct string for bringing up this particular bone from the infinite heap of the Internet

Will a mecanum wheel work if the wheels on the circumference (normally at 45 degrees) are at some other angle? Or two different ones, as there is the angle in the XZ plane and the other in the YZ plane? (RHS, Z as direction of forward movement)

I think (?) the limit (XZ at 90, YZ at 0) would be the outer wheel of an omni wheel set, and only roll horizontally (X axis). But others, like a 30 degree angle for both? Would this create a wheel that would be more efficient (with some definition) in certain directions?

Thanks,
Jim

Yes to all. I don’t know how you would define efficient in that way, but a shallower angle (ie closer to an omni wheel) would increase force along the normal wheel axis.

Think about it like how the rollers come closer to a free roller the closer to perpendicular you get, and closer to an Omni that they get the closer you get to parallel. Technically a mecanum is a rotated Omni.

If I understand your question correctly - your terminology is a little unconventional - the answer is yes, but there are easier ways to do what you’re getting at. Normally you refer to the wheel itself as the wheel, and the “circumference wheels” as rollers.

A mecanum or omni wheel is a wheel that can exert (or resist) force only in a positive or negative direction along a particular vector. For normally mounted mecanums those vectors are 45 degrees inward/frontward for the fronts and 45 degrees outward/forward for the rears. Omnis mounted with the wheel itself angled in/out at these angles give (neglecting roller friction losses) exactly the same relative force vectors. What matters is the direction forces can be transmitted to/from the ground, i.e. the direction of the roller axes at the point the rollers contact the ground. With some caveats, the angles between the wheels proper and the angles on which the wheels mount to the chassis are just mechanical details.

Defining “efficiency” in this context as the ratio of force in the direction the robot is being driven to torque at the wheel axle (/ the wheel radius), in the normal orientation the vectors are arranged to make these ratios as nearly equal as possible over all directions. For conventional mecanum and 45/45/45/45 omnis these ratios are .707 forward/back/sideways and .5 (average for all four wheels; half are 1, half are 0) diagonally.

You can indeed change these ratios by changing the roller/wheel angle. The as the angle between the conventionally mounted mecanum wheel axle and the roller axles increases from 45 degrees to 90 degrees, i.e. becomes an omni wheel, force efficiency increases toward 1 forward/back and decreases toward zero sideways.

I’ve not seen a non-45 mecanum, but you can get the same effect by changing the angle at which the mecanum or omni wheel itself is mounted to the chassis. Ignoring the angle of the wheel proper, look at the angle between travel direction and the roller axis, take cosines and sum for all wheels.

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Likewise, a steeper angle would decrease traction-limited force - and increase theoretical free speed in the forward/reverse direction. I played with this a couple of years ago to see if I could make a two-speed robot which shifted speeds by rotating. It didn’t work very well at the FTC scale without sensors; I may pick it up again someday with encoders and a gyro.

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