Ok , so if I want 90 degrees per second rotation how quick is that and how fast would the motor have to be?

The radius of the sphere is 700mm and C equals 2πr.

The circumference is 4398.23mm.

Divide that by 4 and we get our 90 degree slice of the sphere.

1099.5575, or 1100mm to make it slightly easier.

For sake of example, since I still haven’t found the ideal motor, lets use this one.

It runs at 2750 rpm, or nearly 46 times a second.

If we use a 150mm mecanum wheel then the distance the wheel covers with its 471 mm circumference every second (46fps) is 21,676mm.

This is assuming zero inertia and perfect traction, but the motor is obviously not going to turn our sphere nearly 5 times a second.

We can slow this speed by reducing the size of the driving wheel but this isn’t practical since a tiny wheel won’t work.

Instead we can calculate the optimal motor speed for a 150mm mecanum wheel.

1,100 divided by it’s 471 circumference is 2.33, or 140 rpm.

This figure can be higher but any slower and we lose the desired rotation rate.

This motor on ebay is listed as “**Three Phase** 0.25kw Motor and Worm Gearbox 140 rpm output 14mm **Hollow Bore** 9Nm” for £120. Not especially cheap…

Finding the right motor with the right combination of speed, torque and price might be tricky but not impossible.

Next to calculate the torque requirement…

I’ll spend a little time trawling through motors on ebay to see what else is available.