Hi,

I’m a young enthusiast of robotics from Finland. I built my first Mecanum wheeled robot about 1 year ago but it was about 2 months ago when I read Ether’s explanation about forces that act on Mecanum wheel that made me understand more why the robot is able to go in different directions. I have however two questions that I couldn’t figure answer for, so I decided to make and account and ask here.

In this drawing made by Ether force Ff comes from the motor torque so we deliver this force (it is our input):

https://www.google.com/search?q=mecanum+wheel+forces&client=firefox-b&source=lnms&tbm=isch&sa=X&ved=0ahUKEwjx6o3Z8oPeAhVEDSwKHQyRC_EQ_AUIDigB&biw=1760&bih=975#imgrc=13BKmtMcx-qIHM:

If we neglect friction in bearings, force Fc will be the actual force that pushes the wheel (so it will be our output). If we move in 45degrees angle only two wheels are driven which means that our input force is 2Ff and output force that pushes vehicle is 2Fc. Force Fc is bigger than Ff which means that output force is higher than input force. That in turn means that efficiency is higher than 1 which is not possible. Can someone explain where I make mistake in my logic?

My second question is about determining speed of the wheel when we take into account friction forces of bearings. I’ve seen couple articles about forward and inverse kinematics of Mecanum wheel but all of them are in situation when there is no resistive forces present and angle between Fc and Ff is 45degrees. Does someone know how to calculate velocity of the wheel when this angle is smaller?

Thank you very much for your help.