Society of Robots - Robot Forum

Mechanics and Construction => Mechanics and Construction => Topic started by: crazyengineer on March 12, 2013, 08:09:09 PM

Title: Torque Calculations Verfications
Post by: crazyengineer on March 12, 2013, 08:09:09 PM
Okay, so I'm deriving the relationship between torque and the mass. I just want to verify my derivation is correct. I'm creating a wheeled robot which it has two wheels each connected to its own motor and a ball caster at the end of the bot. The robot is traveling on a perfectly flat surface

Torque=force*wheel_radius => force=Torque/wheel_radius

Friction_force=kinetic_friction_ coefficient*normal force

Assuming a 2D plane, the normal force is equal to the weight of the robot

Friction_force=kinetic_friction_ coefficient*mass*gravity

So the summation of forces is equal to mass*acceleration. Since the friction force is opposing the force generated from the motor, and the two motors' torque will add together, I can make this assumption

mass*acceleration=2*(Torque/wheel_radius)-kinetic_friction_ coefficient*mass*gravity

After some algebra, I was able to determine the following

Torque=(wheel_radius/2)*(mass*acceleration+kinetic_friction_ coefficient*mass*gravity)

Title: Re: Torque Calculations Verfications
Post by: jwatte on March 13, 2013, 10:49:53 AM
That would be true if you were dragging the wheel over the surface. However, the wheel is rolling, so the friction force you need to model is rolling friction (plus losses in transmission) which is generally a lot less than sliding friction.

Also, using "2" is confusing, because that's a hard-coded constant based on your number of motors (which is 2.) Using "Nmotors" or doing the calculation for the sum, and later dividing by number of motors, would be clearer IMO.
Title: Re: Torque Calculations Verfications
Post by: crazyengineer on March 13, 2013, 10:59:11 AM
Okay! When I did a quick  Google Search (, I found that rolling friction is


So I need to replace the friction force in my equation with the rolling friction force? Also, I'm neglecting the effects of transmission for the time being.