Motor Torque and Force

Robot Wheel Diameter vs Torque 

You probably noticed that thelarger the diameter of the wheel, or higher the rpm, the faster yourrobot will go. But this isn't entirely true in that there is another factorinvolved. If your robot requires more torque than it can give, it will goslower than you calculated. Heavier robots will go slower. Now what you need todo is compare the motor torque, your robot acceleration, and wheeldiameter. These three attributes will have to be balanced to achieve propertorque.

Motor Torque and Force 

High force is required to push other robots around, or to go up hills and roughterrain, or have high acceleration. As calculatable with statics, just by knowing your wheel diameter and motor torque, youcan determine the force your robot is capable of.

Torque = Distance * Force
Distance = Wheel Radius
Force = Torque / Wheel Radius

Acceleration 

But you also want to be concerned with acceleration. For a typical robot onflat terrain, you probably wantacceleration to be about half of your max velocity. So if your robotvelocity is 3 ft/s, you want your acceleration to be around 1.5 ft/s^2. Thismeans it would take 2 seconds (3 / 1.5 = 2) to reach maximum speed.
Remember that:

Force = Mass * Acceleration

There is one other factor to consider when choosingacceleration. If your robot is going up inclines or through rough terrain, youwill need a higher acceleration due to countering gravity. If say your robotwas going straight up a wall, you would require an additional 9.81 m/s^2 (32ft/s^2) acceleration to counteract. A typical 20 degree incline (as shown)would require 11 ft/s^2.

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How do you calculate how much additional acceleration youwould need for a specific incline?

acceleration for inclines = 32 ft/s^2 *sin((angle_of_incline * pi) / 180)

You must add this acceleration to what you already requirefor movement on flat terrain.

Note that motor acceleration and torque are not constants,and that motor acceleration will decrease as motor rotational velocityincreases. As it's very dependent on the motor, this tutorial will gloss rightover it for simplicity.

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