[patrickrd]

This is a great question but the answer is complicated. There are a couple things I think you might be wondering about.

1) Stiction. This is a made-up term for how much force is required to get an object to transition from static (not moving) to dynamic (moving). All wheels tend to dig into the ground and at a microscopic level, interweave with the abnormal properties of the ground material. This creates a bond between the ground and wheel. A certain amount of force is needed to break this bond, or overcome the "stiction." Stiction comes from many places in a mechanical system other than the wheels, too: ball bearings, grease in gearboxes, and many others. The more steps you have in your transmission, the more stiction you probably will have. Stiction -- to my knowledge -- is not a real scientific term, but it is commonly used. Generally, if you want to know how much force is required to overcome stiction, you've got to build a prototype and measure it. It is good practice to assume very large stiction when designing a robot or any mechanical device, until you can measure what it actually is.

2) Dynamic friction. When a robot starts to move (after overcoming friction), the robot will accelerate depending upon how much torque it transmits to the ground. The more torque, the faster it accelerates. Remember, torque equals force times distance, so force equals torque divided by distance. Since F = m*a, a = F / m. Substituting in what force equals, a = T / (d * m). With a wheel, you use the radius as d. Also, when there is more than one force, the SUM of the forces equals mass * acceleration. Thus, if there are losses in the system due to friction, then you have to subtract all the friction forces to get your net force. Again, you normally have to measure friction.

3) Gear ratios. Remember your gear ratios. The torque on the wheel is equal to the torque of the motor times the gear ratio. The speed of the wheel is equal to the torque divided by the gear ratio. The force that causes acceleration of the robot is the torque of the wheel, divided by the radius of the wheel.

Hope this helps.

Patrick