Figure1 attached shows the top view of a vehicle with standard wheels
attempting to rotate counter-clockwise but not yet moving because the
torque being applied to the wheels is too low. The +Y axis is the
"forward" direction.
Assume the following:
- Four identical standard non-steerable wheels of radius "r"
- Wheels are located at the corners of a rectangle
- Axis of each wheel is parallel to the X-axis
- Coefficient of friction "mu" is the same in all directions
- The same magnitude torque "tau" is being applied to each wheel
- Let f2 = trackwidth/wheelbase
- The right wheels are being torqued “forward”
- The left wheels are being torqued “backward”
- The vehicle is in static equilibrium
- CoM aft of CoG. Vehicle is on a flat, level floor.
- Let f1 = (distance from CoG to CoM)/(distance from CoG to the point midway between rear wheels)
- Let W be the weight of the vehicle.
- Fn is the total friction reaction force of the floor on the bottom of wheel #n,
and Fnx Fny are its components. n= 1,2,3,4.
Problem:
Find the torque tau in terms of mu, r, W, f1, and f2 required to break the
static friction and start the vehicle rotating.