Dogdish motion equations

If you check out the URL you'll find my analysis of the math for the motions of the three wheels of the dogdish vehicle. Basically this math describes the constraints that must be satisfied when steering the vehicle along any path. Although there are six controlling degrees of freedom (the steering and speed of three wheels), the motion of the vehicle has only three (rotation and xy velocity). Only a subspace of steering configurations are wheel-slip free. I analyse this relationship. Any potential movement of the vehicle can be re-parameterized as a time varying rotation speed and ground velocity. I do this for the simple case of tricycle motion. If rotation and horizontal motion are specified independently then there are some funky spirograph motions and I analyse these in the document.
URL: http://research.microsoft.com/users/swinder/dogdish.pdf