Chapter 6: From Velocity to Trajectories: Inverse Kinematics of Rigid Surfaces with Rolling Contact

In this chapter, we consider two surfaces subject to rolling contact and obtain the contact trajectories when the angular velocity of the moving surface is present. We obtain three scalar entities that generate the contact trajectories to realize the given angular velocity of the moving surface: the rolling direction φ, the rolling rate σ, and the complementary spin rate ω_spin.