ABSTRACT
This chapter gives a description of the kinematics for a general n degree of freedom, open-chain robot manipulator using the tools. It present a brief treatment of redundant and parallel manipulators using this same framework. The chapter contains a derivation of the product of exponentials formula for the forward kinematics of an arbitrary open-chain manipulator. The chapter discusses the inverse problem of finding a set of joint angles which causes the end-effector to have a desired configuration. It makes extensive use of a set of subproblems originally proposed by Bradley Paden and Kahan which are very closely related to the exponential representation of rigid body motion. The chapter derives the velocity and force relationships between the end-effector and the joints, and introduces the manipulator Jacobian for a robot. It examines the Jacobian of the manipulator, which relates infinitesimal joint motions to infinitesimal workspace motions.
