Kinematics of Rigid Body Systems

This chapter presents a systematic formulation for expressing the kinematic relationships concerning a mechanical system such as a manipulator or a mechanism. A kinematic chain is such that its members are connected serially. The kinematic chains are divided into two categories as kinematic branches (i.e. open kinematic chains) and kinematic loops (i.e. closed kinematic chains). A general rigid body system may consist of one or several kinematic chains. The main purpose of the chapter is to derive the necessary equations in suitable forms as a preparation for a subsequent detailed kinematic analysis of the system. It includes two comprehensive examples. In the first, the three-joint arm of a spatial serial manipulator is studied as a typical open kinematic chain. In the second, a spatial slider-crank mechanism is studied as a typical closed kinematic chain. The necessary kinematic equations are derived in order to express the position, velocity, and acceleration relationships.