Clifford Algebra Synthesis of Serial Chains

Abstract

In this chapter we formulate design equations for a spatial serial chain using the matrix exponential form of its kinematics equations. These equations define the position and orientation of the end effector in terms of rotations about the joint axes of the chain. Because the coordinates of these axes appear explicitly, we can specify a set of task positions, and solve these equations to determine the location of the joints. At the same time we are free to specify joint parameters or certain dimensions to ensure that the resulting robotic system has certain features.