Dual Quaternion Synthesis of Constrained Robotic Systems

This paper presents a dual quaternion methodology for the kinematic synthesis of constrained robotic systems. These systems are constructed from one or more serial chains such that each chain imposes at least one constraint on the movement of the workpiece. Serial chains that have constrained workspaces can be synthesized by evaluating the kinematics equations of the chain on a finite set of task positions. In this case, the end-effector positions are known and the Denavit-Hartenberg parameters become design variables. Here we reformulate the kinematics equations in terms of successive screw displacements so the design variables are the coordinates defining the joint axes of the chain in a reference position. Then, dual quaternions defining these transformations are introduced to simplify the structure of the design equations. The result is a synthesis formulation that can be applied to a broad range of constrained serial chains, which can in turn be assembled into constrained parallel robots. We demonstrate the formulation and solution of the dual quaternion design equations for the spatial RPRP chain.