Dual Quaternion Synthesis of a Parallel 2-tpr Robot

This paper presents a synthesis methodology for parallel robots based on the dual quaternion synthesis of serial constrained robots, that is, serial robots with less than six degrees of freedom. This methodology uses a dual quaternion formulation of the kinematics equations. The goal of the synthesis problem is to determine the dimensions of the robot from a specification of its workspace. The workspace of a constrained serial robot is a subset of the group of spatial transformations which can, in turn, be represented by a subset of dual quaternions. The basic approach is to specify the dual quaternion kinematics equations for each transformation of a discrete approximation to the desired workspace. The structure of these dual quaternions allows a systematic elimination of joint parameters for many constrained serial robot topologies. While the actual finite position synthesis methods are suited only to a small set of simple spatial serial chains, this new formulation can be applied to many serial chains with a greater number of degrees of freedom and joints. The multiple solutions obtained can in turn be combined to create parallel robots. Here we present the theory and formulate and solve the synthesis equations for the 2 TPR parallel robot.