Position and orientation characteristics of robot mechanisms based on geometric algebra

The operable representation of robot mechanisms is the key to the computerization of type synthesis of parallel mechanisms (PMs). Geometric algebra, an effective mathematical tool for geometric representation and computation, is introduced to describe the position and orientation characteristics (POC) of robot mechanisms, including serial and parallel mechanisms, in this paper. According to the correspondence between the POC of the joint axis and the motion output characteristics of the moving link, the POC union is defined by the outer product operation for the serial kinematic chain and the POC intersection is defined by the shuffle product operation for the parallel kinematic chain. In this paper, a moving coordinate system independent of the position of a mechanism is established for the expression of the joint axes. The direct symbolic algorithm for the motion output characteristics of robot mechanisms, including union and intersection, is proposed and validated via several case studies of 3R open chain, Sarrus linkage, 3-RCC PM and 3-RPS PM. The analysis procedure shows intuition and explicitness that is suitable for computer-aided derivation of the POC set of a mechanism.