Structural Analysis of Parallel Mechanisms Using Conformal Geometric Algebra

The operable description of parallel mechanisms is the key to automatic derivation of structural analysis and synthesis. Conformal geometric algebra is introduced to describe robot mechanisms in this paper. A group of basis bivectors {e(23), e(31), e(12), e(1 infinity), e(2 infinity), e(3 infinity)} is established to express position and orientation characteristics of the joint axis. The union of each joint's characteristics of serial mechanisms is defined via outer product operation and the intersection of each limb's characteristics of parallel mechanisms is defined by shuffle product operation, respectively. In this work, a new algebraic symbol algorithm for end-effectors' characteristics is proposed and proved validity via two case studies of 3-RRR and 4-URU PMs which is suitable for computer-aided derivation of mechanisms position and orientation characteristics.