Structure Synthesis and Reconfiguration Analysis of Variable-Degree-of-Freedom Single-Loop Mechanisms With Prismatic Joints Using Dual Quaternions

This paper deals with the structure synthesis and reconfiguration analysis of variable-DOF (variable-degree-of-freedom) single-loop mechanisms with prismatic joints based on a unified tool—the dual quaternion. According to motion polynomials over dual quaternions, an algebraic method is presented to synthesize variable-DOF single-loop 5R2P mechanisms (R and P denote revolute and prismatic joints, respectively), which are composed of the Bennett and RPRP mechanisms. Using this approach, variable-DOF single-loop RRPRPRR and RRPRRPR mechanisms are constructed by joints obtained from the factorization of motion polynomials. Then reconfiguration analysis of these variable-DOF single-loop mechanisms is performed in light of the kinematic mapping based on dual quaternions as well as the prime decomposition. The results show that the variable-DOF 5R2P mechanisms have a 1DOF spatial 5P2P motion mode and a 2DOF Bennett-RPRP motion mode. Furthermore, the variable-DOF 5R2P mechanisms have two transition configurations, from which the mechanisms can switch among their two motion modes.