A Synthesis Method of Spatial Over-constrained Mechanisms Based on Kinematics of Serial Manipulators

摘要
This paper proposes a modular method based on the kinematics of serial manipulators to synthesize over-constrained mechanisms. Because the PPP manipulator has an unlimited work space, its end-effector can be constrained to trace a trajectory identical to those of another open-chain manipulator, including a P joint single link and an RR dyad. In doing so, two open-chain manipulators can be concatenated to form closed-loop mechanisms, including PPPP, PPPRR, or PPCR mechanisms. To design over-constrained mechanisms efficiently, the Denavit-Hartenberg convention is adopted to describe the PPP manipulator kinematically, and the Euler angles are utilized to derive geometric constraints of synthesized over-constrained mechanisms. Next, kinematic equations of the PPP manipulator can be modularized and applicable to analyze different closed-loop mechanisms. At last, by adjusting link lengths, twisted angles, and joint angles of the synthesized PPPRR and PPCR mechanisms to form other over-constrained mechanisms configurationally. The novelty of this research lies in modularizing the over-constrained mechanism into two movable serial manipulators whose end-effectors share identical trajectory and orientation. Thus, defining geometrical constraints of the over-constrained mechanism can be transformed into finding angular parameters describing the orientation of these two serial manipulators such that the end-effector coordinate system of two manipulators can properly be aligned. Angular parameters of the serial manipulators can be easily determined by means of Euler angles, which yields an advantage of easy calculation since it only involves the computation of Euler angles parameters. The presented method can be extended to the kinematic synthesis and analysis of more spatial closed-loop mechanisms.