Bifurcation and stability analysis for 3SPS+1PS parallel hip joint manipulator based on unified theory

Abstract

For a parallel hip joint manipulator, the unified kinematics and stiffness model are established based on a novel unified theory, and then the bifurcation and stability are analyzed under the same unified theory framework. In bifurcation analysis, a chaos method is first applied to solve the non-linear bifurcation equations in order to get the full configuration of the parallel hip joint manipulator, which improves the convergence rate and accuracy. Based on the full-configuration solution, the single-parameter and double-parameter simulation for the bifurcation and stability of the parallel hip joint manipulator is performed. The bifurcation simulation results show that the configuration only changes along the corresponding path but cannot change to other paths when the configuration of the parallel hip joint manipulator is at a certain path. The stability simulation results show that when the parallel hip joint manipulator enters into an uncontrolled domain of a bifurcation posture along different paths, the posture component which changes dramatically will lose control first, and the other posture components will move along the changed configuration. In this paper, the kinematics, stiffness, bifurcation and stability of the parallel hip joint manipulator are solved under the same theory framework, which improves the solving efficiency and enriches the mechanical theory for the parallel manipulators.