Kinematic Analysis And Optimization Of A 2-URR-RRU Parallel Manipulator

In this paper, a novel 2-URR-RRU parallel manipulator(PM) with one translational degree of freedom(DOF) and two rotational DOFs is proposed. A detailed discussion of the kinematic and optimization of the PM is presented. The main contents cover the following aspects:A CAD model of the 2-URR-RRU PM is established. A fixed coordinate system, a moving coordinate system, limb coordinate systems and relevant parameters for kinematics are determined. Based on the screw theory, the DOF of the 2-URR-RRU PM in initial and general positions are calculated, which can be verified by the G-K formula. The results give exact expressions of the axes of one translation and two orientation DOFs.According to the closed-loop vector method and spatial geometry, direct kinematics and inverse kinematics of the 2-URR-RRU PM are analyzed. Analytical solutions of inverse kinematics and numerical solutions of direct kinematics are obtained. The Jacobian matrix and velocity equations are carried out by taking differentiation of the inverse kinematics equations. The Jacobian matrix is used to investigate the singularity of the PM, which reveals that this manipulator only has inverse singularities, with no forward or combined singularities.The architecture parameters of the mechanism is constrained by the length of the rod, the maximum rotation angle and the singularity limitations. The workspace is obtained by numerical search method. A spiral line in the workspace is simulated by Solid Works, which verify the results of inverse/ direct analysis.The motion/force transmission performance of the 2-URR-RRU PM is analyzed by adopting the Global Transmission Index(GTI) and Global Transmission Workspace(GTW) as the optimization objectives. Method of dimensionless parameters are used and the optimal design space is obtained. Architecture parameters of the PM corresponding to good motion/force transmission performance are selected from the optimal design space.The research of this paper lays the foundation for the future study of dynamics, dexterity analysis and stiffness analysis, which also provides the theoretical basis for the engineering application of the 2-URR-RRU PM.