Kinematic Analysis And Optimization Design Of A 2-PRU-UPR Parallel Manipulator

Nowadays,the traditional industrial machine tools have been unable to meet the increasing requirements of manufacturing parts in the advanced manufacturing industry.Thus,the parallel manipulator with high precision and stiffness has highly value in this engineering application.In this paper,the kinematics and performance analysis of 2-PRU-UPR parallel manipulator(PM)is presented.The main contents are summarized as follows:A 2-PRU-UPR PM is proposed.And a coordinate system of this PM is established.The degrees-of-freedom(DOFs)of the 2-PRU-UPR PM is carried out by using the screw theory.The result shows that the 2-PRU-UPR PM always has two rotational and one translational DOFs.The inverse kinematic analysis of the 2-PRU-UPR PM is presented by using the closed-loop vector method.The inverse kinematics equation is derived from the geometric constraint.The forward kinematic analysis is calculated by numerical method.And the 3D model of the 2-PRU-UPR PM is created by using SolidWorks.Eight groups of single numerical solution and one group of ellipsoid surface machining are simulated.These simulation examples verify the correctness of the kinematic analysis of the proposed PM.The conclusion shows that the 2-PRU-UPR PM has the unique forward or inverse kinematic solution in the effective workspace.According to the kinematic analysis,the velocity equation based on input-output relationship is carried out.Furthermore,the inverse,forward and combined singularities of the proposed PM are discussed.Considering the limitation of actuation links and rotation angle,the reachable workspace(without singularity)is plotted by numerical search method.The performance of the 2-PRU-UPR PM is analyzed by using the local transmission performance index(LTI)and the virtual work(VW)stiffness index.These two indices are defined as the optimization objectives.The architectural parameters of this PM are optimized by using the method proposed by Liu.Under the condition of the optimized parameters,the mechanical design of the 2-PRU-UPR PM is presented.Then,the static stiffness of the key load-bearing parts is verified by ANSYS.Finally,the actual prototype of this PM is proposed.The achievements in this paper have contributed to the development of 2-PRU-UPR PM in the field of machine tool.