Singularity And Stability Analysis Of 2(3HUS+S) Parallel Manipulator For Hip Joint

Due to the advantages with high stiffness,high bearing capacity and high precision,the parallel manipulator is applied to various fields.However,there are some disadvantages,such as singular bifurcation,which has been the hot spot all over the world.In order to simulate the friction and wear test of artificial hip joint and improve the working efficiency of the experiment,a novel 2(3HUS+S)parallel manipulator with double moving platforms is designed in this paper.Furthermore,the workspace,singularity,performance characteristics and motion stability are analyzed in detail,which provide theoretical support for the following motion control strategy and singularity avoidance.The main contents of this paper are as follows:1)The inverse / forward kinematics and workspace of 2(3HUS+S)parallel manipulator are analyzed.Based on the novel 2(3HUS+S)parallel hip joint simulator,the analytical expressions of displacement,velocity and acceleration are obtained by using the rotating matrix.According to the motion curve of ISO 14242-1: 2002(E),the inverse kinematics is analyzed.In the view of the geometric relation,the forward kinematics model of the manipulator is solved,and the result is verified numerically by the inverse kinematics.The workspace of the test machine is obtained under the constraint conditions with the displacement of the slider,the angle of the motion pair and the interference of the connecting rod.Meanwhile,the influence of the radius of the moving platform,the radius of the fixed platform and the length of the connecting rod on the workspace are analyzed.2)The singular surface and configuration bifurcation of 2(3HUS+S)parallel manipulator are analyzed.The singular condition is established,and the singular surface is obtained.In addition,the singular surface within the range of small attitude angles is analyzed.In order to better analyze the trend of the singular surface,the hierarchical analysis of singular surface is carried out.Based on the established forward kinematics model,the single bifurcation parameter configuration path curve is obtained,and the configuration bifurcation is analyzed.Furthermore,the exact positions of bifurcation points are obtained by numerical iteration method.Finally,the relationship between the multiple solutions of the forward kinematics and the singular surface is analyzed.3)The performance characteristics of 2(3HUS+S)parallel manipulator are analyzed,which provide the theoretical basis for the structural optimization design.In the workspace,based on the motion and force Jacobian matrix,the two performance indexes of the dexterity and static bearing capacity are analyzed.In view of the stiffness matrix,at γ=0,the distribution of the maximum / minimum stiffness value and KSI index are analyzed.The influences of attitude and structural parameters on the dexterity and static bearing capacity are analyzed.The multi-objective problem is transformed into the single objective problem by weighted summation method,and the genetic algorithm is used to optimize the structure parameters of the objective function.Lastly,the comparison is analyzed before and after optimization.4)The motion stability of 2(3HUS+S)parallel manipulator is analyzed.The configuration curves of double bifurcation parameters are obtained,and the configuration bifurcation is analyzed.On the basis of the bifurcation curve,the variation of bifurcation characteristics at the bifurcation point is analyzed when the position of the slider is disturbed.Based on the configuration bifurcation curve,the bifurcation transformation coefficient is introduced,and the stability of the bifurcation points are analyzed by the opening size of two configuration curves.Moreover,the results provide theoretical support for the following research on the singularity avoidance and control strategy.