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SUMMARYIn this paper, the kinematic accuracy problem caused by geometric errors of a 2(3HUS+S) parallel manipulator is described. The kinematic equation of the manipulator is obtained by establishing a D–H (Denavit–Hartenberg) coordinate system. A D–H transformation matrix is used as the error-modeling tool, and the kinematic error model of the manipulator integrating manufacturing and assembly errors is established based on the perturbation theory. The iterative Levenberg–Marquardt algorithm is used to identify the geometric errors in the error model. According to the experimentally measured attitudes, the kinematic calibration process is simulated using MATLAB software. The simulation and experiment results show that the attitude errors of the moving platforms after calibration are reduced compared with before the calibration, and the kinematic accuracy of the manipulator is significantly improved. The correctness and effectiveness of the error model and the kinematic calibration method of the 2(3HUS+S) parallel manipulator for simulation of hip joint motion are verified.

Due to the singularity existence of a parallel manipulator, the manipulator may cause bifurcation when passing the position of singular point. When a set of motion input parameters are given, it is possible to produce two or more configurations at the bifurcation point, which makes the manipulator generate two movement trends when the manipulator moves to the bifurcation point: retention configuration and non-retention configuration. When the manipulator moves to a point on the non-retentive configuration curve, the manipulator may lose control and generate uncontrolled DOF. Few works have dealt with the relation between the singularity and the input parameters, as well as the properties of the manipulator nearby the singularity. In this study, a 2 (3HUS+S) parallel manipulator is presented. Based on the established forward kinematic model, the configuration curves of parallel manipulator are obtained. The configuration curves are analyzed, demonstrating that the manipulator contains eight configurations for a single input. At the bifurcation point, based on the radius of an uncontrolled circle, the motion controllability of parallel manipulator is analyzed, and the result indicates that as the control accuracy is increased, it is beneficial to improve the controllability of parallel manipulator at the bifurcation point.

The working efficiency of a parallel manipulator with double moving platforms is better than a parallel manipulator with a single moving platform. In this study, a 2 (3HSS+S) parallel manipulator is presented, and the topology model of the parallel manipulator is established. After calculating, the position and velocity of the manipulator were analysed, and the workspace was obtained under the constraint conditions of parallel manipulator. Within the workspace, the motion dexterity was studied using the reciprocal of the condition number of the motion Jacobian matrix. The static load-bearing performance was analysed through the two norms of the force Jacobian matrix. The two performance indices, which are motion dexterity and static load bearing, indicate that the manipulator has favourable performance characteristics in the range of positive values of angle, which is the rotation in z-axis, but it has a singular position in the range of large negative values of angle. Within the scope of the singular point, the maximum and minimum eigenvalues of the stiffness matrix and the kinematic stiffness index (KSI) were analysed. It has been concluded that the stiffness characteristics are poor near the singular points, and the correctness analysis of the two performance indices has been verified by the results.

In the paper, a novel 2(3HUS+S) parallel manipulator, which has two moving platforms, is proposed. The parallel manipulator is adopted to simulate hip joint motion and can conduct an experiment for two hip joints simultaneously. Motion experiments are conducted in the paper, and the recommended hip joint motion curves from ISO14242 and actual hip joint motions during jogging and walking are selected as the simulated motions. The experimental results indicate that the 2(3HUS+S) parallel manipulator can realize the simulation of many kinds of hip joint motions without changing the structure size.