Dynamics And Vibration Control Analysisof Parallel Manipulator For Hip Joint

Due to the external loads and periodic inertia forces, the parallel manipulator with large load and high speed moving has elastic deformations that bring about the motion errors of the moving platform, and it’s difficult to compensate by the calibration method. While carrying out the tribological experiment for hip joint simulator, with the motion frequency 1HZ, the active branched-chains of the experimental device will produce nonlinear elastic deformations depending upon the friction torques, which decreases the kinematic accuracy for the actual motions of the human hip joint. For 3SPS+1PS parallel manipulator, the key component of 3SPS+1PS bionic parallel test platform, its dynamic, dynamics characteristics and optimal design, fatigue reliability and active vibration control are analyzed. The main contents are summarized as follows:1) Based on the KED, the dynamic modeling of 3SPS+1PS parallel manipulator was studied. The dynamic equations of each element and branched-chain of the parallel manipulator were established by proposing a spatial flexible beam element with circular section. According to the kinematic and dynamic constraint relationships between the moving platform and the active branched-chains, the overall system elastodynamic equation of 3SPS+1PS parallel manipulator with flexible links was obtained by assembling the dynamic equations of the branched-chains and the rigid moving platform. Then dynamic response of the parallel manipulator was solved by Newmark method. The results showed that the elastic displacements of the moving platform, the driving forces of the active branched-chains and the constraint forces of the intermediate branched-chain as well as the moving platform were simulated by the numerical method.2) The dynamic characteristics and optimum design of 3SPS+1PS parallel manipulator including the natural frequency were studied. Regarding the dynamic stress and natural frequency as the dynamic characteristic parameters, and according to the solutions for the elastodynamic equation, the maximum dynamic stresses of the active branched-chains and the variations of the first four order natural frequencies in the workspace were solved. The relationships between the section sizes of the chains, the mass and center height of the moving platform on the first three order natural frequencies are studied. Moreover, choosing the first order natural frequency/mass ratio of the parallel manipulator as its evaluation index of the dynamic characteristics, the structure parameters were optimized under the circumstance that the maximum normal stress satisfied the constraint conditions. Thus, the maximum dynamic stresses of the active branched-chain were decreased and the natural frequency of the system was increased so as to improve the dynamic characteristics of 3SPS+1PS parallel manipulator.3) According to the maximum dynamic stresses of the active branched-chain, the stress cycles at all stress spectrum levels were add up by rain flow counting method. Based on the Corten-Dolan fatigue reliability analysis theory, the fatigue life model of the parallel manipulator was derived and the fatigue lives of the branched-chains were calculated. In the end, in light of the fatigue reliability analysis method, the fatigue reliability of 3SPS+1PS parallel manipulator was analyzed, and that under different structural parameters was studied. It is verified that the structural parameters after being optimized could apparently improve the fatigue life and reliability of the parallel manipulator.4) Basing the principle of sliding mode variable structure control, the active vibration control of 3SPS+1PS parallel manipulator was studied. Without considering the influences of the piezoelectric actuator and the sensor on dynamic model, and in accordance with the finite element method and the modal theory, the modal dynamic model of 3SPS+1PS parallel manipulator was established. Regarding the modal displacement and modal velocity as the state variables, the slip plane was determined by optimization method on the premise of satisfying the performance requirements of the parallel manipulator, and the slip plane controller was designed based on Liapunov’s direct method. The active vibration control of 3SPS+1PS parallel manipulator was realized by adopting the converse piezoelectric effect of the piezoelectric actuator to control the first four order modal frequencies.