Singularity And Its Avoidance Of The Parallel Test Mechanism For Artificial Hip Joint

Parallel manipulator is being used more and more widely, due to its significant advantages such as flexible motion, small accumulated error and high load ability. At the same time, its complex singularity, as the inherent defect that limits its applications, has always been one of the focuses and the difficulties of the researches on parallel manipulator. This paper focuses on the singularity and its avoidance of a 3SPS+1PS type parallel manipulator, which is the core module of a hip joint simulator, and provides the theoretical supports and solutions for its effective control and stabel motion. The work can be concluded as follows:Section 1 introduces the backgrounds and the research status.Section 2 analyzes the singularity mechanism through the configuration bifurcation characteristics. An analytical model of forward position analysis for the manipulator is built, with A univariate-form polynomial equation obtained. The closed-form model guarantees the completeness of forward positon analysis. Based on this, the motion behaviour near the singular points and the mechanism of uncontrolled degree-of-freedom are investigated, with the method of the configuration bifurcation characteristics, and it is verified by 3-D motion simulation. Then, a Configuration Stability Index is proposed to measure the controllability of degree-of-freedom. The direction and the magnitude of the self-motion are judged according to its equivalent motion.Section 3 aims at identifying singularity from different points of views. The singular loci of pose parameters are obtained according the Jacobian matrix. The configurations are divided to 2 kinds of spaces according to their distributions, and it is found out that in practice we only need to care for the basic configuration spaces, where the singular loci are degenerated into a single surface. Then, the singular condition is proved to be equivalent to that the univariate-form input-output equation has repeated root in the real number field, thus the singular condition equation of input parameters is obtained, as well as the singular loci of input parameters in the basic configuration spaces. Moreover, the path for the manipulator to simulate the hip joint motion is found out to have travarsed the singular loci twice.Section 4 evaluates the performances of the manipulator, in order to provide a theoretical basis for the optimum design and rational planning of the task space. Based on the Jacobian matrix, the motion transmission index, static load bearing index and the transmission stiffness index are defined, and their distributions in the working space are investigated. The dynamic model of the manipulator is built according to the virtual power principle and the driving force is chosen to be one of the evaluation indexes. The dynamics of the path that simulates the hip joint motion is numerically simulated, and it is found out that the driving force of each leg has a mutation when it comes to the singular point, which would make the drive and control very difficult.Section 5 fouses on the singularity-free optimization for the working path of the manipulator that simulates the hip joint motion. By setting a virtual reference coordinate, and making the moving platform simulate the hip joint motion based on this virtual reference coordinate, the actual path could avoid the singular surfaces. The optimization is conducted, with the pose of the virtual reference coordinate as the design variables, the motion transmission index and the driving forces as the objects, and the attainable working space as the constraints. The equivalent working path after optimization has no sigularities, besides, the motion transmission performance has significantly improved, and the driving forces decrease substantially and vary gently now.Section 6 is the summary of the whole work, including main conclusions, novelties and prospects.