Fundamental Research On Kinematics And Inverse Dynamics For Stewart Platform

Stewart platform is characterized by the high rigidity, large load handling capability, and non-accumulation of position error. Parallel mechanism is the supplement of the series mechanism and become the focus of the research in spatial mechanism. At present, Stewart platform extensive and important applications in many aspects such as aviation, flight, busywork in sea and land, underground exploitation, manufacturing and so on. However, despite the plentiful research achievements in the practical application and theory study in parallel mechanism, there are many challenging problems in kinematics, singularity and dynamics. For example, there is no a uniform method for solving the Jacobian matrix of the parallel mechanism which is deficient degrees of freedom, and searching for an algorithm that could solve all solutions to the forward kinematics of parallel mechanism and so on. In this dissertation, it was systematically dealed with kinematics, singularity, inverse dynamic for parallel mechanism.Jacobian matrix is an important aspect of spatial parallel mechanism. Jacobian matrix is a mapping from input to outout. Method of motion was adopted to solve the Jacobian matrix of spatial parallel mechanism of 6 degrees of freedom. However, there is no a uniform method for solving the Jacobian matrix of the parallel mechanism which is deficient degrees of freedom. In this dissertation, the Jacobian matrix of deficient degrees of freedom parallel mechanism was established by adding imaginary kinematic pairs to each kineamtc branched-chain, which make every branched-chain to transform an imaginary mechanism with six degrees of freedom. The complete Jacobian matrix was derived from the imaginary parallel mechanism. This method is universal for deficient degrees of freedom parallel mechanism. The value of the Jacobian matrix determinant was detected in the course of motion planning based on the inverse kinematics to determine the reasonableness of the trajectory planned.The singularity is an importan aspect that needed to be considered, and the Jacobian matrix palys an important role in this part. It could be determined the singularity of parallel mechanism by simplifiing the Jacobian matrix that had derived from the positon and configruation of the parallel mechanism. A singuilarity configuration was founded by simplifiing the Jacobian matrix, which verified the correctness of the Jacobian matrix. The moblie platform would get unexpect degrees of freedom and an instantaneous screw motion if it is in singularity configuration. The instaneous screw motion could be synthesised by the motion of three pointes that are not located in the same line on the mobile platform. The motion of the three points could synthesis a screw motin only when the intersection point of the three normal planes of velocity located in the plane that is determined by the three pointes.As for the forward kinematics of the spatial parallel mechanism, Stewart platform was seltct as an example in this dissertation, by adopting homotype approach, an equation system of the mechanism structure constrain was established, which was a strong coupling equation system. Universial formula was used to transform nonlinear equation system into polynomial equation system. At last, the initial equation system was established. A predictor—corrector method to get the forward solutions was proposed based on the principle of homotypy, which is an method that could solve all solutions to all possible configuration of parallel mechanism. All solutions of Stewart platform was solved by this method, and all reasonable solutions were determined by considering the continuity of the motion of the platform. The comparison of the results of the homotopy and other algorithm was carried out, which verified the correctness and validity of the homotopy.As for the inverse dynamic of the parallel mechanism, the parameters of the position and configuration were generalized coordinates according to the principle of the Kane, and the linear velocity and angular velocity were generalized velocity. The complete inverse dynamic model was built by considering the gravity and inertial of the all chains and mobile platform. The local frames of axes were located in the mass center of the each kinematic chain, which simplified the computation process inertial tensor of the every kinematic chain in the inertial frame of the axes. At last, the computer simulation was carried out to verify the correctness and reasonableness of the inverse dynamic model. The contrast test was carried out with the existing studing results, which showed that the homotopy algorithm of the inverse dynamics had high precision.