一种并联机构天线座的运动学研究

以3UPS-U型并联机构天线座为研究对象，计算此机构的自由度，建立并联天线座静平台和动平台的坐标系，确定位姿变换矩阵，进而推导出位姿逆解。针对位姿正解的难题，利用方向余弦矩阵约束条件和推杆长度约束方程构造出方程组，求解出姿态角的封闭解。根据此并联天线座的几何特殊性，推导出雅可比矩阵和速度逆解、正解表达式。以理论建模为基础，结合具体参数，进行了数值仿真，求解出位姿逆解和速度逆解。该研究工作为更深一步的理论研究打下基础，为进一步的工程应用提供了理论依据。

Research on Kinematics of an Antenna Pedestal with Parallel Configuration

Based on the model of parallel mechanism antenna pedestal with configuration of 3UPS-U, the DOFs of this mechanism are calculated. By establishing the coordinate system of the movable platform and the static platform of the pedestal, the transformation matrix is determined and the equation of the inverse position is solved. In terms of the difficult problem of the forward position solution, an equation set which uses the constraint condition of the orientation cosine transformation matrix and the constraint equation of the length of the three rods is constructed, and the closed-form solution of this equation set is obtained. Based on the special geometric characteristic of the pedestal, the Jacobian matrix, forward velocity solution and inverse velocity solution are derived. Based on the theoretical model, the numerical simulation which combines the specific parameters is performed in order to obtain the inverse position solution and the inverse velocity solution. This research lays a foundation for further theoretical study and provides theoretical support for further engineering application.