一种2R1T类球面并联机构的瞬时速度分析

Instantaneous velocity analysis of a 2R1T spheroid parallel mechanism

对一种2R1T(R表示旋转,T表示平移)的类球面并联机构进行了瞬时速度分析.由于机构的动平台中心与基座中心始终关于过3个球关节的平面对称,利用几何法很容易获得动平台的位置解,然而机构的瞬时速度的计算则相对复杂,尤其是角速度的计算严重依赖姿态矩阵或完整雅克比矩阵的正确求解,并且计算效率低、容易出错.为此,采用Riemann对称空间理论方法,从机构子链旋量系的对称性出发,建立各子链关节运动的约束,从而简化机构动平台瞬时速度的计算,机构所有可能的瞬时速度组成了一个线性空间,这个空间的基正好解释了机构的瞬时自由度.最后,给出算例验证了该方法的正确性和有效性.通过ADAMS(Automatic Dynamic Analysis of Mechanical Systems,机械系统动力学)软件仿真与理论计算对比,角速度误差控制在-0.004~0.006 rad/s以内,线速度误差控制在-0.01~0.015 mm/s以内,采用对称空间理论方法计算瞬时速度用时5.187 s.

The instantaneous velocity analysis of a 2 R1 T(R denotes rotation, T denotes translation) spherical parallel mechanism was performed. As the center of the moving platform of the mechanism and the center of the base are plane-symmetric about the three spherical joints, the position solution of the moving platform can be easily obtained by using geometric method, but the calculation of instantaneous velocity is relatively complicated. In particularly, the calculation of angular velocity is heavily dependent on the correct solution of the rotation matrix or the complete Jacobian matrix, and the calculation efficiency is low and error-prone. For this reason, the Riemann symmetric space theory method is used in this paper. Starting from the symmetry of the subchain screw system, the constraints on joint movement of each subchain are established and the calculation of instantaneous velocity is simplified. Instantaneous velocity forms a linear space of which the base just explains the instantaneous degree of freedom of the mechanism. Finally, an example is given to verify the correctness and effectiveness of the method. By comparing ADAMS(Automatic Dynamic Analysis of Mechanical Systems) software simulation with theoretical calculation, the angular velocity calculation error is within a range of-0.004 rad/s^0.006 rad/s;and the linear velocity calculation error is within a range of-0.01 mm/s^0.015 mm/s, the calculation time is 5.187 seconds by using the symmetric space theory.