面对称3-S■R并联机构的运动学分析与尺度综合

Kinematics Analysis and Dimensional Synthesis of a Plane Symmetric 3-S■R Parallel Manipulator

研究面对称3-S■R并联机构位置和速度逆解模型的建模方法,揭示连接动平台与支链转动副轴线方位角对位置逆解复杂程度和机构奇异性的影响规律,得到当该角为90o时可得到位置逆解解析解和避免机构构型奇异的重要结论。采用单调分析揭示出尺度参数对速度雅可比矩阵条件数全域均值和标准差的影响规律,并采用多目标有约束优化算法得到一组可使机构全域运动学性能最优的尺度参数。

An approach for the inverse displacement analysis of a plane symmetric 3-SPR parallel mechanism is presented. Influences of the structural angle of the R joint on the complicity of inverse displacement equations and the singularity are investigated, leading to an analytical solution and a singularity free design as long as the angle is set to be 90%. On the basis of monotonic analysis, a set of homogeneous dimensionless parameters can be achieved by minimizing two global performance indices represented by the mean value and standard deviation of the condition number of the velocity Jacobian.