Delta并联机构工作空间解析及尺度综合

Workspace Resolution and Dimensional Synthesis on Delta Parallel Mechanism

提出了Delta并联机构工作空间解析及尺度综合的方法。利用曲面包络理论得到Delta并联机构单开链子空间边界曲面的解析表达式,求得机构可达工作空间,进而导出工作空间包容的最大内切球体及其位置与尺度参数的关系。最后将上述球体作为设计空间,以雅可比矩阵条件数在设计空间的全域平均值作为机构操作性能衡量指标进行尺度综合,得到使机构操作性能最优的尺度参数。

A method of workspace resolution and dimensional synthesis on Delta parallel mechanisms was presented. The resolution expression of the single-open-chain sub-space boundary surface and the reachable workspace of the Delta parallel mechanism were obtained based on curve envelope theory. Then the maximal inscribed spheroid contained in workspace was educed, and the relationship between its position and the dimensions was established. Taking the spheroid as the design space and using the universal average value of Jacobian matrices condition number in design space as mechanism performance index for dimensional synthesis, the optimal dimensions for the Delta parallel mechanism were obtained lastly.