变胞机构运动特性的旋量代数分析方法

Analysis method of screw algebra for motion characteristics of metamorphic mechanisms

针对已有拓扑结构描述方法无法分析变胞机构的空间结构和运动特性的局限性,提出了变胞机构结构变换的旋量邻接矩阵描述新方法.在此基础上进一步提出了变胞机构运动特性的旋量代数分析方法,这种方法是通过旋量邻接矩阵确定运动螺旋的齐次线性方程组,通过齐次线性方程组的基础解系确定反螺旋系,并得出动平台的运动螺旋系,从而确定变胞机构在各构态的空间结构、构件数和运动副数、自由度等特性.提出了一种新型4-URU并联变胞机构,并采用所提出的方法对这种并联变胞机构进行运动特性分析,验证了所提出方法的正确性和有效性.

A new method using screw adjacency matrix to describe structural transformations of meta- morphic mechanisms was proposed. This method overcomes the limitations of existing topological de- scription methods which cannot analyze metamorphic mechanismsp spatial structures and motion char- acteristics. And on this basis, the screw algebra method for analyzing metamorphic mechanisms＇ mo- tion characteristics was introduced in detail. Firstly, motion screws＇ homogeneous system of linear e- quations was determined by the screw adjacency matrix. Then the equations＇ basic solution set deter- mined the anti-screw system. Finally the moving platformls motion screw system was calculated. Thus metamorphic mechanismsI motion characteristics, such as spatial structure in different configu- rations, the number of components and joints, degrees of freedom were obtained. A new 4-URU par- allel metamorphic mechanism was put forward. The parallel metamorphic mechanism＇s motion charac- teristics were analyzed using the proposed method. This example of analyzing motion characteristics on the parallel metamorphic mechanism verifies that the proposed method is correct and effective.