基于杆组邻接矩阵的平面机构综合方法

Structural Synthesis Method of Planar Mechanisms Using the Assur-group Based Adjacency Matrix

为在平面机构综合中能够求解出包含R副和P副的全部运动链,给出一种基于杆组邻接矩阵的平面机构综合新方法。通过对前期研究提出的杆组邻接矩阵进行修正,构造改进的杆组邻接矩阵。基于改进的杆组邻接矩阵,求解给定杆组的所有装配方式,并同步辨识同构体,获取杆组装配关系的杆组邻接矩阵。根据提出的约束条件,采取逐级构造杆组邻接矩阵方法,求解杆组间的可行连接方式,并同步辨识同构体,从而获取全R副杆组间的连接关系的杆组邻接矩阵。将所有类型杆组代入求得的杆组连接关系矩阵,获取所有类型杆组可构成的全部机构构型,包含主动件和机架变换问题。以平面6杆机构为例,应用该方法首次求出包含R副和P副的所有机构构型为364种,验证了提出的综合方法的有效性和实用性。

In order to obtain all kinds of kinematic chains that both with R and P joints in the structural synthesis of planar mechanisms, a new structural synthesis method of planar mechanisms is developed by integrating Assur groups as elements in the modified adjacency matrix. A modified group-based adjacency matrix Jis hence proposed based on the previous study. All assembly forms of Assur groups in the modified group-based adjacency matrix can be determined. The connection forms of all R joints of the Assur groups in the assembly forms are permutated step by step following the proposed connection constrains and isomorphism is detected in the process. Structural forms with R and P joints are hence obtained using permutation of all types of Assur groups in the connection forms, and the inverse problems are revealed in the synthesis. This generates a total of 364 kinds of structural forms of 6-bar linkages with R and P joints which are determined for the first time using the proposed method and demonstrates the efficiency and practicality of the proposed method.