基于Assur杆组元素的平面机构的拓扑描述

Topological Representation of Planar Mechanisms Based on Assur Group Elements

通常邻接矩阵仅描述机构中构件间连接关系,不能直接对基于Assur结构组成理论的杆组及其连接关系进行描述及变换。基于此,将杆组作为基本元素,替代邻接矩阵中的单一构件元素,构造一种基于Assur杆组元素的机构结构拓扑矩阵——杆组邻接矩阵。该矩阵对角线元素由代表主动件、机架和Asuur杆组和/或扩展Assur杆组三种基本元素组成,非对角线元素代表各基本元素间的连接关系及运动副的类型,清晰地描述了基于Assur结构理论的平面机构的结构组成。Assur杆组元素用于普通平面机构的拓扑描述,扩展Assur杆组元素用于变胞机构的拓扑描述。该矩阵为应用Assur结构组成理论系统的进行结构综合,特别是计算机辅助结构综合和分析提供了新的途径。实例验证了该矩阵的有效性和实用性。

The general adjacent matrix only provides the links connecting information of the mechanism,so that neither Assur group nor theirs connecting ships,which to be used in the mechanism synthesis based on Assur structure theory,are not described directly by the matrix.Assur group are treated as an element instead of the link element of the adjacent matrix,and a new kind of structural topological matrix so called group adjacent matrix is proposed.The diagonal elements of group adjacent matrix are composed of driver link,frame and Assur group and/or augmented Assur group,which clearly shows the topological structure of planar mechanisms based on Assur structure theory,and non-diagonal elements describe the connection ships and the types of the connecting joints of the diagonal elements.The Assur group element is for the structural study of general planar mechanisms,and augmented Assur group element is for the structural study of planar metamorphic mechanisms.The group adjacent matrix provides a new systematic way of structural synthesis of planar mechanisms,especially for the computer-aided structure synthesis based on Assur structure theory.Examples show that the matrix is efficient and practical.