A novel methodology for determining the singularities of planar linkages based on Assur groups

Abstract

In this paper, a simple and effective methodology for judging the singularities of planar linkages is presented, which is based on Assur groups. The methodology determines the geometrical configurations of the Assur groups in singularities. Based on the singularities of a simple two-bar group, the possible singularities of all Assur four-bar and six-bar groups are given by the concept of instant centers. Then the general process and rules of determining singularities are obtained and shown through several examples of the 1-DOF planar linkages. These linkages include the two six-bar linkages and the several eight-bar linkages composed of Assur six-bar groups. The singularities of them verify the proposed methodology, which reveals that the singularities of a linkage only depend on the Assur groups. Therefore, as long as the singularities of Assur groups are determined, all the possible singularities of the linkage composed of these groups can be determined. This methodology is independent of linkages, so it is universal for all planar multi-bar linkages which can be divided into these Assur groups.