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.

中文翻译：

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一种基于 Assur 群确定平面连接奇异性的新方法

摘要 本文提出了一种基于Assur群的简单有效的平面连杆奇异性判断方法。该方法确定奇点中 Assur 群的几何配置。基于一个简单的两杆群的奇点，所有 Assur 四杆和六杆群的可能奇点都由瞬心的概念给出。然后通过1-DOF平面连杆的几个例子获得并展示了确定奇点的一般过程和规则。这些连杆包括两个六连杆机构和几个由 Assur 六连杆组组成的八连杆机构。它们的奇异性验证了所提出的方法，这表明链接的奇异性仅取决于 Assur 群。所以，只要确定了 Assur 群的奇异点，就可以确定这些群组成的连锁的所有可能的奇异点。这种方法独立于连杆机构，因此对于所有可分为这些 Assur 组的平面多连杆机构来说都是通用的。 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .