Abstract The branches of motion in the configuration space of a reconfigurable linkage can intersect in different ways leading to different types of singularities. In the vast majority of reported linkages whose configuration spaces contain multiple branches of motion the intersection happens transversally, allowing local methods, like the computation of its tangent cone, to identify different branches by means of their tangents. However, if these branches are of the same dimension and they intersect tangentially, it is not possible to identify them by means of the tangent cone at the singularity as the tangent spaces to the branches are the same. Although this possibility has been mentioned by a few researchers, whether linkages with this kind of tangent intersection of branches of motion exist is still an open question. In this paper, it is shown that the answer to this question is yes: A local method is proposed for the effective identification of branches of motion intersecting tangentially, and a method for the type synthesis of linkages that exhibit this particular type of singularity is presented.

中文翻译：

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运动分支的切向交点

摘要 可重构连杆的配置空间中的运动分支可以以不同的方式相交，导致不同类型的奇点。在绝大多数报告的链接中，其配置空间包含多个运动分支，交叉发生横向，允许局部方法，如计算其切锥，通过它们的切线识别不同的分支。然而，如果这些分支具有相同的维度并且它们相切相交，则不可能通过奇点处的切锥来识别它们，因为分支的切线空间是相同的。尽管少数研究人员提到了这种可能性，但与这种运动分支的切线交点是否存在联系仍然是一个悬而未决的问题。在本文中，