A synthesis method for 1-DOF mechanisms with a cusp in the configuration space
A synthesis method for 1-DOF mechanisms with a cusp in the configuration space
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DOI：
10.1016/j.mechmachtheory.2018.09.008
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发表时间：
2019-02
影响因子：
5.2
通讯作者：
P. C. López-Custodio;A. Müller;J. Rico;J. Dai
中科院分区：
文献类型：
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作者：
P. C. López-Custodio;A. Müller;J. Rico;J. Dai
机构奇异性的研究取得了重要进展。然而，这项研究只集中在不同的运动分支相交的情况下，即配置空间（c-空间）的分叉点。其他类型的奇点由于缺乏机制的例子而没有被研究。特别是，在其c-空间中表现出尖点奇点的机构几乎是未知的，除了康奈利和Servatius提出的平面连杆机构，它作为一个例子，其中常见的刚性定义失败。本文提出了一种空间单自由度尖点机构的综合方法。该方法包括合成具有特定特征的空间曲线的机械生成器，然后将该模块与其镜像版本适当地连接。提出了几个例子，包括一个运动型联动，其特征在于由一个奇点，这是一个尖点（1自由度运动）和一个分支的曲线和表面（2自由度运动）。本文讨论了现有的奇点局部分析方法在尖点奇点处失效的问题。所提出的综合方法允许构建机制，应启动研究尖点奇点的研究。
Significant progress has been made in the study of singularities of mechanisms. This research has, however, exclusively focused on situations where different motion branches intersect, i.e. bifurcation points of the configuration space (c-space). Other types of singularities have not been studied due to lack of mechanisms examples. In particular, mechanisms exhibiting cusp singularities in their c-space are almost unknown, besides a planar linkage presented by Connelly and Servatius, which served as an example where the common definition of rigidity fails. In this paper, a method for the synthesis of spatial 1-degree-of-freedom (1-DOF) cusp mechanisms is presented. This method consists in synthesizing the mechanical generator of a spatial curve with specific characteristics and then appropriately connecting this module with its mirrored version. Several examples are presented including a kinematotropic linkage, which is characterized by a singularity that is a cusp (1 DOF motion) and a bifurcation of a curve and a surface (2-DOF motion). It is discussed that all available methods for the local analysis of singularities fail at cusp singularities. The presented synthesis method allows for constructing mechanisms that shall initiate the research into the study of cusp singularities.