Computing the Branches, Singularity Trace, and Critical Points of Single Degree-of-Freedom, Closed-Loop Linkages
Computing the Branches, Singularity Trace, and Critical Points of Single Degree-of-Freedom, Closed-Loop Linkages
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DOI：
10.1115/1.4025752
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发表时间：
2014-02-01
影响因子：
2.6
通讯作者：
Wampler, Charles W.
中科院分区：
文献类型：
--
作者：
Myszka, David H.;Murray, Andrew P.;Wampler, Charles W.
本文研究了具有指定输入角和一个设计参数的单自由度闭环连杆机构。对于设计参数的固定值，连杆具有输入奇点，即相对于输入角度的转折点，其将运动曲线分成分支。连杆机构沿着每个分支的运动可以从输入单调地驱动。当设计参数改变时，分支及其连接的数量，简而言之，运动曲线的拓扑结构，可能在某些关键点处改变。允许设计参数变化，奇点形成称为临界曲线的曲线，其投影是奇点迹线。许多临界点是临界曲线关于设计参数的奇点。临界点有简洁的几何解释为过渡链接。本文提出了一种计算奇异迹线及其临界点的一般方法。作为一个例子，该方法被用于斯蒂芬森III连杆机构，并找到了一个范围内的设计参数的输入角能够旋转一个以上的革命之间的奇点。这个特性与出现在奇异轨迹上的尖点的临界点有关。
This paper considers single degree-of-freedom (DOF), closed-loop linkages with a designated input angle and one design parameter. For a fixed value of the design parameter, a linkage has input singularities, that is, turning points with respect to the input angle, which break the motion curve into branches. Motion of the linkage along each branch can be driven monotonically from the input. As the design parameter changes, the number of branches and their connections, in short the topology of the motion curve, may change at certain critical points. Allowing the design parameter to vary, the singularities form a curve called the critical curve, whose projection is the singularity trace. Many critical points are the singularities of the critical curve with respect to the design parameter. The critical points have succinct geometric interpretations as transition linkages. This paper presents a general method to compute the singularity trace and its critical points. As an example, the method is used on a Stephenson III linkage, and a range of the design parameter is found where the input angle is able to rotate more than one revolution between singularities. This characteristic is associated with critical points that appear as cusps on the singularity trace.