The Synthesis of Planar RR and Spatial CC Chains and the Equation of a Triangle
The Synthesis of Planar RR and Spatial CC Chains and the Equation of a Triangle
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平面RR和空间CC链的综合及三角形方程
DOI：
10.1115/1.2838647
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发表时间：
1995
期刊：
影响因子：
--
通讯作者：
J. McCarthy
中科院分区：
文献类型：
--
作者：
J. McCarthy
本文给出了一个由三角形的两个顶点及其内角确定一个顶点的方程的平面和空间形式。对Sandor和Erdman设计RR链的标准形式方程稍作修改，得出平面三角形方程，这一事实是将空间三角形的等效方程确定为CC链的标准形式方程的基础。两个平面方程的同时解决方案产生的RR链的固定枢轴和其浮动链接的相对位置极点之间的Burmester的关系的解析表达式。一个类似的解决方案，同时空间三角形方程产生罗斯的概括这一见解，具体而言，固定轴的CC链视图两个相对的螺旋轴在一半的双曲柄旋转角。这些结果为将基于复数的平面连杆机构综合技术推广到空间连杆机构综合提供了基础。
This paper formulates the planar and spatial versions of an equation that determines one vertex of a triangle in terms of the other two vertices and their interior angles. The fact that a slight modification of Sandor and Erdman's standard form equation for the design of RR chains yields this planar triangle equation is the basis for identifying the equivalent equation for a spatial triangle as the standard form equation for CC chains. The simultaneous solution of two of the planar equations yields an analytical expression of Burmester's relationship between the fixed pivot of an RR chain and the relative position poles of its floating link. A similar solution of simultaneous spatial triangle equations yields Roth's generalization of this insight, specifically, the fixed axis of a CC chain views two relative screw axes in one-half the dual crank rotation angle. These results provide the foundation for generalizing planar linkage synthesis techniques based on complex numbers to the synthesis of spatial linkages.