The duality between the singularity of Bricard mechanism and the Singularity of Stewart platform

被引:0
|
作者
Slavutin, Michael [1 ]
Shai, Offer [1 ]
Mueller, Andreas [2 ]
机构
[1] Tel Aviv Univ, IL-69978 Tel Aviv, Israel
[2] Uni Michigan Shanghai Jiao Tong Uni Joint Inst, Shanghai, Peoples R China
来源
PROCEEDINGS OF THE ASME INTERNATIONAL DESIGN ENGINEERING TECHNICAL CONFERENCES AND COMPUTERS AND INFORMATION IN ENGINEERING CONFERENCE, 2014, VOL 5A | 2014年
关键词
body bar graph; singularity; wrench screw; relative twist screw; cyclohexane molecule;
D O I
暂无
中图分类号
TM [电工技术]; TN [电子技术、通信技术];
学科分类号
0808 ; 0809 ;
摘要
The duality (known also as symmetry) between serial chain manipulators and fully parallel mechanisms is well known in the literature. This paper takes this idea one step further, by introducing a systematic method that transforms mechanical systems into other and different mechanical systems so that the wrench screws in the original system gives rise to the relative twist screws in the second system. The mathematical foundation of this work relies on using the BB graph, a variant of graph representation widely used in mechanisms, possessing both the topology and geometry of the original system. From the dual graph of the latter it is possible to construct the dual system at a specific configuration. Relying on the equivalence between the dual systems, it is proved that if the screw system of a mechanism is at the singular position, so is that of its dual. This idea is demonstrated by showing the dual system of a Bricard mechanism, which is a 6/6 Stewart Platform in the singular position. The paper also shows that the cyclohexane molecule is dual to the 6/3 Stewart platform at the singular position, providing another perspective of the known mobility of this molecule.
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页数:9
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