This paper presents a generalization of Kutzbach-Gru¨bler criterion for mobility analysis of kinematic chains based on group theory. This new mobility criterion applies to exceptional linkages and reduces to a group theoretic representation of Kutzbach-Gru¨bler criterion for trivial linkages. Furthermore, it is shown that using sets and groups of Euclidean displacements, one can distinguish between trivial, exceptional, and paradoxical linkages. Using these concepts, formal definitions of trivial, exceptional, and paradoxical linkages are presented and it is shown that there are two classes of paradoxical linkages. In addition, a new class of linkages is identified that have partitioned mobility. This work builds upon and extends the work of Herve´ and Fanghella and Galletti in application of group theory to analysis of kinematic chains.
- Design Engineering Division and Computers and Information in Engineering Division
On Mobillity Analysis of Linkages Using Group Theory
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Rico, JM, & Ravani, B. "On Mobillity Analysis of Linkages Using Group Theory." Proceedings of the ASME 2002 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. Volume 5: 27th Biennial Mechanisms and Robotics Conference. Montreal, Quebec, Canada. September 29–October 2, 2002. pp. 429-446. ASME. https://doi.org/10.1115/DETC2002/MECH-34249
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