Abstract
A single-loop mechanism with n≤6 helical joints which has a finite mobility with a degree of freedom f≥1 is overconstrained. Here the case f=1 is considered. For the finite mobility of an overconstrained mechanism it is sufficient, that the first-order closure condition is fulfilled in an open neighborhood of the actual position of the joint axes. Since the explicit functional dependencies of the closure condition are unknown, a Taylor-series expansion yields necessary conditions for the mobility of the mechanism. According to Alexandrov (1998) it is sufficient for the finite mobility of the mechanism if all higher-order mobility conditions up to a maximum, but unknown, order m are fulfilled. Special solutions for necessary mobility conditions are discussed which guarantee that all higher-order necessary conditions are fulfilled. By this these special solutions are sufficient for finite mobility. Some of this special mobility conditions are presented.
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© 2012 Springer Science+Business Media Dordrecht
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Bartkowiak, R., Woernle, C. (2012). Sufficient Conditions for the Mobility of Overconstrained Mechanisms. In: Lenarcic, J., Husty, M. (eds) Latest Advances in Robot Kinematics. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-4620-6_36
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DOI: https://doi.org/10.1007/978-94-007-4620-6_36
Publisher Name: Springer, Dordrecht
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