Using Self-Motion in Redundant Manipulators to Cope with Painlevé Paradox

Hesham A. Elkaranshawy


automation and manufacturing, motion planning, Painlevé paradox, redundant manipulator, friction


For general multibody systems, Painlevé paradox could take place at realistic values of the coefficient of friction. Hence, it is the reason of a wide range of bouncing motion, observed during sliding of robotic manipulators on rough surfaces. Most of the published works focus upon the variation of parameters that leads to the paradox or solving the paradox. Contrary to that, in this research work, the focus is on reducing the effect of Painlevé paradox on robotic manipulators during their functional operation. First, a precise new mathematical form for the condition leading to Painlevé paradox is specified for a general multibody system. Using that condition, a paradoxical region is identified for redundant manipulators. Consequently, the self-motion, inherited in redundant manipulators, is used to escape the paradox zone in several cases. In a number of other cases, it is used in extending the span of the motion of the contact point before interring to the paradox zone.

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