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Analytic Characterization of a Class of Three-Contact Frictional Equilibrium Posture in Three-dimensional Gravitational Environments
Department of Mechanical Engineering, Technion, Haifa, Israel
* To whom correspondence should be addressed. E-mail: rimon{at}tx.technion.ac.il.
Quasistatic legged locomotion over uneven terrains requires characterization of the mechanism's feasible equilibrium postures. This paper characterizes the feasible equilibrium postures of mechanisms supported by three frictional point contacts in a three-dimensional gravitational environment, for a subclass of contact arrangements, called tame, for which the friction cones lie above the plane spanned by the contacts. The kinematic structure of the mechanism is lumped into a single rigid body B having the same contacts with the environment and a variable center of mass. The equilibrium postures associated with a given set of contacts become the center-of-mass locations of B that maintain a feasible equilibrium with respect to gravity. The paper establishes the relations between the feasible equilibrium region and the classical support polygon principle. For tame 3-contact arrangements, the paper identifies and characterizes geometrically three types of boundary curves of the feasible equilibrium region, where two of them are obtained is closed-from, and the third is given implicitly as a solution of a set of nonlinear equations, which can be traced numerically. The three types of boundary curves are then associated with the onset of three different modes of non-static contact motions. Finally, the paper reports on experimental results that verify the theoretical predictions by using a 3-legged prototype.
First published on September 28, 2009 |
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