Geometric Characterization and Experimental Validation of Frictional 3-Contact Equilibrium Stances in Three-Dimensions

Quasistatic multi-legged locomotion consists of a sequence of equilibrium postures where the mechanism supports itself against gravity while moving free limbs to new positions. A posture maintains equilibrium if the contacts can passively support the mechanism against gravity. This paper is concerned with computation and graphical characterization of equilibrium postures for mechanisms supported by frictional contacts in a three-dimensional gravitational field. For a given set of contacts, this problem reduces to the computing feasible region R, defined as the center-of-mass positions that maintain equilibrium while satisfying the frictional constraints. This paper continues a previous work by the authors, and provides a new method for computing the boundary of R for 3-contact stances. The paper also gives physical and geometric interpretations for the boundary of R and discusses its relation with the classical support polygon principle. Finally, the paper reports experimental results that validate the theoretical computation.