In this paper, the motion of an elastically suspended rigid body unilaterally constrained by contact at multiple locations is studied. In this problem, each individual contact may or may not constrain the body’s motion. Whether a contact provides an active constraint or not is determined by: 1) the commanded motion of the body’s compliant support, 2) the direction of the constraining surface normal, 3) the number and direction of other potentially constraining surfaces, and 4) the elastic properties of the support. Here, the investigated problem is restricted to quasistatic motion and frictionless contact. We show that the set of possible constraints that are active for a given set of contacts, elastic behavior, and commanded motion is unique. We also develop a procedure to determine the set of active constraints. This procedure is then used as part of a larger procedure to determine the compliant motion of the rigid body.

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