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This paper examines the phenomenon of frictionless contact between rigid bodies that are already subject to kinematic constraints from some other source. Such contacts occur frequently when robots interact with their environments, in which case, the additional constraints come from the robot mechanisms. A proper analysis of these contacts must consider both sets of constraints. This paper presents a general model of constrained-body contact, expressed in invariant terms; a method of resolving equations of motion into decoupled subsystems with respect to the contact's motion and force freedoms; an equation of motion for possibly redundant robots experiencing constrained-body contact, which employs a novel decomposition of the robot's joint space into dynamically decoupled subspaces; and a dynamically decoupled hybrid motion/force-control system based on the same decomposition. It is shown that disturbances from an unknown dynamic environment are automatically confined to the force-control subsystem, and that a modification to the control law can factor these disturbances out of the controlled response.