This thesis examines the stability of manipulators with structurally compliant links during contact with a surface that exhibits structural compliance. An experimental robot has be designed to perform contact task experiments under varying dynamics. The contact surface is a part of the Variable Impedance Machine, whose dynamics can be arbitrarily varied to represent any mass-spring-damper cvstem.

A dynamic model of the experimental facility was developed which was programmed to simulate the facility. The results from simulation and experiments agreed well. Using singular perturbation theory, a stability formulation was presented in which three dynamic cases were considered:​ 1) the robot links are much stiffer than the environment, 2) the environment is much stiffer than the links and 3) the links and environment have equal stiffnesses. The theory predicted stability for the first case under certain assumptions but was inconclusive for the second and third cases. Experiments and simulations showed stability for all three cases.