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In this paper, robust control strategies are presented systematically for both holonomic mechanical systems and a large class of nonholonomic mechanical systems in the presence of uncertainties and disturbances. First, robust control strategies are presented for both kinds of systems using the bounds of system parameters, respectively. Then, adaptive robust control strategies are presented by tuning the parameter estimates online. Proportional plus integral feedback control is used for force control for the benefit of real-time implementation. The proposed control strategies guarantee that the system motion converges to the desired manifold with prescribed performance while the constraint force remains bounded.