Abstract : Terrestrial manipulators with more DOF than the dimension of the workspace and space manipulators with as many manipulator DOF as the dimension of the workspace are both redundant systems. An interesting problem of such redundant systems has been the repeatability problem due to the presence of nonholonomic constraints. We show in this paper, contrary to the existing belief, that integrability of the nonholonomic constraints is not a necessary condition for the repeatability of the configuration variables. There exist certain trajectories in the independent configuration variable space that are like 'holonomic loops' along which the redundant manipulators exhibit repeatable motion. In this paper we present a simple method based on optimization techniques for designing repeatable trajectories for free-flying space manipulators and terrestrial manipulators under pseudoinverse control. Nonholonomic mechanical system, Motion planning, Configuration space, Repeatability, Pseudoinverse control, Free-flying space manipulator, Holonomic loops.