A computational technique for obtaining minimum-time trajectories for robot manipulators is described in this paper. In the analysis, limitations to link movements due to design constraints are taken into consideration. Numerical examples based on a two-link planar robot arm shows the feasibility of the technique proposed. A physical explanation for the general characteristics of the observed trajectories is also presented. The importance of appreciating optimal control issues in designing robot manipulators and in planning robot workstation layouts is emphasised.