In this paper, a direct method for obtaining the trajectory set points is investigated in discrete-time, which is different from the other conventional schemes. We consider the tracking of a straight line path, where the trajectory set points for manipulator control are determined exactly on the straight line path. For the purpose of the munimum-time operation of manipulators, the problem is formulated as a maximization of the Cartesian distance between two consecutive servo time instants. The maximization is subject to the smoothness and torque constraints. Several algorithms are developed and utilized to maximize the Cartesian distance. The proposed approach has been simulated on a VAX-11/780 computer to verify its performance.