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There are a number of trajectory planning algorithms which generate the joint torques/forces required to drive a robot along a given geometric path in minimum or near-minimum time [1, 3, 5, 6, 7, 9]. These methods make fairly specific assumptions about the form of the joint torque/force constraints, thereby limiting their applicability. A method, called the perturbation trajectory improvement algorithm (PTIA), is developed here which can generate the joint positions, velocities, and torques required to move a robot along a specified geometric path in minimum time under very general torque constraints. The PTIA starts with a non-optimal trajectory which meets all the required torque constraints, and perturbs the trajectory in such a way as to always decrease the traversal time for the path. This perturbation process continues until the torque constraints prevent any further improvement in the traversal time. The torque constraints may be expressed in terms of quantities related to torque rather than torque itself; it is possible, for example, to limit velocity, acceleration, jerk, and motor voltage, either singly or in combination. The perturbation trajectory planner also is very simple to implement, and many of the calculations are independent of each other and can therefore be done in parallel, As a demonstrative example, the PTIA is applied to the first three joints of the Bendix PACS Arm.