Summary: This paper considers a solution to the problem of moving a robot manipulator with minimum cost along a specified geometric path. The optimal traveling time and the minimum mechanical energy of the actuators are considered together to build a multi-objective function and the results depend on the associated weighting factors. The optimization problem is subject to physical constraints. The mathematical model takes into account the manipulator nonlinear coupled equations of motion. Numerical results for manipulator arms with three and six degrees of freedom are presented.