In redundant manipulation systems, the end-effector path does not completely determine the trajectories of all the individual degrees of freedom (dof) and the additional dofs can be used to enhance the performance in some sense. The paper deals with utilizing the redundancy to minimize energy consumption. A full linear electromechanical model is used, and the exact energy consumption is calculated. The optimization includes also displacement limits via penalty functions that are included in the cost function. The optimal trajectory is feasible in the sense that it can be obtained by a finite input voltage and all the velocities are continuous. The solution is based on projections that separate the system and the input into two parts. One that is completely determined by the end-effector path and the other that is free for optimization. The important and delicate issue of boundary conditions is resolved accordingly. Simulation results show that redundancy, even with limited joint motion, can lead to a considerable reduction in energy consumption.