It is important to minimize the energy dissipated by the reduction gears and motors in a three-jointed vertically articulated manipulator. This paper proposes an optimal design method for simultaneously determining eight design variables, which are three motor masses, three reduction gear ratios, a counterbalancer mass for the third link and an offset between the first and the second links. Using these design variables, the equation of motion and the dissipated energy can be expressed as functions of the moment of inertia and the Coulomb friction torque of the joints and the inertia matrix of the manipulator. Optimal design variables can be determined by minimizing the dissipated energy under the constraint conditions for the motors and the offset. The numbers of stages for the reduction gear trains are determined from the optimal gear ratios. Simulations show that the proposed design method can reduce the dissipated energy more effectively than the inertia matching method.