Control moment gyros (CMGs) are an energy-efficient means of reactionless actuation currently used for attitude control in some spacecraft. In this work, CMGs are compared to direct-drive actuation for robotic applications. Torque, power, and energy of the gimbal motor are calculated using principles of angular momentum and virtual power. Scissored-pair CMGs produce output torque along the joint axis, facilitating comparison with joint motors. A mechanical coupling enforcing scissored-pair symmetry eliminates undesirable gyroscopic reaction torques and accompanying power costs while simplifying analysis. Strictly controlling CMG rotor speed doubles the CMGs? energy costs, whereas implementing minimal rotor speed control while assuming constant rotor speed reduces the energy costs without compromising the analyses. A single-link robot actuated with scissored-pair CMGs uses the same energy as direct drive for a large range of gimbal inertias and maximum gimbal angles. The transverse rate of the robot base does not affect this result if angular momentum is conserved about the joint axis. The equations of motion for an n-link robot with CMGs are presented in a recursive form. A two-link robot with orthogonal joint axes and axisymmetric bodies reduces to two, independent, single-link robots. In contrast, a two-link robot with parallel joint axes favors CMGs when the joints rotate with opposite sign, e.g. reaching motions. Direct drive is preferred when the joints act in unison, e.g. throwing motions. Conceptually, CMGs and direct drive may be analyzed as idealized body and joint torques, respectively. The mappings from actuator torques and velocities to generalized torques and velocities explain differences in power cost between the two actuation methods. A proposed power-optimal robot includes both types of actuation. The optimal distribution of joint and body torques for two- and three-link planar robots is calculated and applied to a three-link robot tracing a closed triangle. The combined actuation method easily outperforms the others in a Monte Carlo simulation. A planar robot with joint motors and CMGs currently in development illustrates the design of a CMG-actuated robot.