Abstract: The single-gimbal control moment gyroscope (SCMG), which is widely used in aerospace field, has the advantage of torque amplification effect. It is based on the principle of torque amplification with some hypotheses. In this paper, the output characteristics of SCMG are analyzed without those hypotheses. By considering the motion of the mounting base, the output torque model of SCMG with a two-dimensional input and three-dimensional output is obtained, in which the adjustable and nonadjustable parts are identified. In order to analyze the output characteristics of SCMG, two parameters are defined. One is the ratio of the norms about the SCMG's output to input torque vectors. The other is the ratio of the norm about the SCMG's used and unused torque vector, which is to represent the utilization ratio of the SCMG's output torque. In all feasible regions, the results show that the characteristic parameters of torque output are is not always greater than 1, i.e., SCMG does not always has torque amplification effect and efficient torque utilization, which are closely related to the state of SCMG. Finally, for the spacecraft attitude maneuver task with two SCMGs, the simulation of non-diagonal singular robust control and optimal control is completed. It is found that the control effect is closely related to the output characteristic parameters which are determined by the system state. At the same time, the optimal control with a SCMG is used to realize the three-dimensional attitude maneuver of a spacecraft based on the three-dimensional output characteristics of SCMG. The simulation results show that the SCMG always has the torque amplification effect and the efficient torque utilization in the process of optimal control.