In recent years, cable-driven revolute joints have been successfully applied in various robotic fields. However, two major concerns remain unsolved. (i) The pull-only characteristic of cable requires additional actuators or a passive low-bandwidth resetting mechanism for bidirectional rotation. (ii) The actuation performance is constrained by the nonlinear relationship between the rotations of the revolute joint and the motor. This paper proposes a general actuation mechanism for a large group of cable-driven revolute joints of various shapes and sizes. A pulley with two separate non-circular tracks, which can retract and release two-side cables simultaneously and independently, is designed to achieve high-bandwidth bidirectional rotation with only one motor while creating a linear relationship between the joint and motor rotations. The profile of the pulley track is depicted with differential equations and the calculation process facilitates revolute joints of various symmetric or asymmetric configurations. The design is verified by the simulation with a numerical example of real-world parameters. Results show the advantages of the proposed mechanism in contrast with the conventional pulley with a circular track profile on both concerns. This mechanism can potentially enlarge the application of cable-driven revolute joints with space and payload limitations, in addition to the requirements of highly dynamic performance.