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Power-to-weight ratio of actuators is extremely important for robots, particularly mobile robots. The combination of electric motor and speed reducer, which is the most common driving mechanism for robots, can utilize the motor in the area where its power output is high when the reduction ratio is appropriately designed relative to the load. However, in the case of applications in which the load significantly changes, the motor has to be operated in the area where its power output significantly drops. This problem has restricted the capability of mobile robots, especially biologically inspired robots. Therefore in this paper I focus on a continuously variable transmission (CVT). Crank-type CVTs, which have been used for robotic joints, have the major disadvantage of a limited range of motion due to the dead point of the crank. Thus, this paper proposes the Radial Crank-type CVT (RC-CVT), which overcomes this limit of range of motion by increasing the number of links driving the crank of the CVT. This RC-CVT holds promise as an efficient robotic joint as it can utilize ball screws. This paper shows the equations of kinematics and statics of the RC-CVT and also describes the design and test of the prototype. The application to a quadruped robot is also introduced.