To provide a transmission gear of driving torque with which the transmission of torque is released at an arbitary value of set torque against overload torque and to provide driving device for rolling mills.

Tangential load is imparted between rollers by pressing an input roller 10A and output roller 10B against each other, and the torque is transmitted from the input roller to the output roller by the frictional force based on this tangential load. The output roller 10B is supported by a support arm 13A and has the degree of freedom in the direction of tangential force. On the support arm 13A, by making the holding force Fh act onto the tangential force Ft generated by the transmitted torque of the roller, the output roller 10B is held in the direction of the tangential force.