Inscribed-type spherical speed reducer with uniform reduction ratio in all directions

A spherical motor is an actuator that can generate rotational motion about all three orthogonal axes. However, it is difficult to obtain high output torque from most electromagnetic spherical motors, primarily due to limitations inherent in electromagnetic actuators, such as restricted magnetic force and thermal constraints. Since its torque cannot be increased using planar gears, spherical speed reducers that transmit rotational torque along three orthogonal axes through sphere-to-sphere contact are required. One major limitation of conventional spherical speed reducers is that their size increases significantly as the reduction ratio becomes higher. To address this issue, we propose a novel inscribed-type spherical speed reducer, in which the deceleration mechanism is integrated within the output sphere. This configuration enables a more compact design, reducing the overall size to approximately half that of conventional designs. To predict the angular velocity and transmitted torque, theoretical models for the rotation and torque transmission of the speed reducer were developed. According to the proposed model, the reduction ratio of the spherical speed reducer is 1/3. To verify the validity of these models, experiments were conducted to measure angular velocity and torque. The theoretical results agreed well with the experimental results. In addition, the theoretical torque exhibited an average relative error of 1.63 % compared to the experimental result. Therefore, it was confirmed that the rotation and torque transmission models were valid. These results demonstrate that a reduction ratio can be obtained in all directions of the 3-DOF of the spherical speed reducer, unlike conventional 1-DOF reducers.