Abstract
In order to construct a system with multiple-degrees-of-freedom by using the motors with one degree of freedom, the same number of motors as the degree of freedom is necessary. On the other hand, because a spherical motor has three degrees of freedom, it is possible to realize a system with three degrees of freedom by one spherical motor and, therefore, it can reduce the size of the system. A spherical speed reducer is necessary to increase the output torque for a multiple-degrees-of-freedom system. We proposed a spherical speed reducer capable of decelerating in the same ratio independent on the rotation axis and demonstrated its applicability by speed reducing experiments using a prototype speed reducer. However, when the reduction ratio becomes large, the entire mechanism of the speed reducer will become large. In this study, we have investigated the optimization of the sphere arrangement so that the entire mechanism can be made as small as possible. This paper applies a discrimination method using Hesse matrix to identify a convex region for applying the sequential quadratic programming method that can be applied only for a convex region of objective function. This paper shows some optimization results using the sequential quadratic programming method and the arrangements of spheres corresponding to the optimization results.
