Application of Sequential Quadratic Programming for a Compact Spherical Speed Reducer that Decelerates Uniformly Independent on Rotation Axis and Investigation of the Validity of the Optimal Solution

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