“Brachistochrone”Effect of the Universal Cycloid Gear

The brachistochrone is a cycloid and is also a tautochrone. The evolute of the cycloid is still a cycloid. The study of the universal cycloidal gear found that,the tooth profile of the universal cycloid rack is at the high velocity region of the tautochrone. In the universal cycloidal gear,when the meshing line in the gear of all the teeth and gear of the rack are perfectly coincident with the same modulus,the extremely low controllable sliding rate of the performance can be deduced. The sliding ratio of universal cycloidal gear is 80% lower than the involute gear,it shows the superiority of the universal cycloidal gear.