Abstract
A spherical gear is a mechanism for transferring motion. This type of gear has more than one direction of freedom, so it is very suitable for a flexible robot wrist. In general, spherical gear mechanisms have two degrees of freedom. Thus, from a geometric viewpoint, a mathematical derivation for producing a spherical gear with discrete ring-involute teeth is a conjugate problem. A rack-cutter that distributes ring teeth on a plane generates the spherical gear. Based on the envelope theory of a two-parameter family of rack-cutter surfaces, mathematical and geometric models of a spherical gear with discrete ring-involute teeth are proposed. Using CAD software, a geometric model of a spherical gear can be assembled. The developed spherical gear transmission has a gear ratio that is not 1, and an example is provided to demonstrate the double DOF transmission ratio of 4:3.
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