Mathematical model and manufacturing of a human or a robotic knee joint

Abstract

This paper proposed two imaginary planar rack-cutters to create a spherical gear pair with ring-involute teeth. The spherical gear pair can be used to a knee joint mechanism. The imaginary planar rack cutter consists of two kinds of conical tooth. One is convex conical teeth to create a spherical gear with concave ring-involute teeth; the other is concave conical teeth to create a spherical gear with convex ring-involute teeth. Based on two-parameter envelope theory and coordinate transformation matrix, the planar rack cutter with concave teeth or convex teeth can derive the mathematical model of the spherical gears with convex teeth or concave teeth, respectively. Through the obtained mathematical model, a computer-aided software package and a 5-axis CNC machine, the real prototype of the spherical gear is manufactured. The real prototype of the spherical gear is used to replace knee joint mechanism of a skeleton.