The Synthesis of an N-Lobe Noncircular Gear Using Bézier and B-Spline Nonparametric Curves in the Design of Its Displacement Law

Abstract

This paper presents a method for defining the relationship between the angular coordinates of N-lobe noncircular gear wheels using Bézier and B-spline nonparametric curves. After designing the displacement law, conjugate pitch curves are obtained using an analytical method that takes the driver angular coordinate as an input variable. With N-lobe noncircular gears, the number of speed cycles per revolution can be increased. In addition, N-lobe noncircular gears are well balanced because they rotate around their geometric center. Bézier nonparametric curves and B-spline nonparametric curves are used to obtain the displacement laws of an N-lobe noncircular gear. Using these functions, an N-lobe noncircular gear that satisfies a given relationship between the rotation angles of the driving and driven wheels can be designed or a given transmission ratio can be obtained.