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TECHNICAL BRIEFS

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

[+] Author and Article Information
Héctor Fabio Quintero Riaza

Mechanical Engineering Faculty, Universidad Tecnológica de Pereira, Pereira, Columbiahquinte@utp.edu.co

Salvador Cardona Foix, Lluïsa Jordi Nebot

Mechanical Engineering Department, Universitat Politècnica de Catalunya, Barcelona, Spain

J. Mech. Des 129(9), 981-985 (Sep 18, 2006) (5 pages) doi:10.1115/1.2748453 History: Received June 09, 2006; Revised September 18, 2006

## 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.

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## Figures

Figure 1

Example of the derivate of a Bezier curve (25)

Figure 2

Design of N-lobe noncircular gear using Bezier curves as displacement law

Figure 3

Example of the derivate of a B-spline curve [28]

Figure 4

Design of N-lobe noncircular gear using B-spline curves as displacement law

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