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

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.

Copyright © 2007 by American Society of Mechanical Engineers
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Grahic Jump Location
Figure 1

Example of the derivate of a Bezier curve (25)

Grahic Jump Location
Figure 2

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

Grahic Jump Location
Figure 3

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

Grahic Jump Location
Figure 4

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



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