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Journal for Geometry and Graphics 13 (2009), No. 1, 101--112
Copyright Heldermann Verlag 2009

Two Synthesis Methods for Non-Circular Cylindrical Gears

Gert F. Bär
Institute for Geometry, University of Technology, 01062 Dresden, Germany

Two synthesis methods for the design of non-circular cylindrical gears are presented here. One of the methods generalizes the use of n-lobed ellipses as pitch curves. It is shown that n-lobed hyperbolas and parabolas can be used as well as internal rolling n-lobed ellipses. The resulting transmission ratio is determined by the two lobe numbers of the gears and one real design parameter. The other synthesis method solves the following problem: Prescribed input and output functions of revolution of two planes rotating about two fixed points are given. Determine centrodes (pitch curves) which realize this motion between the two planes by rolling on each other. The general solution takes account of additional mechanical constraints.

Keywords: Mechanism, kinematics, non-circular gears, lobed conics, pitch curves, transmission.

MSC: 53A17

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