Gear Geometry and Applied Theory, Second Edtion
An invaluable reference for designers, theoreticians, students, and manufacturers, this text covers the theory, design, geometry, and manufacture of all types of gears and gear drives.
TABLE OF CONTENTS Gear Geometry and Applied Theory, Second Edtion
Chapter 6: Conjugated Surfaces and Curves
6.1 ENVELOPE TO A FAMILY OF SURFACES: NECESSARY CONDITIONS OF EXISTENCE
Introduction
Consider coordinate systems S 1, S 2, and S f that are rigidly connected to gears 1, 2, and frame f (gear housing), respectively. Gear 1 is provided with a regular surface ? 1 that is represented in S 1 as follows:
The gears must transform prescribed motions (say, rotations about crossed axes) and stay in line contact at every instant. The location and orientation of gear axes and function 
( 
) are given. Here, and are the angles of rotation of the driven and driving gears. The required type of contact of gear tooth surfaces (at a line at every instant) can be provided if the tooth surface of gear 2 is determined as the envelope to the family of surfaces, 
, that is generated in S 2 by surface ? 1.
The theory of enveloping is represented in differential geometry by Favard [1957] and Zalgaller [1975], and in the theory of gearing by Litvin [1968, 1989, 1994] and Sheveleva [1999].
Henceforth, we consider the necessary and sufficient conditions of existence of ? 2. The necessary conditions of existence of ? 2 provide that ? 2 (if it exists) is in tangency with ? 1. The sufficient conditions of existence of ? 2 provide that ? 2 is indeed in tangency with ? 1 and...
Copyright Faydor L. Litvin and Alfonso Fuentes 2004 under license agreement with Books24x7
