Page 592 - Dynamics of Mechanical Systems

0593_C17_fm Page 573 Tuesday, May 7, 2002 7:12 AM

17

Mechanical Components: Gears

17.1 Introduction
As with cams, gears and gearing systems are fundamental mechanical components.
Indeed, in the design of machines and mechanical systems, gears are even more common
than cams. Gears are perhaps the most common of all mechanical components. From
another perspective, however, gears may be viewed as special kinds of cams. Gears and
gearing systems have two purposes: (1) to transmit motion, and (2) to transmit forces
during that motion. Hence, gearing systems are often called transmissions.
Gear design is a very old subject dating back to antiquity with the use of cog-type
devices as early as 330 BC or earlier [17.6]. Numerous books, monographs, articles, and
research reports have been written about gears. (The references at the end of the chapter
represent a small sampling of writings that could be of interest and use for further study.)
In recent years, the technical literature has grown dramatically as a result of increased
numbers of research efforts stimulated by a quest to obtain higher precision, stronger,
more efficient, and longer-lived gearing systems.
The large body of information and knowledge about gears cannot be fully documented
or even summarized in a single book chapter, or for that matter even in a single volume.
Hence, in this chapter, we will simply attempt to summarize the most fundamental aspects
of gearing systems, with an emphasis on gear geometry and kinematics. We will not
discuss in any detail such topics as gear vibration, gear strength or deformation, or gear
wear and life. Readers interested in those subjects may want to consult the references.
We begin our discussion in the next section with a brief review of the fundamental
concepts of gearing and of conjugate action (uniform motion transmission). In subsequent
sections, we discuss gear tooth geometry, gear nomenclature, gearing kinematics, and gear
trains. Section 17.16 has a glossary of commonly used gearing terms.

17.2 Preliminary and Fundamental Concepts: Rolling Wheels
The transmission of motion and forces is commonly called power transmission. With gears,
power transmission almost always occurs between rotating shafts. For the most part, these
shafts are parallel (as with spur and helical gears), but they may also be intersecting (as
with bevel and spiral bevel gears) or even nonparallel and nonintersecting (as with hypoid
and worm gears). In the sequel, we will develop our analysis with parallel shaft gears
and specifically with spur gears. The analysis of other types of gears is fundamentally the
same but somewhat more detailed due to their more complex geometries.

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