Synopsis

Abstract

In gear sets the acronym CDL stands for the centre distance line; this is the line of the shortest distance between the axes of the two rotating shafts. All gears sets of whatever kind include not only those whose axes are skew, but also those wherein the zone of the meshing is remote from the CDL. Chapter 1 deals with those parts of gear theory that apply to all gears of whatever kind. It isolates the main kinematic parameters and relates these with one another. They are C the centre distance namely the shortest distance between the axes of the two rotating shafts, Σ the angle between the said axes, k the angular velocity ratio (k being less than unity), and, derived from these, p the pitch at the pitch line. The pitch line (the axis about which each wheel screws with respect to the other) is explained and located; this line cuts the CDL perpendicularly and thus lies in a plane parallel with the unique pair of parallel planes that contain the two shaft axes. The magnitude of p (mm/rad) is worked out and presented algebraically. Both the pitch line and its pitch are openly held to be (and later shown to be) of fundamental importance in design. The offset, which is roughly speaking the radial distance from the CDL to the zone of the meshing, lacks a precise definition at this early stage. It is, however, not yet relevant.