General Spatial Involute Gearing

It has been hard for me to escape the imprint of my early, strong, but scattered trains of thought. There was, at the beginning, little to go by; and I saw no clear way to go. This book is accordingly filled with internal tensions that are not, as yet, fully annealed. Subsequent writers may re-present the work, explaining it in a simpler way. Others may simply invert it. I mean by this that, by writing it backwards, from its found ends {practical machinable teeth) to its tentative beginnings (dimly perceived geometrical notions), one might conceivably write a manual, not on how to understand these kinds of gears, but on how to make them. Indeed a manual will need to be written. If this gearing is to be further investigated, evaluated and checked for applicability, prototypes will need to be made. I wish to say again however that my somewhat convoluted way of presenting these early ideas has been inevitable. It has simply not been possible to present a tidy set of explanations and rules without exploring first (and in a somewhat backwards-going direction) the complexities of the kinematic geometry. There remains, now in this book, a putting together of primitive geometric intuition, computer aided exploration of certain areas, geometric explanations of the discovered phenomena, and a loose sprinkling of a relevant algebra cementing the parts together.

Prologue. - Synopsis. - One Basic Kinematics of the Gear Set. - Two The Fundamental Law of Gearing. - Three Mating Involute Helicoids. - Four Key Aspects of the Geometry. - Five (A) The Simplicity of Equiangularity. - Five (B) Synthesising an Equiangular Set. - Six The Plain Polyangular Option. - Seven Worm Drives Offset and Non-Offset. - Eight Exoticism by Accident or Design. - Nine (A) Helicality Tight Mesh and Backlash. - Nine (B) Mechanics of the Phantom Rack. - Ten Mathematics of the Machining. - 11 Aspects of the Physical Reality. - 12 The Screw Systems and Gear Design. - Table of Numerical Results. - Notes and References. - Symbols Index Including List of Acronyms Subjects and Authors Index Alphabetical.