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.
