The Plain Polyangular Option

Abstract

On looking again at chapter 22 in [1] one sees that I was dealing there with non-offset meshing. I was dealing, in other words, exclusively with the crossed helicals. There is no mention of doubly departed sheets in [1]; neither is there of offset. Until the appearance of the fundamental law and its generally applicable ramifications became clear, however, it was not easy to make progress. But the said law has now appeared [14], and I have, thereby, been able to devise in this book (for comfort) a circumscribed, first approach to the otherwise chaotic scene of general spatial involute gearing. I described that first approach in chapter 5A, introducing there the term equiangularity. At WkEx#1 I took the case of a modest, non-extreme, somewhat special, but openly practical gear set exhibiting equiangularity. Find the data at §5B.01: Σ was only 50° (the set being thereby oblique); k was only 3/5; and the work began at §5B.09. At WkEx#2 a more confronting case was taken. Find the data at §5B.45. I found there some workable teeth for another equiangular set. Angle Σ was 90° (the set being thereby square), and k was a somewhat demanding 9/41. Recall the difficulties encountered in choosing the angles δ; these were overcome by using the newly discovered ellipses of obliquity.