Here is some history that bears repeating - or at least re-reading. So take a few minutes to give it up for a long-gone Brit named Henry Maudslay
(August 22, 1771 - February 14, 1831) - also known as "A Founding Father of Machine Tool Technology." You might
also consider him an early leader in inspection, as he also invented the first bench micrometer capable of measuring to one ten-thousandth of an inch.
This paper presents the geometric design of hypoid gears with involute gear teeth. An
overview of face cutting techniques prevalent in hypoid gear fabrication is presented. Next,
the specification of a planar involute rack is reviewed. This rack is used to define a variable
diameter cutter based upon a system of cylindroidal coordinates; thus, a cursory presentation
of cylindroidal coordinates is included. A mapping transforms the planar involute rack into a variable diameter cutter using the cylindroidal coordinates. Hypoid gears are based on the envelope of this cutter. A hypoid gear set is presented based on an automotive rear axle.
In 1964, a young and tidy Bob Dylan sang away in that infamous voice of his,
all nasally and grating yet wonderfully distinct, opining to the fervent masses: “The times, they are a-changin.”