Not sure where to start with this question so here goes. If anyone can help or direct me onto other resources I'd much appreciate it !!
My question relates to gearing and the development of their geometry with basic tools. In particular how an 18th century clockmaker by the name of John Harrison developed his distinct type of gearing known as Chordal Pitch. As the name suggests he based his geometry on a chord and used it to develop the pitch (distance between the teeth) of the driving gear and the pitch of the mating driven gear.
I'm sure he only had rudimentary tools to work with, so my question is: If you had to accurately scribe two mating gears with only a compass and rule how would you do it ? How would you accurately divide a circle to produce say 60 divisions, then assure the mating gear shares the same chord length (pitch) in a mating gear of say 8 divisions ?
My math/geometry is abysmal but I can generate the geometry easily using CAD by dividing a circle (driver) then generating a polygon (driven) from 1 division. I'm pretty sure he didn't have a PC so I'm just very curious if anyone can think of a method using basic tools.
Many thanks in advance.