I need a drawing of a 41-sided polygon.

Factual Questions
21

Several more observations that come to mind.

A conmutator is circular, not polygonal. You want to divide a circle into 82 circular segments, 41 contact segments and 41 smaller insulation segments.

In any case vector graphics are ideal for this and it can easily be done with Inkscape or other vector graphics program.

Even if you are restricted to raster graphics it is trivial to calculate the coordinates in Excel and then take them to the plane.
An electrical motor or generator, in a very, very abstract sense, can have half the poles and be spun twice as fast but this is a bit like saying the motor in your car could have half the cylinders and turn twice as fast. Sort of conceptually true but in the real, practical world there are reasons why electric motors and generators are made with more poles and turn slower. And note that poles and windings are different things.
In a wave type winding the number of windings and the winding/segment pitch must be relative primes but this does not completely disallow even number of windings & segments. 40 windings-segments with pitch 19 would also work. As pitch 19 is prime any number of windings-segments would work with it but generally you see prime numbers of windings in wave configurations.

It’s been so many years since I studied all this that I have forgotten most of it already. :frowning:

22

Oops I meant 1 and 21, 2 and 22, 3 and 23,etc.

23

41 windings, pitch 20: 1, 21, 41, 20, 40, 19, 39, 18, 38, 17, 37, 16, 36, 15, 35, 14, 34, 13, 33, 12, 32, 11, 31, 10, 30, 9, 29, 8, 28, 7, 27, 6, 26, 5, 25, 4, 24, 3, 23, 2, 22, 1.

24

Wherein I demonstrate that I’m a theoretical physicist, and not an engineer. When it comes to practical matters like this, sometimes my guesses are wrong.

25

I notice

which is probably not coincidence. My guess is that windings = 2 x pitch +/- 1 is the most common arrangement and if I looked further into it I might find out a reason that makes it mandatory. For every two consecutive windings you advance or go back one position until you’ve gone around the clock.

As I said, I’ve already forgotten most of all this and it was not my major anyway. I specialized in electronics “small volts” and we used to make fun of the guys doing the “big volts” as old-fashioned stuff.