TIP: Formula for rubber drive band path length

[N_Cook]

ie the stretched length where it is too restricted to pass a thread around
to measure. Or to measure without taking apart a worker, to obtain a spare,
before having to take apart to replace. Using callipers, pair of rods and
ruler or whatever to take measurements of diameters and so radii and gap,
templates, whatever intrusions will allow.

2 pulleys , small diameter "a" and big diameter b and gap between the 2
pulleys c.
So distance between pulley centres is a +b +c
Straight belt section between the two pulley rims (doubley tangential) is x
N is the angle, in degrees, between the line-of-centres and the b radius to
the tangent point of the large pulley. Also the angle between this extended
line and the radius a of the small pulley.

Parallelogram with parallel sides a, b and the other two sides x and (a+b+c)
and two right angles.
So reducing the parallelogram by lenghth "a" down to a right angle triangle
of lengths x, b, (a+b+c) and N between b and (a+b+c)

x = sqrt [(a+b+c)^2 - (b-a)^2]

and N= cos(-1) [ (b-a)/(a+b+c)]

Then band length = 2x + 2*Pi*a (2N/360) + 2*Pi*b[1 - (2N/360)]

Confirmed practically in one case anyway

 

[N_Cook]

confirmed, my error , a+b+c beween centres is correct, a and b are radii.
I edited , incompletely, from diameters to radii, also the word radius gauge
templates should have been inserted after the word ruler