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i have two pulleys of known radii. i also have a belt of known length (radii). I need to find the distance between the two pulley centres so that the belt raps neatly around both pulleys.

I've had a go at it for a while now and the furthest i have come is:

1)

to make an equation that is not solvable (i have an angle inside and outside a cosinus function)

&

2)

to start the problem off with the distance between the pulleys being the sum of the radii then working out what the belt length should be for that distance, then subttracting this length from the actual belt length which gives me the length that is left over on the belt. However when i work backwards from here, substituting a new belt length between the pulleys using the leftover lengths i realise that the angles the tangents(belt) form on the pulleys also change and therefore my whole equation comes crashing down on itself.

so, how can i go about calculating this distance?

thanks,

wernher

edit: although this is not a homework question, i believe it falls under the criteria of a textbook type question. sorry for posting this here.

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# Distance between 2 pullies

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