Here's my problem;

I have a belt drive grinder that is missing most or all of the pulleys;

The drive motor is 16,000 rpm

The speeds desired are: 42,600, 27,900, 23,400, 12,500, 10,600, 7,000, 5,375, 4,150 and 3,200

The manufacturer lists the following pulleys: .75, 1, 1.2, 2, 3, and 4. I have on the machine pulley #1 which is 0.875 diameter and #3 is 2.233 diameter

The combinations listed on the nameplate are:

driven rpm - drive : driven

42,600 #1.2 #4

27,900 #1 #2

23,400 #2 #3

12,250 #1.2 #1

10,600 #3 #2

7,000 #3 #1.2

5,375 #3 #1

4,150 #3 #.75

3,200 #4 #.75

What is required is the diameters of all of the pulleys given that 16000/(2.233/.875)=6270 instead of 5,375 it's possible that neither #1 and #3 are the correct sizes though #1 is probably correct.

It's been 50+ years since I took my college math so I'm not sure this is even the correct part of the forum to post the question, any help would be appreciated. As well as solving the problem, I'd like to know how it's done.