Calculating Gear Teeth: Finding Unknowns and PCD | Homework Help

[Rastanking]

Homework Statement

I wonder if anyone can point me in the right direction as to where to start with this problem. There are 3 gears

A sun gear which is in the centre with 45 teeth, pitch 15mm and revolves at 63rpm CW

This drives an arm which connects the sun gear to a planet gear, the arm rotates at 9rpm CW

The planet gear, teeth unknown, speed unknown

The ring gear rotates at 21rpm ACW, teeth unknown.

The question asks us to find number of teeth for the planet and ring gear and the PCD of the ring gear.

I know that the teeth of the ring = 2 x teeth of the planet + teeth of the sun but how do I find out that when there are 2 unknowns?

Any help would be appreciated

Thanks in advance

Homework Equations

The Attempt at a Solution

I've attempted to calculate the gear ratios between the sun and the ring gear which works out at 1:3 and the gear ratio of the sun to arm which works out at 1:7

From there I am a bit lost as to what to do next

 

[Valkarie]

. Is there some way of using these gear ratios to find out the number of teeth for the planet and ring gear?