Planetary Mechanism Bevel Gears

[dbeckam]

Homework Statement

The toothed bevel wheel 1, which rotates about the fixed axis A, is in mesh with the bevel planet gears 2 rigidly connected to the bevel planet gears 4. The planet gears 2 and 4 form a rotational pair with the driving element 6 which rotates about the fixed axis B. The satellite pinion 2 is meshed with the fixed gear wheel 3; the satellite pinion 4 is meshed with the conical toothed wheel 5 that rotates around the fixed axis B. The numbers of revolutions per minute n1, of wheel 1 and n5, of wheel 5 are related by the condition:

Relevant Equations

Thank you very much for the help.

 

[Baluncore]

Interesting, but do you have a question ?

 

[dbeckam]

Interesting, but do you have a question ?

I tried to demonstrate it and got the same expression but with -z2*z5 + z3*z4 instead of z3*z4+z2*z5. So my question is how to prove that relationship.