Cycloid Mechanism Understanding

[danmauch]

I made a hypocycloid 2 stage gear assembly. The inner cage has 11 pins and the cam has 10. The output stage has 6 pins on the output ring and the cam has 5 teeth. My understanding of the output ratio is that  the number of teeth on the inner cam times the number of teeth on the output cam is the ratio. Thus I should have a 50/1 ratio. However this is where I am stumped because when I rotate the input shaft 12 times the output ring turns once. Where am I going wrong?
Here is a picture of the assembly.

Dan Mauch

[ArtF]

Dan:

The actual formula is r = (Pins - Lobes) / Lobes for each stage..

so your first stage is 11 outside pins, 10 inside lobes = (11-10)/10 = 1/10 = 10:1
Second stage is        6  outside pins,  5 nside lobes = ( 6-5) / 5 = 1/5 = 5:1

  So I also get 50:1 using your numbers. Ive never actually made one and I cant see
from the photo how yours works, Ill do some research..

Art
               

[danmauch]

This really got me stumped. I just made a new output cam and cage. The inner cage and cam are the same. The new outer cam has 9 teeth and the cage has 10. Now that should be 100 to 1 ratio. When I rotate the drive shaft 100 turns I get a 1 rev of the output cage just like it should so arrrgggghhhh why does the 5 tooth cam only give me give me 50 /1?

Dan Mauch

[ArtF]

Dan:

  The annoyin thing is I know the answer, Ive simply forgotten it, I had to research this once before, was surprised at the answer and have forgotten it since. I'll keep dwelling on it. :)

Art

[ArtF]

lol.. I remember now. There is a formula for how the ratio's accumulate. Its

end ratio = (b+1) / ( b - a) where

a = 1st stage ratio and b = second stage. You have a 1/10 as first, and a 1/5 as second so

ER = ( 1/5 + 1) / ( 1/5 - 1/10) = 1.2 / .1 = 12:1

If stages are evenly numbered you can simply multiply them.. eg: 1/10 x 1/10 = 1/100


Art

[danmauch]

Thank you, thank you. That makes perfect sense. I was starting to think the laws of phyics where conspiring against me.
dan mauch

[ArtF]

lol..thats how I felt originally
Art