Cycloid Mechanism Understanding

[BobL]

Hi Dan;

Sorry for the delay, but lately we've been having small issues with the forum's automatic notification system, so I'm assuming Art didn't see this post at all, and I would  prefer he answers you on this, so I'll make sure he is notified of it, hope he gets back to you soon.. 


Thanks
Bob
???

[ArtF]

Hi Dan:

  Ahh, I understand the confusion. ( Sorry for the delay, I didnt get notification as Bob suggested.)
 
  In the spur screen, there is a choice for EPI gears, however, though such gears are called EPICycloidal
gears, they dont actually follow the math as youd expect, they instead represent the clockmakers EpiCycloidals
which are based solely on Epicycloidals generated by a specific radius ,( 1/2 of the mate's radius), this means
they always have a straight root. Good for the clockmakers, but not configurable to what youd expect as you wont get
anything other than a straight edged hypocycloidal inside. In future these types of Epi's will get further restricted
to the gears in the swiss clockmaking standard which are actually circular arc representations of epi's. In other
words the epi's on the spur page are clockmakers gears not really the math forms of epi/hypos as you need for such
speed reducers.

  Your right though, the cage gears ARE the same type of curves. You dont really have to modify the pin, they would
  work as the reducers do in any pin size. What you typically see in reducers are a third for of the epi/hypo gear sets
  where the pin size and outside curves are modified to match what a paper out there refers to as the most efficient form
  of hypocycloidics to reduce friction.
 
  Id use the pins as the outside ring. You actually then just cut a circle and put in half pins. The hypo's GM makes to
  match should then work fine to make speed reducers as the ones on this thread.
 
  So you can use the cage gears to get the forms now, but in future Ill be giving you better ways to make them as well
    as including the math of the third form as well.

Art

[danmauch]

Thank you, Thank you. I  I was going nuts trying to make the spur gear epi/cyc look like a hypocycloid gear. Your reply really confirms my conclusions about latern gears.
Thanks
Dan Mauch

[ArtF]

:) .. When I first started doing this, I figured.."Hey, how much can there be to know..its only gears.." lol

There is an unending supply of little tidbits to know about gears... and Im still learning everyday. 

Art

[danmauch]

Yesterday I laser cut a 10/1 ratio lantern and pin  gearset. The pinion has ten teeth and the cage 11 with a .68'D shaft ( the bearing was added just to see how things would rotate but will be removed on the next cut)and .5 pins. I modified the pins in my cad by 1/2. The picture shows the tooth profile but it doesn't look like the hypocloid shape that I have seen elsewhere.  It does rotate and seems to perform like a hypo  but would like your comments.
Dan Mauch

Hi Dan:

   Ahh, I understand the confusion. ( Sorry for the delay, I didnt get notification as Bob suggested.)
   
   In the spur screen, there is a choice for EPI gears, however, though such gears are called EPICycloidal
gears, they dont actually follow the math as youd expect, they instead represent the clockmakers EpiCycloidals
which are based solely on Epicycloidals generated by a specific radius ,( 1/2 of the mate's radius), this means
they always have a straight root. Good for the clockmakers, but not configurable to what youd expect as you wont get
anything other than a straight edged hypocycloidal inside. In future these types of Epi's will get further restricted
to the gears in the swiss clockmaking standard which are actually circular arc representations of epi's. In other
words the epi's on the spur page are clockmakers gears not really the math forms of epi/hypos as you need for such
speed reducers.

   Your right though, the cage gears ARE the same type of curves. You dont really have to modify the pin, they would
   work as the reducers do in any pin size. What you typically see in reducers are a third for of the epi/hypo gear sets
   where the pin size and outside curves are modified to match what a paper out there refers to as the most efficient form
   of hypocycloidics to reduce friction.
   
  Id use the pins as the outside ring. You actually then just cut a circle and put in half pins. The hypo's GM makes to
  match should then work fine to make speed reducers as the ones on this thread.
   
  So you can use the cage gears to get the forms now, but in future Ill be giving you better ways to make them as well
     as including the math of the third form as well.

Art

[ArtF]

Hi Dan:

  Probably work.. ( more than 1 way to skin a cat..), but hres the approach Id take.. It probably looks more normal to you.
I started with an internal lantern with 1 tooth difference.. ( you can use more for different ratios..). ( photo 1)
Then I cut the pins in half with a circle and removed their back side (photo 2), then joined each with semicircles that clear the gears lobes as in ( Photo3).

  As I say, there is a paper pubished ( Id have to find it) , that describes a modification of the equations for better
friction control which I hope to add in future..

Art

[danmauch]

Ahhh . I see you must have used a dp of 2, 3or 4 . I used a dp of 5 which explains why my gears did match what I thought they should.

Thanks


Dan

Hi Dan:

  Probably work.. ( more than 1 way to skin a cat..), but hres the approach Id take.. It probably looks more normal to you.
I started with an internal lantern with 1 tooth difference.. ( you can use more for different ratios..). ( photo 1)
Then I cut the pins in half with a circle and removed their back side (photo 2), then joined each with semicircles that clear the gears lobes as in ( Photo3).

  As I say, there is a paper pubished ( Id have to find it) , that describes a modification of the equations for better
friction control which I hope to add in future..

Art

[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