Backlash free rotary table

[Zoidberg]

Thats for one stage. When you use 2 stages you just can't multiply the ratios directly, you must take in account for the difference in lobes in the stages somehow! Epicyclic differential or something like that

[PEU]

I have a new questions

if one were capable of cutting these hypocycloids to the best tolerances, say for example cut them with wire edm or better, what would be the tolerances needed to be kept between the cam and the pins? 0.01mm (0.0004")? less?

What determines the play/backslash?

If you machine to the closest tolerances, a lubricating film would help or bind the mechanism?

The little grasshopper wants to know


[edit] Interesting video: http://www.smcyclo.com/modules.php?name=Pages&sp_id=277

[NEATman]

That is a interesting video. I especially like the part how the pins on the output shaft were captured between the holes in the two rotors.

Keith

[PEU]

my 100:1 reducer, sorry for the crappy vid

"http://www.youtube.com/watch?v=vvIyG6DhlZE"]YouTube - Reductor Hipocicloidal


Pablo

[BillTodd]

Nice work Pablo

sorry for the crappy vid

The video was good

[ZincBoy]

Nice work Pablo! Glad to see the reducer working well for you. The video is great.

The formula for working out the final drive ratio is as follows:

1 stage:
ratio1=(#lobes1 - #pins1)/#lobes1
Note: the negative value indicating that the output motion will be reversed vs the input

Now, when you add the second stage, you do not use the same formula as the differential nature modifies it.

2nd stage formula:
ratio2=(#lobes2 - #pins2)/#pins2
Notice the division by the number of pins, not the number of lobes.

Total Ratio = ratio1*ratio2

In drives that have #pins-#lobes=1 for both stages, the final ratio can be simplified to be:
ratio=1/(#lobes1*#pins2)

Also, this does not work if #lobes1=#lobes2 as there is no differential action.

So as long as your desired ratio can be factored in at least two, you can create it with two stages. This does explain the observed behavior in my design, so it is at least true for #lobes1=#pins2=10. I used the paper here on hypocycloidal friction drives to work out the details.

As to the question of how little clearance is required between the cam and the pins, it depends on the construction of the reducer. There seem to be two types of commercial reducers. One type that uses preloaded rollers as cam follower. The other has a series of offset cams that run against solid pins (as my and Pablo's designs do).

For the preloaded roller design, there is no clearance required (in fact it should be slightly negative).

For the solid pin designs, the commercial units seem to have two or three cam plates operating out of phase from each other on separate eccentric centers. I would surmise that this is to allow preload of the cam plates against the pins while still allowing enough clearance to allow them to rotate.

I also found an interesting paper on the modification of the cam for optimum performance in the solid pin version. It involves modifying the cam so that the peaks and valleys will not contact the pins. This is done to avoid the portions of the cam that simply add friction and do not contribute to motion (pressure angle is not favorable). The paper is here. The translation is not great, but the math is fine.

Forgot to add the picture of the single stage reducer I built before I developed the cam generation script. It works somewhat, but it is "sticky" due to the non-optimal lobe shape.

[Zoidberg]

Thanks for the correct formula! Now my program almost works as i want. Need to fix so i get negative ratios for the reversing combinations! Do you know how to calculate the direction of the output correctly?

[ZincBoy]

Thanks for the correct formula! Now my program almost works as i want. Need to fix so i get negative ratios for the reversing combinations! Do you know how to calculate the direction of the output correctly?

To the best of my knowledge, a single stage will always be reversing and two stages non-reversing. The sign of the ratio result of the formula indicates the direction (-ve for reversing).

[PEU]

I wonder how these reducers, the ones shown with holes in the Sumitomo video, are made, they also look cool to make on our cnc mills

I have to find some acrilyc blocks, these hypocycloidal reducers would look supercool if one is able to see the inner action thru transparent acrylic.


Pablo

[ZincBoy]

I wonder how these reducers, the ones shown with holes in the Sumitomo video, are made, they also look cool to make on our cnc mills

I have to find some acrilyc blocks, these hypocycloidal reducers would look supercool if one is able to see the inner action thru transparent acrylic.


Pablo

Hi Pablo,

Here are some pictures of the first cycloidal reducer I machined. It is a single stage, 20:1 reduction and very similar to the Sumitomo ones. Well, conceptually anyway... This was before I created the script to generate the cam profile and was trying to interpolate it. Since the cam profile is not perfect, it is sticky when rotating it and I never finished the input section.

I was actually thinking about making a clear output stage for my 100:1, but I probably will get distracted by something else first

[PEU]

As I asked about the 1st reducer I ask for this one again, can you show us how its assembled? Last pic confuses me. How does it work?

after you posted this the other day:

For the solid pin designs, the commercial units seem to have two or three cam plates operating out of phase from each other on separate eccentric centers. I would surmise that this is to allow preload of the cam plates against the pins while still allowing enough clearance to allow them to rotate.

I wondered how the balancing would be done, I mean stabilizing and not reducing using extra cams, I tested my reducer attached to my lathe and it wobbled considerably

Thanks!

[ZincBoy]

As I asked about the 1st reducer I ask for this one again, can you show us how its assembled? Last pic confuses me. How does it work?

after you posted this the other day:

In the first image from left to right you see the housing (ring gear), the cam (disk) with the holes, and the slow speed output with the drive pins. The eccentric shaft would drive the bearing in the cam and causes the precession that would be coupled to the slow speed output.

In the second image, you see the slow speed output inserted in the housing.

The last image shows the cam assembled and engaging both the housing and the slow speed output.

Unfortunately, I can't make a video of this one in motion as it does not move smoothly without a fair bit of force. Getting the cam profile correct using the script was the breakthrough that made this work in the dual stage design.

The page at Darali Drives does a good job of explaining how it works

I wondered how the balancing would be done, I mean stabilizing and not reducing using extra cams, I tested my reducer attached to my lathe and it wobbled considerably

Thanks!

Zoidberg showed some good designs where the cam was counter balanced. To make this work, you have to calculate the mass of the eccentric shaft, bearing, and cam. To balance this out, you will need a weight that has a center of gravity and mass equal to the aforementioned. Place the weight at 180 degrees and your balance issues are solved. Ideally you would machine pockets into the cam and insert lead weights to balance the system. Or for a heavy cam, lightening pockets into the heavy side of the cam. This would avoid the bending moments on the eccentric shaft that would otherwise occur.

The dual (or n) cam design solves the balance issue by placing identical cams at 180deg (or 360/n) spacings. That way you get the advantage of a balanced system as well as more (usefully) engaged pins resulting in increased shock loading. One thing to note is that the multi cam systems only work for the single stage design (at least as far as I have figured out). The reason for this is that the slow speed drive pins engage all cams.

If your eccentric shaft is not dead on, then any difference between the shaft offset and the cam/pin offset will result in "wobble". When I machined my eccentric shaft, I thought that holding a 0.001" tolerance was enough. I was wrong. There are definite areas of binding in my 100:1 reducer due to not getting the shaft right. The workaround to this seems to be creating an eccentric bearing with a concentric shaft through the whole works. Part of the problem is that my Taig is quite happy to deliver sub 0.001" tolerances, while my manual work on the lathe isn't quite up to par

[Zoidberg]

To the best of my knowledge, a single stage will always be reversing and two stages non-reversing. The sign of the ratio result of the formula indicates the direction (-ve for reversing).

Not sure about that! Have to do some simulations and find out

[LaRdA]

Now i tested to machine the reducer Zoidberg draw for me and it works.

"http://www.youtube.com/watch?v=cnJCWX2nr4M&fmt=22"]YouTube - hypocycloid reducer

[PEU]

Very nice machining work, is that steel or alu?

I plan to machine one in alu this week, did you had to polish the surfaces after machining or it worked right away?

cool !

[LaRdA]

Thanks, its steel and it worked without polishing.

[skmetal7]

that is very nice machining! good job! do you know what type of steel it is? i can see some chatter marks in your stator, but it looks like the rotor doesnt come in contact in those areas. rotor looks nice and smooth. what were your tolerances? looks like a tight fit.

oh yea, nice pics too!

[NEATman]

There has been some discussion about making a cycloidal reducer with a transparent output stage to display.

I was just thinking that it would make for a very cool clock mechanism. If I am doing the math correctly, to get 60:1, you would need 10 lobes and 9 pins on the first stage (10:1), and 7 lobes and 6 pins (6:1) on the second stage to get you 60:1.

If the eccentric shaft extends through the center of the reducer, it could mount the minute hand, while the 60:1 output could mount the hour hand. Has anyone seen a clock like this before?

Also, very cool prototypes - I'll have to free up some shop time to make one.

Keith

[PEU]

I need some help machining a cam. I want to try to machine the reducer designed by zoidberg (different ratio, same cam eccentricity) but I don't know how to properly machine the eccentric bushing.

From a previous attempt with 2mm eccentricity, my idea was to add a 2mm supplement to one of the jaws of my 3-jaw autocentering chuck and end up with the piece I wanted.
Well, after I machined both sides to the required diameter, the resulting cam wasnt 2mm but something closer to 1.2mm.

So my question is, how does one calculate the amount of offset needed to supplement a jaw to do a certain cam or eccentric?

Thanks!

[Zoidberg]

why dont turn it a bit oversize.. then mill the outside and then drill the hole for the axle.. then you should be pretty close