[just george]

Hi everyone, I'm posting because you guys are the most mechanically minded people on the entire internet and I thought this would be an interesting puzzle. I am having big arguments about it with everyone, because everyone has a different theory.

I have 2 shafts on bearings that are parallel, with a timing pulley welded to each one, joined by a timing belt.

What I have to do is make one of the shafts, over the course of 360 degrees of rotation, change speed. It has to move very fast, then very slow, then very fast, then very slow.

So to repeat:

0-90 degrees: turn very fast
90-180 degrees: turn very slow
180-270 degrees: turn very fast
270-360/0 degrees: turn very slow.

So, what shape do the pulleys have to be to do that?

I think that I need one round pulley on one shaft, and one elliptical pulley on the other.

What do you guys think?

note to mods: if this is in the wrong spot, let me know. This isn't for a cnc machine, it's for a hobby, so I didn't know where to put it

[vegipete]

What does "very fast" and "very slow" mean? 105% and 95% of the input shaft? 200% and 50%?

As the 'ellipticalness' of the pulley increases, the center-to-center distance will vary more and more
during one rotation, to the point that a tensioner would be needed. Also, the speed variations will
be sinusoidal, not merely fast/slow.

[awerby]

This sounds like the action of a set of gears with an escapement mechanism like in a watch. You need to shift from one gear (slow) to another (fast) and back all within a single revolution. There are clockwork mechanisms like that, but if you're asking me, it can all be done easily with a stepper motor, without all the mechanical complications. Just program your motor to do all that speeding up and slowing down and save yourself the headache...

Andrew Werby
www.computersculpture.com

[dmalicky]

Good posts above. A pair of elliptical pulleys would be better, as the required belt length would be more or truly constant. A pair of elliptical gears gives the motion you want (start at 3:43, driver on left):
Mechanical Principles (1930) by Ralph Steiner [4min selection] - YouTube
So elliptical pulleys are likely to work, too. Some math/geometry on the ellipse tangents could show whether the belt length stays constant. If not, there is likely a pulley shape for constant belt length that could be derived. Eccentric pulleys might work, too.

Here's a cool one that does your motion at 2x speed (start at 0:10):
Unusual gears - YouTube
Or if "very slow" could be defined as "stopped", there are Geneva mechanisms like 0-0:10 in the last video.

And here's another clever one at half your speed:
Variable Speed Gears - YouTube

[just george]

You guys are champions - finally people who think like me

vegipete: when I say very fast and very slow, I mean something like a 1000% increase in speed so that shaft 2 turns 160 degrees. The more I think about it, the more I realize that while an elliptical gear would work, that an escape mechanism would be better, and another element added to the device.

awerby: I agree that a stepper would be better, but it has to be fully mechanical. You're right though - sensors attached to the axle to trigger the stepper so as to keep the movement in phase would be idea, but unneccessarily complicating. I might end up doing it, but...not yet.

Where do I find more info on escape mechanisms? Would it be possible to do that if the rotation speed is in excess of 500 rpm? How do these things work - springs or something?

dmaliky: thanks I downloaded all of those videos and will review.

If I ever design an engine or something, this is the place I'll come. Even the mech eng students I chatted to drove me nuts

[RICHARD ZASTROW]

just george, there's a 4 book set titled "Ingenious Mechanisms". Available from Industrial Press

Dick Z

[just george]

Thanks Richard, I'll hunt it down

So when I figure out the best way to do it, is it acceptable to forum moderators if I post a job in the classifieds section for someone to make the pieces and mail them to me? Is that commonplace around here? I could do it in Australia, but I'm tired of paying $140 per hour for someone to make something - everytime I modify my device, it costs me 2 weeks wages, and them a day

[just george]

I think I figured it out.

2 big cogs that are only partially toothed attached to Shaft 1 side by side. The cogs are aligned on Shaft 1 so that the toothy bits are on opposite ends.

2 small cogs that are 50% toothed mounted on Shaft 2, also so that teeth are on opposite sides.

For purposes of explanation, lets say that that there are 10 teeth on every cog.

Shaft 1 cog 1 has 10 teeth in the region 0 degrees to 10 degrees.
Shaft 1 cog 2 has 10 teeth in the region 180 degrees to 190 degrees.
Shaft 2 cog 1 has 10 teeth in the region 0 degrees to 180 degrees.
Shaft 2 cog 2 has 10 teeth in the region 180 degrees to 360 degrees.

As shaft 1 turns from 0 degrees to 10 degrees, shaft 1 cog 1 engages shaft 2 cog 1 and turns shaft 2 from 0 to 180 degrees as it moves from 0 degrees to 10 degrees. Shaft 1 continues to turn while shaft 2 is stationary.

When Shaft 1 reaches 180 degrees, shaft 1 cog 2 engages shaft 2 cog 2, turning shaft 2 from 180 degrees to 360 degrees as shaft 1 turns from 180 degrees to 190 degrees. Shaft 1 continues to turn until it reaches 360 degrees/0 degrees, and the process starts again.

All I need is some pin or other to keep shaft 2 in the correct position when it isn't moving, so that the system stays in phase with shaft 1.

Ha!

[Geof]

An aspect you need to keep in mind is shock loading especially with an escapement type mechanism. You do not mention how fast these rotating gears move: Does one go from 180 to 360 degrees in 1 minute or 1 millisecond. I am one of the most mechanically, as opposed to electro-mechanically, minded guys on CNCzone but this is one problem I would give to someone who could do it using servos or steppers simply because it is possible to control acceleration and speed. The position relationship could easily be monitored using absolute encoders and the position holding with brakes on the servo or just simply by the stepper. An added advantage to doing it electro-mechanically is that playing with the movement ratios, angular amplitude and speed is trivial being just a programming change. If you are not exactly fixed on what ratio, amplitude and speed is best it is almost certain that it would be less expensive to do it electro-mechanically.

And you should not complain about $140 per hour (Assie dollars I assume), if I wasn't retired you would pay me $150CAD per hour to build something and I wouldn't even consider it unless the total project was worth over $5000.

[RICHARD ZASTROW]

Geof needs a refill of his champagne cellar, blew too much cash on that last river cruise.LOL

Dick Z

[just george]

Hey fellas, made a video of the final design and put it on youtube in case anyone here wants to have a look

variable speed gear mechanism - YouTube

also made another thread for anyone who wants a quick job making them

[just george]

And you should not complain about $140 per hour (Assie dollars I assume), if I wasn't retired you would pay me $150CAD per hour to build something and I wouldn't even consider it unless the total project was worth over $5000.

No I wouldn't. I'd just learn how to do it myself. Do not underestimate the tightarseness of Australian inventors

[hanermo]

It does not work like that .. if you are making "real mechanisms" ie ones with requirements like angular relationships, reliability, speed, resolution and accuracy.
It costs about 1$ in drill bits to make holes in a steel plate.

It costs about 20.000$ to make so-so indexing plates.
It costs about 100.000$ to make good indexing plates.
Indexing plates cost about 20-40$.

This is the fallacy many get into - "thats too expensive".
Usually and mostly When they have NO ides about how hard, or expensive, it is to make "marca acme" in the first place.

I made a CNC milling machine.
It took 13.000 hours, 2000 kg of steel, and about 20k in bits and bobs.
The vast majority are unable to do "marca acme" and dont have the gumption, time and funds to do things at all - never mind "right".

The second (also very common) fallacy is also "it HAS to cost" say 130 per hour.
NOT NECESSARILY.
This is usually, e.g., from those who spent say 100.000$ in mechanical means to make good index plates, and now complain that I make them just as well, and 10 x faster, using some optical means that only cost 500$ for the measurement kit.
Mostly, these people are trying to protect ("their") captive market.

Most inventors give up.
Of the rest, most come up with ways and means to have the "bits and bobs" made by someone professional, ie with the right skills and tools.
Investors are a common way.
About 1/20 or 5% learn how to make things themselves- and invest sufficient time and money until they get some respectable results. Usually, after that, they start to pay the people in the first paragraph to make them, and dont consider it "too expensive" anymore.

500$ servos, and 500$ planetary gearheads, and 200$ computers are DIRT CHEAP if you are trying to make accurate, controlled, motion in a timely manner.
2000$ to make an *accurate mechanism* is dirt cheap.
It used to cost a clockmaket 20 years of learning, and 10.000 hours, to do the same.

The biggest error is thinking "I can make it" in a "few hours..", or "few days.." for 50$.
A handmade clock has 50$ worth of metal in it.
Handmade clocks cost 70.000$ and up.

Things these people with "obvious" pricing usually dont now about are things like
-materials quality (springs must be homogenous and hoghly reliable),
-finishing (how to polish and finish clockwork),
-accuracy (how accurately the holes need to be drilled, and positioned)

and then add things like "periodic error",
tools (do you know what accurate sub 0.1 mm drills cost ?),
magnifying tools, measurement tools, and processing tools.

and THEN add "work hours".

OTOH, many people who make magnificent things "their way" think absolutely everything has to be "hand made".
This is usually not the case.
And often, you can shave 99% off the cost by buying most stuff ready made, and only making, finishing, polishing or adapting a few bits yourself.

E.g.
It is not worthwhile making your own leadscrews (unless your biz is making leadscrews).
Using two leadscrews can lead to real 0-backlash, very cheaply, for example.
The cost of 2 screws is about 10x cheaper than a real 0-backlash screw that has a limited lifetime, when subject to heavy loads (like in a cnc indexer, for example).

E.g.
This would be a double-envelope ground screw, with two opposing internal preloads done by grinding.
A 40 mm diameter screw like that costs about 10.000$. Add 2000 $ for the bearings.
You can do the same for under 1500$ using two screws and separate bearings.

And now for 2000€ you can make it 4x stiffer, and 5xstronger, and 10x more long lived, by using a 50 mm screw.
Difference of 500€ only vs the 12.000 for the single screw, and about 18.000 $for a bigger 50 mm single screw (bearings costs almost double, as well).
And the more expensive one will last only 100-1000 hours under heavy load, until it develops some backlash.
After which it is toast.
The 2 separate screws can be adjusted to the same zero backlash at least 100 times.

No I wouldn't. I'd just learn how to do it myself. Do not underestimate the tightarseness of Australian inventors