How to mechanically produce modified SINE wave motion

[teliocide]

TL;DR Summary

Many mechanical actions produce sine wave motion.
I require a mechanism that modifies the sine wave so it is flattened at its peaks.

Piston displacement as a function of time produces a sine wave.
I need to modify the motion so the the time the piston spends at both the bottom of the stroke and the top of the stroke are extended.
The motion curve would approximate a clipped audio wave.
The attached image shows three motions.
The "Desired function" maybe too harsh so I imagine a hybrid between this and the modified Sine may be better for smooth mechanical operation.
So I am searching for a mechanism (a mechanical arrangement) that can produce this.
I am aware this can be achieved with a Cam and various engaging and disengaging mechanisms, but these are not ideal solutions.
I am imagining a solution of rods and levers not that dissimilar to Walschaerts Valve Gear.

Cheers
Greg Paterson

 

[berkeman]

Welcome to PF.

Use an AFG (arbitraty function generator) that you load with your modified waveform to drive a power amplifier driving a mechanical acutuator. Problem solved.

 

[teliocide]

Thanks
That is a solution, an electrical solution, not a "mechanical" solution and not the solution.
I am sure there is some ancient mechanical solution out there.

 

[Baluncore]

Welcome to PF.

Look at the Fourier transform of your preferred profile. You can generate a harmonic with a gear running on the crank pin. That gear has an eccentric hub that controls the piston.

Look at radial plots of functions like: r = 1 + sin(n⋅t) / (1+n²) ;
for -π < t < +π; with values of n = 2, 3 or 4.
Notice the flat sides and the circular corners.

 

[berkeman]

Thanks
That is a solution, an electrical solution, not a "mechanical" solution and not the solution.
I am sure there is some ancient mechanical solution out there.

Whelp, do you know what a mechanical cam mechanism looks like and how it works?

 

[teliocide]

Welcome to PF.

Look at the Fourier transform of your preferred profile. You can generate a harmonic with a gear running on the crank pin. That gear has an eccentric hub that controls the piston.

Look at radial plots of functions like: r = 1 + sin(n⋅t) / (1+n²) ;
for -π < t < +π; with values of n = 2, 3 or 4.
Notice the flat sides and the circular corners.

I have many of these but they are a compromise. To get the ideal function a cam would have large flat sections and at any speed faster than snail speed the cam follower would bounce. Rounding of the flat sections means less time is spent at peak displacements.
The two attached videos show the ideal cam and the possibility of encapsulating the follower.
But as I said another approach is preferred.
Hmmmm this forum does not support mp4 files so I have had to covert mp4 to GIF making the file much larger. NB From 159kb Mp4 to a 7mb gif which is too large the system tells me. Excellent.
So here I post 4 stills from the video

 

[teliocide]

CAMs? .... I meet a lot on internet forums.
X

 

[Baluncore]

Are you prepared to use a rotating crank with two gear wheels, rather than a cam?
Here is the function: y = Sin( theta ) + Sin( 3 * theta ) / 10 ;
It has a maximally flat top and bottom.

 

[teliocide]

Very impressive. It is very much what I anticipated from the fusion of the two graphs i posted earlier.
Please can you send a rough diagram showing me the arrangement of the gears I will then make a 3D model.
After months of questions your solution is the only one that comes close. Many Thanks.

 

[Lnewqban]

Welcome, @teliocide !
Please, see:
https://507movements.com/mm_166.html

 

[teliocide]

Thanks
I know this well.
Unfortunately it involves a "engage-disengage" mechanism suitable only for very slow speeds

 

[Baluncore]

Very impressive. It is very much what I anticipated from the fusion of the two graphs i posted earlier.
Please can you send a rough diagram showing me the arrangement of the gears I will then make a 3D model.

There are a great many mechanical implementations. It could be done by roller chains, or gears and cranks. Here is a first guess at a possible solution.

The crank turns and moves an N-tooth planet gear around a concentric fixed 3N-tooth gear wheel.
The centre of the N-tooth gear runs true on the crank pin, so the gear teeth always mesh, but the hub is made eccentric, with an offset equal to one tenth of the crank stroke.
The N-tooth gear hub generates the attenuated 3'rd harmonic, added to the crank fundamental.
The big end of a long connecting-rod runs on the eccentric hub of the N-tooth gear.
There will be a slight error due to a short diagonal crank on the rising and falling edges, but the top and bottom will be error free and maximally flat.

That mechanism generates; y = Sin( theta ) + Sin( 3 * theta ) / 10 .

If you are game to introduce the 5'th harmonic also, there are slightly wider flats with;
y = Sin( theta ) + Sin( 3 * theta ) / 11 - Sin( 5 * theta ) / 90 .
Those amplitude coefficients of 1/11 and 1/90, are a good guess, but are not flatness, nor Chebychev optimised.

 

[teliocide]

Perfect flatness is probably not desirable as the mechanism needs to move smoothly, so approximate is probably better.
I will put together a static model and once you give my interpretation your approval I will animate it

 

[teliocide]

Here we go...................

 

[Baluncore]

That looks good.
When it comes to gear tooth count, a minimum of 20 will give quiet running.

Being flat at the tip should not present an acceleration problem, since it must stop there, to reverse. The important thing is that it does not oscillate at the extremes, like a Chebyshev approximation does.

Because the flattening is symmetrical, the harmonics employed must be odd, like a square wave. Notice here, that the sign of the harmonic alternates, unlike in the Fourier transform of a square wave.
I looked at the fundamental plus one odd harmonic from the range 3, 5 or 7.
Notice the harmonic h, coefficient must be 1 / (1+h²) for maximal flatness.

They can all use the same mechanism, just with different gear tooth counts and hub eccentricity. The three flat-top equations I plot here are;
y = Sin( theta ) + Sin( 3 * theta ) / 10 ; red
y = Sin( theta ) - Sin( 5 * theta ) / 26 ; magenta
y = Sin( theta ) + Sin( 7 * theta ) / 50 ; yellow
With a sinewave in ; grey
Overlying those functions are zoomed in views of the flat tops.

You should select the harmonic that best suits your application.
The planet gear spins proportionally faster for the higher harmonics, but throws much less distance.

 

[Tom.G]

When it comes to gear tooth count, a minimum of 20 will give quiet running.

Also, for maximum gear life, the tooth count on the two gears should not have a common divisor.

If they have a common divisor, say X, then the same teeth mesh every X revolutions. Any minor defect on one tooth will concentrate extra wear on the teeth in meshes with.

Cheers,
Tom

 

[Baluncore]

Also, for maximum gear life, the tooth count on the two gears should not have a common divisor.

If they have a common divisor, say X, then the same teeth mesh every X revolutions. Any minor defect on one tooth will concentrate extra wear on the teeth in meshes with.

That is called a "hunting tooth" system because each tooth meets every other tooth on the meshed gears.
So, how do you suggest we get a 3:1 ratio without there being a common divisor?

 

[Baluncore]

Maybe use a no-common-factor idler gear between the two gears. Or use chain sprockets, connected by a roller chain with a length having no-common-factor to the sprockets.

 

[Tom.G]

So, how do you suggest we get a 3:1 ratio without there being a common divisor?

I was hoping that the drive speed could compensate. If not, then a compensating gear ratio is needed elsewhere in the drive train.
(I know, not perfect, just hopefully 'close enough',)

 

[Baluncore]

The crank shaft is the only drive train, one gear is static and so does not rotate, the other rides the crank pin. Hunting teeth are speed independent.
If a hunting tooth was required, we could introduce an idler gear, without common factors, between the 3:1 gears. Alternatively, use 3:1 chain sprockets, connected by a roller chain with a link count, having no common factor with either gear.

 

[Tom.G]

The crank shaft is the only drive train, one gear is static and so does not rotate, the other rides the crank pin.

OK... I must have missed that. I interpreted the OP as needing something to drive the piston, not the piston driving something. That led me to think the 30 tooth gear was the driver.

 

[Baluncore]

OK... I must have missed that. I interpreted the OP as needing something to drive the piston, not the piston driving something.

You might be right, as we know not what the OP plans.

If the rod is driven to turn the crank, I would do everything possible to avoid a wide and flat TDC and BDC, as that would mechanically lock the system for a greater part of the rotation.

 

[teliocide]

Forget about 3:1 it does not work.
https://vimeo.com/manage/videos/886060121

This is the piston motion

This is the path of the big end

I tested 2:1 with 40 and 20 teeth gears

The small dip at the peaks can be removed by changing the position of the Big End relative to the the axis of the small gear.
I shall play some more.

This is my 3D model

The one I am building is very different

 

[teliocide]

OK... I must have missed that. I interpreted the OP as needing something to drive the piston, not the piston driving something. That led me to think the 30 tooth gear was the driver.

It is to drive a piston.

 

[Baluncore]

Forget about 3:1 it does not work.

Apologies.
It is very easy with epicyclic planetary gears to forget to add or subtract 1 from the ratio. I knew it could be a problem, I just hoped I could get away with it for the first guess at a mechanism.

After rolling 180 degrees around the fixed gear, the planet should be upside down, but it appears to have been also turned over by the crank, since the top of the planet is then in contact with the bottom of the fixed gear.

Think really hard about it, or simply try a gear ratio of 2 or 4.

It is the gear carrier that causes the ratio ±1 problem, the piston movement profile should still be that plotted for the 3'rd harmonic.

 

[Swamp Thing]

Whelp, do you know what a mechanical cam mechanism looks like and how it works?

Someone whose first language isn't contemporary colloquial American English might decide to look up "whelp" : https://www.google.com/search?q=whelp

 

[berkeman]

"whelp" : https://www.google.com/search?q=whelp

A puppy! Awww.

 

[Lnewqban]

Thanks
I know this well.
Unfortunately it involves a "engage-disengage" mechanism suitable only for very slow speeds

Could you clarify the stroke frequency of that piston and power to be transferred?
What about working conditions regarding keeping proper lubrication in place and not contaminated?

 

[Baluncore]

Could you clarify the stroke frequency of that piston and power to be transferred?
What about working conditions regarding keeping proper lubrication in place and not contaminated?

I believe the piston concerned is the displacement or regenerator piston in a Stirling engine. That piston displaces the working gas, so does not seal, and needs no lubrication.

The OP has an answer to his question, and a mechanism design that will work.

A PM from the OP tells me that he has left the forum.
"Thanks for your help but I am pulling the plug on this forum.
Too many derogatory comments and demeaning remarks so I may as well be on Facebook."

I quite understand that. We need to make a wide allowance for "the buildup", a stressful time in Northern Australia, prior to the arrival of the monsoon rains. The term "going troppo" applies to normally sane people who remain up there, at this time of the year.
https://www.abc.net.au/news/2018-05-15/going-troppo-what-evidence-is-there/9747436

 

[berkeman]

A PM from the OP tells me that he has left the forum.
"Thanks for your help but I am pulling the plug on this forum.
Too many derogatory comments and demeaning remarks so I may as well be on Facebook."

Was it something I said...?

 

[Baluncore]

Was it something I said...?

Under the circumstances, the trigger could be anything.
We should pray for an early monsoon, and a welcome back.

 

[berkeman]

Under the circumstances, the trigger could be anything.

Do you see anything in our responses that may have bothered the OP? The thread seemed to be going okay to me...

 

[Baluncore]

There were the usual "reading and understanding the question" problems, and some wrong assumptions while "getting to know the OP's capability".

It was typical light-hearted banter, in parallel with the topic, nothing directly personal, but our interpretation is not subject to the stress of inescapable and debilitating heat.

 

[Tom.G]

FWIW, I did get the impression that this overall thread was being rather more derogatory/aggresive than usual here.

 

[Averagesupernova]

Was it something I said...?

Likely. You are those most abrasive member I have found on this forum! Lol. J/K. I can't imagine you can be at fault. I might be though, stuff I say always gets taken the wrong way. And I didn't even post in this thread. That's how bad I am.
-
Seriously though, some people just have a thinner skin to start with...