A miniature version of this machine should be used in all schools and university to teach Fourier Analysis and Additive Synthesis. This is absolutely amazing.
I suffered through through digital signal processing classes and seeing a physical manifestation of the Fourier transform (instead of a Matlab function) is fascinating. It's about time such a ubiquitous technical concept got a proper documentary about it.
Desmaad It depends on your definition of computer. In the old sense of the word it definitely is a computer because it computes. However if you look at the modern idea of what a computer is (in essence a Turing Machine), this does not qualify. That doesn't make this machine any less impressive though.
@@Falcrist Yes, more thought into making them into cheap irreparable pieces of crap that break just after the warranty expires...And charging the same price as you would for a servicable machine. Just look at the user manuals most modern machinery has, and tell me where do you see schematics?
@@rockytom5889 and yet less wasteful than the overbuilt, under-engineered crap that was made for decades and decades. The stuff that gets venerated due to survivorship bias while we all forget how much energy it wastes. If you want, we can mandate that stuff is more repairable, but that will require abolishing capitalism... And in order for things like your phone to be repairable by the average person, they would have to be 10 times the size.
When developing a machine like this, do they go by a general understand combined with trial and error, or do they simply plan out everything in advanced and just make minor corrections to the design?
We don't know: we cannot get any real info on its design and construction, other than a 1898 paper written by Michelson and Stratton. That paper is in our book -- available for free in PDF.
Mechanically it consists of relatively standard elements used in instruments, their understanding of the mathematics along with plenty of experience probably got them fairly close without much need for trial and error. The fact that there are very low loads on the mechanism also helps as it allows you to get away with a lot. JMHO
It's my experience when doing something repetitive, that my mind starts looking for ways to simplify the system or offload mechanical repetition onto some kind of helper. Like putting a stop on a cutting tool so I don't have to resolve the same problem over and over. I sometimes come up with some clever jigs to remove repetition when doing the same thing over and over. It is fairly obvious to me, that that's what happened here. The Jacquard loom, Babbage's difference engine, and a hundred other developments arise as a general principle which only needs mechanical aptitude to realize and polish. It's basically a central idea plus a lot of ancillary problem solving. IMO.
As an aerospace engineering student who's had to study Fourier analysis, I am sitting here absolutely slackjawed that this mechanical device can perform such a task, and seeing its operation makes it seem so dead simple in principle, but no less magical
I spotted a source of systematic error in this design. The cams by the gears are connected to the rocker arms via connecting rods; the motion therefore is that of a crank rocker. Crank rockers do not produce pure sine waves; the connecting arm's contribution makes the wave a bit pointy on top and blunt on the bottom. To get a pure sinusoid isolated from circular motion, he should have used a Scotch yoke.
For the little I've researched in the last 10 minutes, the Scotch Yoke was invented in 1920 and used in the Bourke Engine, while the Harmonic Analyzer in this video was designed 20 years earlier. So who knows? Maybe later versions used the scotch yoke :)
I love Bill. I'm a lawyer by training but have always had a fascination with engineering and Bill teaches me without gimmick or condescension. A first rate teacher. Go watch his lecture about the Titanic.
Wow. I was expecting some kind of additive displacement of the different sinusoids (e.g. some kind of stack of cams or something), but this is using springs to convert displacement to force, which is much more easily summed, and then converting that force back into displacement through the main spring. By keeping the main spring long and the displacement small at the pivoting arm, the spring constant is going to remain very linear and improve accuracy. The amplitude bars are pure elegance, as is the 'full circuit' at the end, when the crank driving the gears is also moving the paper in perfect time. Can't wait to see the analysis video!
Oh, is that how it does it? I was trying to see linkage on top of linkage summing actual displacements. Converting to force does seem like an elegant solution, but still mind blowing how that can be done without inadvertent feedback distorting the sums.
A machine that can enact mathematical functions is understandable, in that it is mathematics that codifies physical realities. It's brilliant! Thumbs up!
What amazes me is how the linkage can linearly sum displacements without inadvertently causing feedback that would disrupt operation. I've seen summation explained in video on a general mechanical analog computer using wheels, but I have trouble keeping in mind how even that works, and here you have 20 linkages that seem able to to it with linear motion.
Most of the math lingo flew right over my head but I couldn't stop watching. Made more appreciative of this little thing I'm holding that is exposing me to all these curiosities.
Respected sir, I am a mechanical engineering student and I have struggled understanding the Fourier series in my 3rd semester Math course. Thank you so much for bringing life into my dormant understanding about Fourier series.
True. But it seems lots of them show how the parts do integration. I don't remember if I've seen demonstrated how they do differentiation. I can't believe it would be by doing successive approximations, and the way parts have to slip over others, I can't believe there'd be any way to run them backwards.
From what I see in regard to this machine at least in the configuration shown in the video you can arbitrary decide if you call the sinusoid created by the machine cos(x) or if you call it sin(x)
The amazing thing about this is that it's made with a few what look like custom castings suggesting that it was at least in limited production. What would be the market for something like this??
I wish youtube had a "super like" button...because simply likeing this video and commenting how much this miss's of my amazement of this video is not enough to show it
Very interesting machine, kind of like a high-tech linearizing spirograph hooked to a visible V-8 valvetrain hooked to a Stratocaster whammy bar. I don't ever remember seeing this in Altgeld Hall when I was a U of I student (although I probably wouldn't have noticed). I'm glad we have Matlab now.
Just stumbled upon this and thought it was going to be a very early musical synthesizer. The wheels would have to spin a lot faster to do that though... I think the very earliest musical synthesizers were electromechanical machines adding up sine waves. like the tonewheels in an organ. Funny enough that kind of additive synthesis went out of fashion as transistors made subtractive synthesis viable, but made a small comeback in the early 90s due to the ability of digital devices to easily create and add up sine waves.
Instead of using rockers, which introduce a little bit of error from their arc motions, couldn't the rockers have been made with some sort of straight line linkage?
I've been preaching for decades now that we need a resurgence of analog. It may not be as fast or versatile as digital, but it is still orders of magnitude ahead in realiability, and I do believe the pros and cons of each do need to be better understood for the greater good of all.
Yes, this machine is considerably slower than a computer program to calculate the answer. But the big advantage here is because it is so visual and you can physically SEE how each part is related to the other parts, it likely will make it easier to _understand_ why that answer was given.
Could the spring mechanism be replaced with a whiffletree? I'd think the whiffletree's more accurate, but there's probably a reason they designed it this way.
The always something beautiful about seeing harmonized mechanical motion. Like my Dad's old farm equipment. Sure, electronics do it solid-state but they seem like a cheap cop out today for some simple duties a mechanical linkage would be better (and more reliable) at.
Next you need to do a differential analyzer, to go in the other direction. A video on the US Navy Mark 1 Fire Control Computer could also be cool, but I doubt you could get to one easily.
I get how it works, I understand how the size and movement of the parts amplifies, but I guess because I don't understand the underlying math very well it still seems like a mystery. IMO truly great minds were necessary to create machines like this - this is a one-of-a-kind sort of one off invention that pushed innovation in science in a way few will ever know.
Can't understand how the displacements of the springs are summed just because they pull on one bar, which is the most crucial concept of this machine. Any bright person willing to help me out? Really curious
It works by Hooke's Law, that the force applied by a spring is a linear function, the spring constant (a basic physical property of each spring) multiplied by the displacement. If you stretch a spring twice as far, it will apply twice as much force; three times as far, three times as much force, and so on. Since the springs are under tension, even with coefficients of the arms set to zero, that also means that when they are relaxed, they apply less force. The rocker bar acts as a mechanical version of the integration function. Each arm acts through the attached spring, applying its force to the rocker bar. The sum of these forces moves the rocker bar.
While the machine IS great, it is important to remember that Mathematics is after all, the description of Nature so _of course_ there is a mechanical means of describing equations. An Oak Leaf however, would be unimpressed.
Not to sound like a nerdy sound editor, but as a nerdy sound editor, would you have clean recordings of this machine that you could share ? Those gears must sound yummy, the metal squeals ring delightfully ... recording this would be a blast. Cheers.
+FBuilding that IS the actual sound. I too thought there would be wonderful sound but then realized a machine that makes noise like that is one that is damaged or dying. This machine is very very quite because of its precision design.
That’s totally fascinating! I’m sorry though I didn’t really understand it. I was amazed at the mechanics of it. But you lost me at the bakery on the math!
And nowadays all we had to do to solve some complex calculations is to just put the desired variables then boom. I wonder what uncle Michelson had to say when he is presented with software such as MatLab.
Would be interesting to do sin(1x)+(1/3)sin(3x)+(1/5)sin(5x)... on that. Or in this special case 10sin(1x)+(10/3)sin(3x)+2sin(5x)+(10/7)sin(7x)+(10/9)sin(9x)... would it be able to show the "Gibbs Phenomen"? I ask myself.
Hey, I know your comment is old. But I'm a mathematician, and incidentally do research on problems involving Gibbs phenomenon. I point you to the paper "on Gibbs phenomenon and its resolution" by Gottlieb and Shu. There they mention that the machine, in fact, does show Gibbs while reproducing a square wave. I believe the amplitude of the oscillations of your example are well-known, see the Hewitt and Hewitt paper "The Gibbs-Wilbraham Phenomenon: an episode in Fourier analysis" for the details! So I believe that the machine would show Gibbs in that case too.
So humorous on so many levels! It's like listening to a baby unicorn making twitching little attempts at obscenity. Oh yes little child, you are an awesome creature. Adults tremble at the sound of your meager sputters. Maybe some day, you will find that the epithet "fuck you" defines an act of profound enjoyment. But for now, thank you for posting a 100% content-free post, displaying far more about your inherent shortcomings than you realize.
Seriously we need so much more of this on the Internet. Thank you so much for making these.
Human intelligence and mechanical ingenuity at it's best. I'm impressed! Thanks!
Some people put a lot of time into this video. Nice work!
very well produced indeed
Blowing my mind. I love how mathematical operations can be represented through simple physical machines!
Whats blowing my mind is that people invented these machines.
A miniature version of this machine should be used in all schools and university to teach Fourier Analysis and Additive Synthesis. This is absolutely amazing.
Thank you for doing this video series! It is very important to document stuff like this to remind us where we came from.
I love that sliding sound, that echo from the springs gives me chills.
Finally! a FULLY analog synth for my studio, bet this baby has the warmest tone in the universe
2:25 Mmmm, like wearing a blanket made from soup...
Engineerguy videos are always a delight to see! This series is a really wonderful way to show the beauty of engineering.
Looking at how these machines work puts a giant smile on my face c:
Boy, this is such a clever machine. Thank you for sharing it.
I wonder if this calculator is SAT approved.
You made me chuckle 7 years later
@@TheRandompaint Image trying to take that thing into an examination room?
i mean it doesn't have a qwerty or azerty keyboard so... :shrug:
@@TheRandompaint 7 years later it made me chuckle too
@@TheRandompaint lmao i wrote this when i was taking the SAT
now im graduated and do software engineering
I suffered through through digital signal processing classes and seeing a physical manifestation of the Fourier transform (instead of a Matlab function) is fascinating. It's about time such a ubiquitous technical concept got a proper documentary about it.
Amazing how much thought used to went into one machine for one purpose before computers existed.
It *is* a computer, albeit one for a very particular purpose.
Desmaad It depends on your definition of computer. In the old sense of the word it definitely is a computer because it computes. However if you look at the modern idea of what a computer is (in essence a Turing Machine), this does not qualify.
That doesn't make this machine any less impressive though.
More thought goes into machines now than ever has before.
@@Falcrist
Yes, more thought into making them into cheap irreparable pieces of crap that break just after the warranty expires...And charging the same price as you would for a servicable machine. Just look at the user manuals most modern machinery has, and tell me where do you see schematics?
@@rockytom5889 and yet less wasteful than the overbuilt, under-engineered crap that was made for decades and decades. The stuff that gets venerated due to survivorship bias while we all forget how much energy it wastes.
If you want, we can mandate that stuff is more repairable, but that will require abolishing capitalism... And in order for things like your phone to be repairable by the average person, they would have to be 10 times the size.
When developing a machine like this, do they go by a general understand combined with trial and error, or do they simply plan out everything in advanced and just make minor corrections to the design?
We don't know: we cannot get any real info on its design and construction, other than a 1898 paper written by Michelson and Stratton. That paper is in our book -- available for free in PDF.
Mechanically it consists of relatively standard elements used in instruments, their understanding of the mathematics along with plenty of experience probably got them fairly close without much need for trial and error. The fact that there are very low loads on the mechanism also helps as it allows you to get away with a lot. JMHO
It's my experience when doing something repetitive, that my mind starts looking for ways to simplify the system or offload mechanical repetition onto some kind of helper. Like putting a stop on a cutting tool so I don't have to resolve the same problem over and over. I sometimes come up with some clever jigs to remove repetition when doing the same thing over and over. It is fairly obvious to me, that that's what happened here. The Jacquard loom, Babbage's difference engine, and a hundred other developments arise as a general principle which only needs mechanical aptitude to realize and polish. It's basically a central idea plus a lot of ancillary problem solving. IMO.
this is a real chicken or egg question
As an aerospace engineering student who's had to study Fourier analysis, I am sitting here absolutely slackjawed that this mechanical device can perform such a task, and seeing its operation makes it seem so dead simple in principle, but no less magical
I spotted a source of systematic error in this design. The cams by the gears are connected to the rocker arms via connecting rods; the motion therefore is that of a crank rocker. Crank rockers do not produce pure sine waves; the connecting arm's contribution makes the wave a bit pointy on top and blunt on the bottom. To get a pure sinusoid isolated from circular motion, he should have used a Scotch yoke.
For the little I've researched in the last 10 minutes, the Scotch Yoke was invented in 1920 and used in the Bourke Engine, while the Harmonic Analyzer in this video was designed 20 years earlier.
So who knows? Maybe later versions used the scotch yoke :)
Personally, after watching this amazing machine, I needed a Scotch too.
the angle of deflection isn't big enough to cause a problem
I love Bill. I'm a lawyer by training but have always had a fascination with engineering and Bill teaches me without gimmick or condescension. A first rate teacher. Go watch his lecture about the Titanic.
Amazing. Congrats for the fantastic video. I don't know what is more amazing, the machine or your videos.
Wow. I was expecting some kind of additive displacement of the different sinusoids (e.g. some kind of stack of cams or something), but this is using springs to convert displacement to force, which is much more easily summed, and then converting that force back into displacement through the main spring. By keeping the main spring long and the displacement small at the pivoting arm, the spring constant is going to remain very linear and improve accuracy.
The amplitude bars are pure elegance, as is the 'full circuit' at the end, when the crank driving the gears is also moving the paper in perfect time.
Can't wait to see the analysis video!
Oh, is that how it does it? I was trying to see linkage on top of linkage summing actual displacements. Converting to force does seem like an elegant solution, but still mind blowing how that can be done without inadvertent feedback distorting the sums.
A machine that can enact mathematical functions is understandable, in that it is mathematics that codifies physical realities.
It's brilliant! Thumbs up!
What amazes me is how the linkage can linearly sum displacements without inadvertently causing feedback that would disrupt operation. I've seen summation explained in video on a general mechanical analog computer using wheels, but I have trouble keeping in mind how even that works, and here you have 20 linkages that seem able to to it with linear motion.
Most of the math lingo flew right over my head but I couldn't stop watching. Made more appreciative of this little thing I'm holding that is exposing me to all these curiosities.
a marvelously clear and well produced description of a classic mechanical computer. Thankyou!
I read about these machines when I was reading about fourier transforms. Cool to see how they work.
Respected sir, I am a mechanical engineering student and I have struggled understanding the Fourier series in my 3rd semester Math course. Thank you so much for bringing life into my dormant understanding about Fourier series.
I keep getting recommended videos for mechanical integrators. These things are incredible.
True. But it seems lots of them show how the parts do integration. I don't remember if I've seen demonstrated how they do differentiation. I can't believe it would be by doing successive approximations, and the way parts have to slip over others, I can't believe there'd be any way to run them backwards.
Excellent production value in this video. Extremely interesting, too.
From what I see in regard to this machine at least in the configuration shown in the video you can arbitrary decide if you call the sinusoid created by the machine cos(x) or if you call it sin(x)
you need to oil your computer :P 2:25
And to clean off all the old metal shavings. 1:31 Sloppy.
This has melted my brain. Subscribed.
holy shit
genius invention
The amazing thing about this is that it's made with a few what look like custom castings suggesting that it was at least in limited production. What would be the market for something like this??
Such a cool machine, and such a wonderfully explained and edited video. Thanks!
What a great calculator, takes a sine/dosing like no problem. Not afraid of computing at all.
OMG! One really has to be genius to come up with such amazing contraption
summation is the real genius part in this machine. I wonder if we can 3d print this machine. Using elasticity of plastic instead of springs.
I wish youtube had a "super like" button...because simply likeing this video and commenting how much this miss's of my amazement of this video is not enough to show it
What you showed is adding sines, how does it add cosines as well? Are there other wheels/levers 90 degrees out of phase?
Very interesting machine, kind of like a high-tech linearizing spirograph hooked to a visible V-8 valvetrain hooked to a Stratocaster whammy bar. I don't ever remember seeing this in Altgeld Hall when I was a U of I student (although I probably wouldn't have noticed).
I'm glad we have Matlab now.
holy shit i thought it would be way more complicated but really its just simply genius.
Just stumbled upon this and thought it was going to be a very early musical synthesizer.
The wheels would have to spin a lot faster to do that though... I think the very earliest musical synthesizers were electromechanical machines adding up sine waves. like the tonewheels in an organ.
Funny enough that kind of additive synthesis went out of fashion as transistors made subtractive synthesis viable, but made a small comeback in the early 90s due to the ability of digital devices to easily create and add up sine waves.
What if it was small motion of a big cone (like that of a phonograph)
Bill! I missed your show so much!
wow i wasn't expecting you to release 2nd part so soon
Instead of using rockers, which introduce a little bit of error from their arc motions, couldn't the rockers have been made with some sort of straight line linkage?
I've been preaching for decades now that we need a resurgence of analog. It may not be as fast or versatile as digital, but it is still orders of magnitude ahead in realiability, and I do believe the pros and cons of each do need to be better understood for the greater good of all.
Yes, this machine is considerably slower than a computer program to calculate the answer. But the big advantage here is because it is so visual and you can physically SEE how each part is related to the other parts, it likely will make it easier to _understand_ why that answer was given.
look the time that this machine was made, super amazing , super fantastic, super corrido gratulations for old inventor !!!
Awesome machine! Very well explained... can't wait for the next video!
Could the spring mechanism be replaced with a whiffletree? I'd think the whiffletree's more accurate, but there's probably a reason they designed it this way.
Awesome machine and awesome explaination, thanks !
Does somebody know the formula for the upper function at 0:15?
The always something beautiful about seeing harmonized mechanical motion. Like my Dad's old farm equipment. Sure, electronics do it solid-state but they seem like a cheap cop out today for some simple duties a mechanical linkage would be better (and more reliable) at.
Clean the gears up?
Incredibly well made video! Nice job!
Next you need to do a differential analyzer, to go in the other direction.
A video on the US Navy Mark 1 Fire Control Computer could also be cool, but I doubt you could get to one easily.
Why should the spring forces balance out? (on pivot arm)
thank you for your work.. these videos are amazing
Excuse me, can somebody tell me what this machine is used for, or whats the purpose of its work?
How does the machine account for phase, if at all?
This is amazingly clever.
I get how it works, I understand how the size and movement of the parts amplifies, but I guess because I don't understand the underlying math very well it still seems like a mystery. IMO truly great minds were necessary to create machines like this - this is a one-of-a-kind sort of one off invention that pushed innovation in science in a way few will ever know.
Can't understand how the displacements of the springs are summed just because they pull on one bar, which is the most crucial concept of this machine.
Any bright person willing to help me out? Really curious
It works by Hooke's Law, that the force applied by a spring is a linear function, the spring constant (a basic physical property of each spring) multiplied by the displacement. If you stretch a spring twice as far, it will apply twice as much force; three times as far, three times as much force, and so on. Since the springs are under tension, even with coefficients of the arms set to zero, that also means that when they are relaxed, they apply less force. The rocker bar acts as a mechanical version of the integration function. Each arm acts through the attached spring, applying its force to the rocker bar. The sum of these forces moves the rocker bar.
Super clear and concise. Thx ☺
and of course thx for the author for making this video great work!
I love mechanical things. This machine is fascinating.
So uh , what its used for again ?
While the machine IS great, it is important to remember that Mathematics is after all, the description of Nature so _of course_ there is a mechanical means of describing equations.
An Oak Leaf however, would be unimpressed.
What does it provide for people ?
I guess it goes without saying that whoever invented this is a friggin' genius!
Not to sound like a nerdy sound editor, but as a nerdy sound editor, would you have clean recordings of this machine that you could share ? Those gears must sound yummy, the metal squeals ring delightfully ... recording this would be a blast. Cheers.
+FBuilding that IS the actual sound. I too thought there would be wonderful sound but then realized a machine that makes noise like that is one that is damaged or dying. This machine is very very quite because of its precision design.
That’s totally fascinating! I’m sorry though I didn’t really understand it. I was amazed at the mechanics of it. But you lost me at the bakery on the math!
Was this also invented by the Greeks like the Antikythera Mechanism?
Wonderful machine,
thanks for sharing information
we miss you man come back!
I am working on it
The beauty of mechanical Analogue.
WHAT IS THE FUNCTION CALLED?
Can I print out your machine with my 3D printer?
Fascinating. Really clever.
Even if I can calculate them it's still interesting. I would like to have such a machine in the cabinet showcase in my office.
And nowadays all we had to do to solve some complex calculations is to just put the desired variables then boom. I wonder what uncle Michelson had to say when he is presented with software such as MatLab.
I still don't know what it does instead of control the wave that was drawing on the paper.
Why would you list out 1x to 20x when you could say main gear equals 1 exponent 20.
Love your videos.
With this you can import the waveforms into a synthesiser and create a wave table, to make unheard of cool sounds :)
Would be interesting to do sin(1x)+(1/3)sin(3x)+(1/5)sin(5x)... on that. Or in this special case 10sin(1x)+(10/3)sin(3x)+2sin(5x)+(10/7)sin(7x)+(10/9)sin(9x)... would it be able to show the "Gibbs Phenomen"? I ask myself.
Hey, I know your comment is old. But I'm a mathematician, and incidentally do research on problems involving Gibbs phenomenon. I point you to the paper "on Gibbs phenomenon and its resolution" by Gottlieb and Shu. There they mention that the machine, in fact, does show Gibbs while reproducing a square wave. I believe the amplitude of the oscillations of your example are well-known, see the Hewitt and Hewitt paper "The Gibbs-Wilbraham Phenomenon: an episode in Fourier analysis" for the details! So I believe that the machine would show Gibbs in that case too.
01:36, Please clean the crud out of the gear teeth.
fuck you
So humorous on so many levels! It's like listening to a baby unicorn making twitching little attempts at obscenity. Oh yes little child, you are an awesome creature. Adults tremble at the sound of your meager sputters. Maybe some day, you will find that the epithet "fuck you" defines an act of profound enjoyment. But for now, thank you for posting a 100% content-free post, displaying far more about your inherent shortcomings than you realize.
You're a week early! Yay!
Amazing machine!
interesting toy of maths,amazing want to know how to get the unknow X from the fomula with only machine structure.
I love that apparently the engineers ran out of technical jargon and just decided to call a wire, "different wire".
It's actually pretty simple which is what makes it such a great solution but I bet it wasn't simple to arrive at it.
That's astonishing!
There are some crazy smart people in this world.
it's a beautiful machine!
great invention!
captivating, thanks!
What the hell is this used for doe?
great stuff.
This is such a fucking awesome video, so amazing