(4/4) Operation: The details of setting up the Harmonic Analyzer

Рет қаралды 186,550

9 жыл бұрын

► Learn more at: www.engineerguy.com/fourier
► Buy the book on Amazon: www.amazon.com/gp/product/0983...
► Buy the posters on Zazzle: www.zazzle.com/engineerguy
► Main videos in the series:
(1/4) Introduction: • (1/4) Intro/History: I...
(2/4) Synthesis: • (2/4) Synthesis: A mac...
(3/4) Analysis: • (3/4) Analysis: Explai...
► Bonus videos:
Books and Posters: • Video
Page-by-Page: • Page-by-Page Guide to ...
Spinning Machine: • Bonus: Watch the machi...
Rocker Arms: • Bonus: Rocker arms: si...
This series on Albert Michelson’s Harmonic Analyzer celebrates a nineteenth century mechanical computer that performed Fourier analysis by using gears, springs and levers to calculate with sines and cosines-an astonishing feat in an age before electronic computers. Check out the series companion book and learn how to get a free PDF of the entire book at www.engineerguy.com/fourier.

Пікірлер: 223

@MartKencuda 9 жыл бұрын

The videos were really, really well made. The side-by-side views, the overlays showing what's happening on the insides, the general editing that went into it... I applaud everyone who helped make this video and am grateful it exists. I rarely see sines and cosines outside of a calculator, and to see them being made by purely mechanical means makes them seem more "real" to me. Thank you very much for putting these videos out there.

@SteveCrayons 9 жыл бұрын

Thank you very much! I did the editing for this video series. I glad you liked the overlays; it was worth the effort!

@jugosgratis 8 жыл бұрын

+Steve Crayons dude it was the best video editing and production I've ever seen in these kind of videos, hands down. The overlays, the different angles, the zooms in and out, the writing and the explanations, very well thought and done. I often find it hard to understand how this kind of mechanical things work (coming form an electrical engineering background, I'm used to things being in a plane lol), but this way it even felt easy. Really great work to all of you, congrats!

@SteveCrayons 8 жыл бұрын

+jugosgratis I really appreciate hearing you liked it so much!

@Somefox 9 жыл бұрын

The pen adjustment just... boggles my mind. It's like there should be a whole investigation on WHY the pen adjustment ends up being so crucial. Great stuff!

@eghty8fox780 7 жыл бұрын

Gordon Fawks I don't think it has anything to do with the pen or marker position, but the friction it is causing on the paper causing it to move differently at different angles I think if the tools made that hold the marker were more secure and not just bobbing on it's own weight it would be the same at any angle

@mattsyme87 5 жыл бұрын

@@eghty8fox780 I agree mate, it seems there are many places in that machine where friction is causing some errors in the output.

@danielc.freteval5685 4 жыл бұрын

Even more weird as I was expecting the opposite position to be the most accurate since it's the one producing the least amount of friction resistance.

@rodjori 2 жыл бұрын

When the pen is perpendicular to the plane of the paper, the drag starts a rotation of the pen around the axis of its own support.

@dickJohnsonpeter 2 жыл бұрын

@@mattsyme87 yea but the output does correspond almost exactly with electrical analysis, at least that's what he displayed. I'm sure there are things like friction and mechanical inaccuracy that need to be accounted for. It obviously worked well enough though because I'm typing this comment on my phone over wireless and wired data transfer. Which wouldn't be possible without machines like this.

@TheMattgician 9 жыл бұрын

An incredible machine, and an amazing set of videos. It couldn't have been any clearer, the video production is flawless. You've done an outstanding job to make the machine justice.

@SteveCrayons 9 жыл бұрын

Thanks! There were just so many fascinating details in the machine that we wanted to explain them all!

@vanmaren962 9 жыл бұрын

You seriously put so much thought into making these videos clear and understandable. You really should be recognized for your efforts.

@ajleonburguera 9 жыл бұрын

Stunning design and impressive explanation. Every course of Fourier analysis should start with these videos.

@oisiaa 9 жыл бұрын

Wouldn't it be faster to align the gears if you use a straight edge to put between the teeth?

@infinummjb 4 жыл бұрын

I bet it's exactly the point of the groove - in addition to the missing brass pen holder the machine most likely also lacks some kind of ruler to put into the groove. Awesome piece of machinery and design.

@joshcryer 9 жыл бұрын

Incredibly well edited and thorough video series. Just stunning.

@riodoro1 9 жыл бұрын

This is such a beautiful machine. Amazing how today we have FFT and everything is done so fast that You are not able to see how brilliant the mathematics is. Thanks for the video, very well made!

@joshhyyym 8 жыл бұрын

It's still faster than matlab.

@Yorgarazgreece 8 жыл бұрын

+Joshua Mcateer lol i can confirm!

@PilotPlater 9 жыл бұрын

This really is an incredible machine. So many simple concepts combined to make a really complicated machine.

@suzu1002 3 жыл бұрын

Discovering this channel is the best thing ever happened to me this year

@90hamg15 9 жыл бұрын

This video series (and by extension the machine) has helped me understand Fourier analysis and synthesis much better than I previously did. Thanks for the great videos, Bill!

@lonewarrior2936 5 жыл бұрын

Tons of appreciations to engineer guy and team for making such awesome videos. Concepts are explained so thoroughly in such a simple way. Thanks for the efforts of presenting detailed visuals. Makes it easier to understand the concepts and appreciate the brilliance of the engineers.

@Mahmood- 3 жыл бұрын

I'm really happy I could see these series for free and happy that such genius machine exists.

@kingmastodon6085 7 жыл бұрын

Most people are amazed by, and thus remark on, this device's otherworldly intricacy. For me, however, this machine is amazing for another reason. For many people, myself included, math is a tremendously abstract subject. Because of this, some people think that math was simply invented by man. These people have only used digital devices, like computers and calculators to perform operations. What sets the harmonic analyzer apart is that it takes what most people perceive as an abstract operation and turns it into a mechanical one. To me, this indicates that math is "real" and is not invented by man. It is amazing that we can use mechanics to do this. TLDR, sweet machine.

@mr_gerber 5 жыл бұрын

But - most of that maths you're referring to is way older than the computer! How could those mathematics giants _NOT_ have done the math as a real world existing thing? Fourier, Laplace, Newton, Leibniz, Gauss, Euler, Descartes, etc (just to pick some that should be familiar on an engineering channel). All of them from the late 1600s to early 1800s

@evilcam 8 жыл бұрын

Excellent video for a fascinating machine. This was so well put together, and you did such a good job explaining it that this series of videos themselves are an engineering masterpiece, and that doesn't even get at how wonderful the machine is itself. Time to binge watch all of your vids.

@Nimfatyk 9 жыл бұрын

I am so happy that we live in such a connected world, because in the other way I probably would't be able to see such marvels. Thank you very much!

@am-i-ai 2 жыл бұрын

This is an incredibly fascinating video series. I was wholly unaware of Michelson's mechanical inclinations. Thank you, Hammack, for shedding some light on this little piece of history. I now see Michelson under a completely different light.

@Leander_ 8 жыл бұрын

A terrific set of informative videos, as always. Thanks to Bill and the engineerguy team!

@DudokX 9 жыл бұрын

It's crazy from how simple components is this machine actually built! Simple things put correctly together so they can communicate can solve amazing complicated problems.

@IILowDownII 9 жыл бұрын

Thank you for uploading these right away instead of weekly!

@amannvig 9 жыл бұрын

The effort gone into making the videos is commendable. Thank you

@UnPuntoCircular 9 жыл бұрын

Beautiful videos and amazing machine. This is a really awesome explanation. Thanks a lot for taking the time to produce this.

@compu85 9 жыл бұрын

Fantastic job documenting this rare machine!

@vancewade6251 9 жыл бұрын

This is the most incredible mechanical machine I have ever seen. Wow. Great video Bill!

@WingmanSR 9 жыл бұрын

I do a lot of work/play with additive and subtractive synthesis in the context of electronic music, and I must say I have thoroughly enjoyed this series of videos. I think Mr. SeamlessR might find this interesting from an academic perspective.

@jdgrahamo 9 жыл бұрын

Great stuff -- there's obviously a lot of work gone into this series, for which I am very grateful. Excellent production, very clear. And what a fantastic machine!

@DrumApe 4 жыл бұрын

This is one of the most incredible things I've ever seen! And the presentation is fantastic, bar none.

@Saki630 9 жыл бұрын

"What a wonder that machine would have been." -- Instead it should be "what a b!#% it would have been to synch all the gears" This is one of the best videos on KZfaq hands down.

@johnchristian5027 8 жыл бұрын

What a brilliant set of videos for a fantastic machine, many thanks engineerguy!

@necromancerpencil 9 жыл бұрын

Thank you for the detailed descriptions and demonstrations of the Harmonic Analyzer. It's *almost* as good as getting to play with one myself.

@swsephy 9 жыл бұрын

I'm glad you uploaded these videos much sooner than you said you would. This machine is amazing.

@Sebal007 9 жыл бұрын

Great video, but can we have an in depth explanation on why the pen adjustment had such a massive effekt on the outcome?

@engineerguyvideo 9 жыл бұрын

We think it is friction: there is less when you put it at an angle in the direction of travel.

@nothalol 8 жыл бұрын

+engineerguy could it be that the friction when combined with the shape of the pen tip gives the illusion of curvature through it's varied stroke width? i'm thinking about how calligraphy can achieve similar effects by adjusting the pressure and angle the pen is at.

@GamesFromSpace 8 жыл бұрын

I think it has to do with pressure on the pen tip causing it to become more rigid. When it's being dragged it can wiggle more, so it doesn't follow the holder as quickly when it changes direction. Just my guess, of course.

@wez50 7 жыл бұрын

Friction, yes.. But also the surface quality of the paper, viscosity of the ink, velocity of the pen, force of the pen on the paper, the form of the pen itself. These all play a part and create problems for analogue recording with ink.. If a small amplitude vibration is introduced ("dither") then this can be enough to keep the dynamic friction coefficient. Unfortunately the driving force with respect to the pen friction is low and this system of rods and wires looks to be quite springy !. It would be nice to replace the large spring with a voice coil and create a force balance, thus keeping the summing lever still and using the current to drive a chart recorder!

@DrewMarold 9 жыл бұрын

Fascinating machine, and as always, well done for making such an accessible explanation.

@mosesdog2 9 жыл бұрын

Love the production quality of your videos.

@yeswanthbabud2622 2 жыл бұрын

Thank you so much sir. Cannot find words for the effort you took to make these 4 videos. Thanks again.

@borissman 8 жыл бұрын

Holy shit. i feel smarter for a change after searching for random videos on youtube. Thanks man!

@kennyschachat 9 жыл бұрын

Wonderful video series. Great job of clearly explaining every aspect of this amazing machine.

@aaronlowe3156 6 жыл бұрын

Haha, I never thought that I would find myself watching and fully understanding a mechanical sinusoidal computer. This is pretty cool!

@berizzian 8 жыл бұрын

Amazing series, is really inspiring to see how creative minds can use available resources to create elegant and simple machines to perform complex and precise tasks.

@WitoldWitkowski 9 жыл бұрын

Every math student should watch this video at least once per semester.

@dbkingsbury 9 жыл бұрын

11 minutes well spent.

@Nas939 8 жыл бұрын

Such an amazing machine. Very well made series. Thanks!

@Leopr1 9 жыл бұрын

Thank you for showing us this amazing machine.

@electroncraz91 8 жыл бұрын

I'm just about to get into Fourier analysis in my engineering classes. Funny I didn't get it until now by a mechanical machine that looks complex. Now I won't be confused about this in my classes thanks to Bill Hammack's illustrative explanations!

@rickmg2552 9 жыл бұрын

Magnificent video. Thank you. I believe the pen squares the sine waves at the end because when perpendicular to the paper, or sloped in the direction of travel, it causes the square rod to rotate in the square holder, binding. At the minimums of travel at the top and bottom of the sine there is not enough force to over come friction. But when sloped away from the direction of travel the pen can not rotate more toward the paper because it is already in contact, so the square rod remains loose in the guides.

@Patchnote2.0 9 жыл бұрын

I know nothing about the math of what's behind this machine, but I understand how the machine works on a mechanical level. These were some great videos!

@Robert-xp4ii 4 жыл бұрын

That machine is fascinating and the mind that created it, amazing! On a hunch, I looked at your views for parts 1-4 and found that my hypothesis was correct. Between parts 1 and 2, there was a larger drop in views. Fewer ppl didn't watch part 3 but the decrease wasn't as bad. Part 4 had the fewest viewers but only 300 less ppl. I assume that if we were interested by part 3, we were likely to want to view the last part. LOL I love science and math!

@Justin.Franks 9 жыл бұрын

Such an elegantly simple and ingenious design!

@PimpinPoptart06 9 жыл бұрын

Fascinating series of videos. Thanks!

@majorafan09 9 жыл бұрын

Well, depending on the pen placement, you can accurately draw analog waves and digital waves, which I thought was pretty cool! Also, I was decent at mathematics and with trigonometry, but I am not smart enough to operate this machine well. I liked this!

@tzkelley 9 жыл бұрын

Fascinating series--thank you!

@HiAdrian 9 жыл бұрын

Wonderful attention to detail, great video.

@oisiaa 9 жыл бұрын

Amazing machine and amazing video production!

@sr-7124 3 жыл бұрын

The sound of the levers on the rocker arms gets me every time

@s0nnyburnett 9 жыл бұрын

Wonderful series on an amazing machine.

@pubwvj 9 жыл бұрын

Beautiful machine. Beautifully presented. To quickly align the notches when changing the function a thin metal rule may be of assistance.

@ricardohakr97 9 жыл бұрын

I would love to see a series of videos on charles babbage difference engine

@oafkad 9 жыл бұрын

Wow that is cool. I would totally play with one of those for far too long. Fantastic video series as always.

@BaxterRoss 7 жыл бұрын

absolutely stunning video - thank you!

@hunakosdem 9 жыл бұрын

Love this video sequence! I am indeed unhappy about not living in the age of mechanical machines! One thing: Can you cooperate with Nottingham University Numberphile YT channel to cover the mathematical parts? I would love to see some actual functions appearing on the paper.

@TheBigBigBlues 9 жыл бұрын

Yes! Talk to Brady!

@Falcrist 9 жыл бұрын

Sixty Symbols did do a related video about maximum bandwidth... which would actually be really low for this machine.

@heaslyben 9 жыл бұрын

What a wonderful machine! And great videos. Very clear and satisfying.

@j.heasly7365 9 жыл бұрын

I only got to 5:22. So, this machine draws waves on paper?

@heaslyben 9 жыл бұрын

Pearls!

@j.heasly7365 9 жыл бұрын

Oink!

@LukeBeacon 9 жыл бұрын

Wow! That pen orientation thing blew my mind!

@MattTrevett 9 жыл бұрын

I feel like you could easily align the cylinder gears using a flat tool or even a taught string running across all the gears, in the notches. Thanks for the videos.

@playerthree38 9 жыл бұрын

these four videos made more sense than the two semesters i had to take and retake Trigonometry.

@toolhog10 9 жыл бұрын

Very nice video series. Thank You.

@erkangur1 9 жыл бұрын

Wow! Well explained! Great videos!

@manudehanoi 3 жыл бұрын

fantastic series. love your work. A wild guess, the flat peaks and trophs come from what is called "backlash" in machining. Probably because the bushings of the the various bars dont perfectily fit the shafts, so when a lever or a bar changes direction, there is a bit of looseness and delay. This is quite hard to avoid, because very tight fittings would have too much friction and would wear anyway.

@LaughterOnWater 8 жыл бұрын

You seem to suggest the flattened peaks are a bad thing. Is it possible that flatness of wave peaks was intentionally designed to be governed by pen angle orientation?

@markevens 8 жыл бұрын

Truly an amazing machine from a brilliant mind.

@bobbfwed 9 жыл бұрын

I don't know why this is so interesting, but it truly is!

@Formulka 9 жыл бұрын

my brain hurts a bit after the series .. and it's amazing :)

@deadmanwillyimbothdeadandalive 7 жыл бұрын

I feel like if you made this quality of a video for a school project the teacher would show off to every student saying "you could of done this good"

@wsshambaugh 2 жыл бұрын

I counted and it looks like there the cylindrical gears have 30 teeth per 90 deg turn? Meaning you could set different phases for each of the signal component in 3 deg increments. That would be a pain to set up. Though as others have also pointed out, pure sine or cosine should be quick by inserting a wafer into the deep cut.

@DovahKanye 5 жыл бұрын

I bought a machine like this in the 1900s, so glad I finally now how to operate it, been waiting a long time for this tutorial, I wish I knew math however.

@andrewgwilliam4831 6 жыл бұрын

I don't understand any of it, but it's fascinating to see how one man figured out a way to turn abstract mathematics into concrete form.

@mr_gerber 5 жыл бұрын

Often, what is percieved as abstract maths (at least for non-mathematicians), is actually quite concrete and came to be as a tool to describe something real worldly.

@negrotski 3 жыл бұрын

This video series is immaculate, as is this incredible machine. After watching the four videos, my only question is, what does the machine do? 😂

@engineerguyvideo 3 жыл бұрын

I have no idea

@negrotski 3 жыл бұрын

@@engineerguyvideo Well, you really made it seem like you "did" have an idea is all...

@hamsterpoop 8 жыл бұрын

Amazing! Thank you so much for this!

@thomasalexander1563 6 жыл бұрын

Awesome Playlist... 2014 videos,, Wanna see more videos like this in future..

@robinwalters4293 8 жыл бұрын

Is there a distortion of the sine wave from the fact the arms connecting the cams to the rocker arms don't travel exactly vertically up and down but also displace left and right slightly? I assume the cams help to mitigate this, but something else would be required to remove it completely, no?

@SKyrim190 8 жыл бұрын

This is all very fascinating, but what stroke as the most odd stuff to me was how the angle of the pen could change the output so drastically!

@jasondalton6111 8 жыл бұрын

We've found the next project for +clickspring after the clock is finished.

@markfryer9880 8 жыл бұрын

And you just know that Chris would look at this machine and go "Yeah, I could make that and make it work as well as making a video series on its making." Oh it is almost perfect match for Chris.

@jiesheng32000 8 жыл бұрын

+Mark Fryer omg yes if only chris really does it

@markfryer9880 8 жыл бұрын

Yes, this machine has +clickspring written all over it, and it would make one heck of a video series.

@joshua43214 8 жыл бұрын

Ha! I was just trying to decide if I had enough scrap around the shop to make one for myself. It would certainly amuse the folks in my lab even though we don't use Fourier analysis.

@isaace436 3 жыл бұрын

My question really is what pen did they use originally? Fountain and dip pens where, as far as I am aware, all the were around in the 1910s. Early roller ball and ball points didn't come around for some time, if I am not mistaken. Did they use a well attached to it perhaps? Maybe on this smaller one it wouldn't matter as much, but its difficult to write a consistent line with a fountain pen without it running dry, and worse is that they have to be oriented, and only write effectively in one direction. Maybe felt tipped stuff was still around then?

@moth.monster 5 жыл бұрын

Great, will keep in mind if I ever get one of these machines :)

@reddcube 9 жыл бұрын

Well done. Is the machine back in its case? If so, we need a QR code of this playlist.

@TripppleNegative 9 жыл бұрын

This was fascinating

@sixstation6480 3 жыл бұрын

Great work.

@kevinocta9716 7 жыл бұрын

This thing is really fascinating! I feel like this could actually still be useful in digital audio workstations actually. Say, you've found a really nice tone, and you want to know how to construct it using only sin (or cos) waves- Easy! just use this! You could essentially take the output from a guitar and match it with an digital organ (in theory the digital organ has many draw bars for many harmonics!) Also you could do the same idea but with a synthesizer... this kinda blows my mind. (I mean there's probably some digital tool for this, but it's really neat to see how it can work in physical space)

@ahmedexmor 7 жыл бұрын

fruity loops my friend it is already done, and it is mind blowing.

@imrlyboredful 9 жыл бұрын

What a wonderful machine.

@NiTheGod 9 жыл бұрын

why does the orientation of the pen make a difference?

@Maxwell-jn4te 4 жыл бұрын

I guess it is about the alignment of the fiber on the tip. For last two cases, those tip fiber could be combed by the texture of the paper. It requires a certain level of force to re-align them to new direction because doing so requires overcoming the static friction force between thousands or millions of fiber. This only happens when strain accumulate to a certain level, which create those flat top effect. But if tip is pointed to the direction of movement, the tip fiber is being bent 180 degrees backward on microscopic level. They are much shorter and less organized, thus creating less "locking" effect.

@peternosal2829 9 жыл бұрын

so far the best video you made :) great, great work, book is free which is great but I would love to buy hard cover copy of book but price is too high for me... but still, great work...

@holdmybeer 9 жыл бұрын

What a beautiful machine.

@CharlieLOL 7 жыл бұрын

that was super awesome

@tymo7777 9 жыл бұрын

Terrific video! Come guest lecture at the University of Tulsa!

@samueljanda3903 9 жыл бұрын

Bugger that. Get your passport out and visit the University of Melbourne!

@oranac 9 жыл бұрын

Samuel Janda wait what? which Melbourne?? Australia?

@wsshambaugh 2 жыл бұрын

I wonder if they could have used a fountain pen setup such that the nib barely did not touch the paper, but transferred ink through a connecting droplet that wicked ink to the paper via surface tension.

@kamalmanzukie 8 жыл бұрын

say you used this to do fourier analysis on a piece of music. you would lose the time/frequency uncertainty that comes from windowing, correct?

@dickJohnsonpeter 2 жыл бұрын

Is that measuring stick just arbitrary units or do they correspond to actual measurements?

@Justin.Franks 9 жыл бұрын

Couldn't you use different gears in order to obtain tracking speeds other than 1.0x, 2.0x, and 0.5x? For example, using the medium gear (18 teeth) with a large gear (24 teeth), horizontal speed of the paper would be 1.333x or 0.75x. Using the small gear (12 teeth) with the medium gear (18 teeth) would give you 1.5 or 0.667x.

@SteveCrayons 9 жыл бұрын

Yes, you can use those other gear combinations. However, if we tried to use the medium and large gears together the chain that connects them is too short and won't fit all the way around the gears. You could, of course, get a larger chain.

@tdjames916 6 жыл бұрын

Awesome. Thank you.

@JonAbbott 9 жыл бұрын

Does this use a reciprocating dingle arm to reduce sinusoidal depleneration? Just kidding. Great videos! Another fascinating machine to read about is the Antikythera mechanism, which is an ancient device that mechanically predicts astronomical positions and eclipses.

@brothapipp 9 жыл бұрын

So i think i understand how you would use it.... but i am very interested to explore the methods and logic in how a person would take maths and derive at such a machine. to restate, how do you take a function and arrive at a machine?