The Mathematics of Mechanisms ( 

I’m only a few minutes in, but I wanted to say this video is beautiful; the colour scheme, the sizes of everything, the animations, the fading in and out. These are little details that are hard to get right, well done- subscribed ❤

Criminally underrated channel, what a nicely done video.

The math of mechanisms is super fascinating to me. Going into a machine shop is like being a kid in a candy store for me. So much stuff, and every little detail has its reasons for being there in one way or another.

Brilliant, I taught some of this stuff to engineers once upon a time, I wish I'd had this video to show them. Well done

Very nice animations and great video. Please keep it going with videos like this.

Perfect! Deep and simple is more essential than shallow and complex. It doesn't matter how many times I have taught or been taught the same topics, everyone at any level has something to gain from the way you present these fundamentals.

Im loving this movement, SoME is the best thing ive ever seen great to have found you, looking forward for more content, keep the good quality🎉❤

This is really well done! Well-explained, beautifully designed and animated. This immediately makes me want to go out and program a 2D mechanism-based video game

Im taking a Mechanical Design class right now, and am definitely sharing this video with my friends. Its a very clear and concise recap of some of the topics covered in class, and will be helpful in getting a better grasp of the topic.

Great video, very well explained mechanics, looking forward to your future content 🤙🏻

This is so cool! That circle approach is such an amazing method!

Such a well produced video, Glad RU-vid suggested it.

Fantastic video and loved the animations. Well done.

This video is having too much knowledge and awesome way of representation. Crazy, keep up the great work. THANKS

Beautiful graphics and great explanation. Looking forward to more videos from you.

OMG, That's something I've been thinking about for a long time, but never got to it. Thank you for providing such a good video on this topic!!

@mtirado Excellent video, flows well while covering the topic completely enough to serve as video reference material. It's definitely going in my tech reference links. Thanks!

Fantastic videos, amazingly done. 👏👏👏

so interesting and enjoyable, thank you for the lesson!

Congratulations on making this very informative and beautiful video! As an aspiring RU-vidr I know how much hard work it takes

Very nicely explained with simple graphics...

This video is so well produced. Great explanation, simple yet complete. The animations are so cool and well made. Overall, amazing video!!! New sub here! ^^

The discrete Fourier series describes a mechanism which can draw any closed curve using epicycles. If every coupler mechanism can only draw closed curves as well, then there must be an equivalence between two coupled discrete Fourier series and a single discrete Fourier series. Describing what mathematically represents the coupling between the two discrete Fourier series is difficult.

You need to make more videos on Mechanisms! Awesome video, I subscribed hoping to see more from you in the near future!

This is so cool, please make more videos on this topic.

Great presentation !

Wow... It is amazing, thank you so much for this video ❤

So helpful video... 🎉🎉🎉 Thanks for sharing... ❤❤❤

Cannot wait for more videos from you !

exactly the video i was looking for.. pls continue..

More! Please. You have a rare talent: Use it.

That last five bar linkage just threw me through a loop and subsequently jammed me such that √4ac = 0. Immaculate lesson into such a complex topic.

Exelent Video,, very nice.

Gran video, el mejor por lejos. Muy bueno !!!

Beautiful; breath-taking

깔끔하고 멋지네요. 감사합니다~

Excelente vídeo! Thanks you

Great explanation.

This video Is really well done! I would love It if you could also talk about the forces that act on the mechanism. I am a robotic enthusiast and that would be really helpful

I've written a program to simulate the Chebyshëv linkage, which traces the Nilla curve. The bottom is nearly flat, while the top is nearly an arc. At four equally spaced times, it's at three points in a line on the bottom and at the middle of the top. It looks like the cross section through the middle of a Nilla cookie.

Extraordinary 🤩🤩🤩🤩😍 pls upload many more videos like this

This is GORGEOUS!!!

Very interesting, thanks!

Very nice. Makes me want to write a simulator for this. One more project to the backlog lol. It doesn’t seem like it would be too difficult to calculate some physical properties for these after determining big positions based on the constraints. Like torque or linear force.

Amazing 👏

In Robotics those are so simple mechanisms... We have really great methods there - check it out. We just use matrixes for everything.

very nice video, good job

This is so clever and fascinating

exelente video sigue con tu contenido

i really really love this video

This is great for developing walker linkages!

Very nice! I'd love to learn more about how you disambiguate between the cases with multiple solutions. Like, for each place with ambiguity do you just have to pick either the positive or negative root?

¡Que rico! And while manim has its place I'm especially pleased to see explorations of other visual options. (The rectangular boundary is an especially unusual choice and I wish I'd thought of it!)

Buen video, compa

Big clap per your video! Awesome.. please do follow up videos. I would suggest to use a math editor for formulas (latex or similar), so they are more easily readable

Beautiful

Wowwwww mannnnnn, it's greatttt. Pretty clear

Excellent

Well Done.

God tier video and explanation.

Please make more video's like this. ( like if any one wants video's like this )

Really good

the algorithm did you bad, how am I only now finding this channel

The discussion of jamming position was interesting. I have to wonder if there is a way to limit or constrain the configuration space during synthesis such that the number of degrees of freedom can only ever increment or decrement (by one). Similar to the K-map concept the intent would be to prevent simultaneous changes and thus minimize undesirable or indeterminate behavior.

Amazing

Nice video, but i just wanted to understand more about equations, so i hope you will explain it in detail please I liked your visualization ❤

Fascinating video! I'm most interested in the inverse problem, finding a mechanism that produces a certain path. In your example, you show a how to derive a solution of an easy instance of this problem, where a simple four bar linkage is sufficient, and using only three "samples" of position+rotation of a segment that should be reached by the mechanism. But how would one go about synthesising for a path like the one in 13:32?

Its a beautiful video. Thanks for all the effort and thanks for sharing with all of us. Simply amazing. Kind request to share which software or programming language you have used for creating those beautiful animations. Regards.

I would be very pleased if you will make a few videos how to solve some practical tasks about power, inertia, moments etc. In mechanisms

Quite nifty !

So, I've been trying to figure out how to visually represent some stuff - I'm quite hypermobile/have some pretty peculiar stuff going on with my nervous system and I want to find a way to create a hard map of the range of motion of my bones/joints, and then somehow overlay that with my internal/imagined map of my body. For most of my life I've had a bunch of involuntary tics, and since I was a child they were dismissed as a baked in problem of being a flappy autistic person and thus to be pretty much ignored - but upon realising that they were a manifestation of problems with connective tissue/rooted in weird stuff with my nervous system, I started engaging with/adjusting some of them - one in particular had been constantly subluxing my jaw and had (as wild as this sounds) resulted in me losing an enormous range of my sense of touch/pressure detection. Fixed the issue with my jaw and trained myself to pay attention to what my body was actually trying to do and over the past two years my sense of touch/proprioceptive map has exploded outwards from my neck/shoulders/spine. I feel like this kind of map of where my body actually can move, and being able to mark onto that which ranges - while possible, were destructive/overstretched joints would be incredibly useful. It also feels like something that someone must already have done to some degree. Do you have any suggestions on resources to look into? I'm not a mathematician/programmer of any kind - but this feels like the most promising tool with which to build the physical/mechanical part of what I need to create to make useful/discrete statements about what's been happening

Some time ago i was trying to analyze a rather complicated 3d mechanism using this "distance & circles" approach but for some reasons my equations were no longer symbolically solvable. Ive verified my numerically obtained solutions several times and they were correct so the equations had to be correct too. Since then I was interested in a proper way to do the math behind it...

Thanks for the video. Very nice illustrative presentation that’s easy on the eyes and labeled well. I’m curious what software you use to construct models and animate them, is it Adobe AE or something more specific?

This is so well produced! Can you recommend any program where anybody can test such configurations easily?

you need to put anice song or melody as an intro it will make the video better. all the video is amazing

Please create more videos bro, respect from indonesia

Gooood..

I once tried to simulate heusinger gear of steam engine and failed at combination lever. If I recall problem is that contrain is something like end and mid point are allowed to move on two circles and distance is defined by distance of mechanical joints. Third point is on some curve which I cannot properly describe. Other link has the same or similar contrains and intersection of these curves is a solution. Maybe it can be solved for tens of possible positions, drawing line segments between solutions, repeating for other links, finding intersections of line segments approximating these two curves and subdividing intervals to get more precise result. I just can't imagine how people designed that 150 years ago or so, because solving something like 4-5 equations with trigonometric functions is hard. Maybe tthey did not need to know precise position of joint, they just made sure that it satisfies number of degrees of freedom and that it combined movements of two levers with a proper ratio and made some smaller model from sheets of metal with holes and rivets.

This is essentially the math you will be doing in the last 3 semesters of a mechanical engineering bachelor’s.

Nice.

Excellent animation and great explanation! What editing software did you use? THANKS !

Interresting, Giving an arbitrary output motion, ?might the entire linkage soultion set be solved for?

Please make another video of more examples of building mechanics without anything just basic geometry. This way kids in middle schools will be able to use their compas and rulers to draw prototypes

Could you please make more such videos

at some parts of the video u have to get the square of a vector or multiply two vectors with each other But how are you supposed do do that should i multiply/square the single components of the vectors, should i take the cross product of them, should i use the dot product or something different?

A crank slider is a four-bar linkage also.

Gracias. No te imaginas cuanto tiempo estuve buscando un vídeo o un canal como este. Por ahí 10 años buscando , en mi idioma español bo existe tal cosa . En inglés hay mejores vídeos pero éste es el mejor , justo lo que necesito. Gracias.

i think arglin kampling likes this stuff

anyone else feel bad for the universe for having to do so much computation

I love this!

Can complex numbers be applied to this math? I’m curious because there’s a lot of rotation, and complex numbers seem to fit in wherever you see rotation.

At 9:43 the |U|^2 is represented by |U| in the bottom equation that threw me until I saw the mistake.

the old 4-bar linkage mechanism.

Bolo zuban kesari , I really needed this video , really helpful and informative, keep sharing these . ❤

The content of this video have whole chapters in applied mechanics: Dynamics textbooks for engineering 😂

Wow good job. Do these paths have equations ??

Machine dynamics!

But egual identicall component on a movements pedals not have a problem, on a movements, but if not is, have a problem

When can I find the book

In our country this is only taught in high schools.