i'll only save it for later lol i am only at 3rd year college for bsmath... i can't take this kind of math yet lol

26:20 You've created an anti-cam. I hate it. 😂👏👏👏👏👏

hi, can you tell me wich software?

I love the visuals But if you were to ask me about the math I’d go Uuummm… ummmm mmmmmm Idk

I'm sure this wouldn't actually be practical, but if all you need is constant rotation at the input and the output and not necessarily at every intermediate step, you could use wheels as gears, right? It seems like it should be possible to cancel out all the jerkiness so that the input and output rotate together smoothly, with only internal gears moving at non-constant rates.

great video but I will say it would have been nice to see the gear partners spinning like gears once the problem was solved, instead of rolling around each other. still great stuff though keep it up

I hate it when my gears slip but in the wrong way.

It's pronounced 'envolope'.

Hey, it's the Rubix Cube!

18:49 I've yalling "bezier curve" all the time lol

Isn't the rotation property of complex numbers more a result of multiplying any number pairs by coordinates on the unit circle, rather than the fact of one of the coordinates being imaginary?

when youre so fed up with scrolling thru tt that youre watching how a gear is made for any shape 😭 (its interesting tho)

What if R is not constant and is a tensioned spring instead?

The slippage is more perpendicular to the axel-line for the gears than expected considering the hook the video claims in the beginning, but also the gears in the example seem to break contact before they would drag against eachother by dezign Also, misinformation should be determined by the listener and not governed by a central body or even someone else, that’s how fascizm begins, hence The First Amendment

another rotation to get dialup

When it got to the envelope I stopped understanding but that was probably my fault cause I spaced out when he was talking

cannot be asked to watch half an hour of yipyap someone tell me where he answers the question that is the title, which is the only reason i clicked on this video, to find out what gear shape meshes with a square, i click and i'm greeted with a half hour long video, it doesn't require 30 whole minutes to tell me what gear shape meshes with a square.

This was too difficult for me, i don't have the mathematical backing to understand some of the concepts. Sad because i really wanted to get it.

Imaginary numbers looks like x,y coordinates. Why its written as a+bi when its just vector (a,b)? Its main feature is rotation by multiplying on i, which can be done with usual vector with similar rotation rule.

great work/presentation! you got a new fan ;)

Beep boop beep boop beep

one of the best videos I've seen for some time

I would argue that the curve with the line along the y-axis is still connected with the path definition (Disclaimer: I am not a mathematician, so feel free to correct me if I'm misusing terminology; more notes at bottom). There are only two possible scenarios for the "endpoints" of the separated curves without the vertical line (these "endpoints" reflect the y-value of the function immediately to the left and immediately to the right of x=0). The endpoints are either located at effectively the same point to create what would normally be a removable discontinuity or located at different y-values to create what would normally be a jump discontinuity. These types of discontinuity usually refer to functions where the limits at the x-value are known. In this case, the limits from the left and right are undefined due to the oscillating pattern. However, the function is bounded between two y-values, so we know that the "endpoints" of both sides will each have a y-value between -1 and 1. This would mean that adding a line at x=0 that ranges from y=-1 to y=1 should attach to both disconnected "endpoints" regardless of where they are positioned relative to the y-axis. Although we cannot determine the precise values of the path function as it meets the y-axis, similar to the way that we cannot determine a finite limit at x=0, an indefinite path function must exist that traces the vertical line to connect the two segments. Note: This is the result of a bunch of concepts and theorems back from Calculus 1 that have been scrambled together from memory to try to make something that resembles a decent explanation. The main inspiring concepts aside from discontinuity were the Intermediate Value Theorem and the Squeeze Theorem. It's also 2:30am as I'm finishing this (I got hyperfixated on number stuff again), so please let me know if there's something that doesn't make sense, and I'll try my best to clarify later

Now you just need to show how to solve for two identical gears :)

18:50 just an aside: would that graph be described as a45 degree rotated parabola? My mind went in the direction of a graph for an equation similar to y=1/x where x is greater than 0. I don’t remember the specifics or how to test in this instance, but would that actually satisfy the requirements for a parabola?

So, on a practical level, i could rotate a gear around a point a known distance away to find out a gear to mesh with a gear i currently have?

Now, can you design a gear capable of turning a 4 dimentional cube on a single axis?

Have you ever heard of a Wankel engine? It's a convex triangle spinning inside of a shape I can't describe. You should do a video on it it is very interesting how they solved that clipping issue you talked about.

i came here to see both gears spin off stationary points and was disappointed

I was playing around with one of my game projects written from scratch in Java last year, and was making a 2D GUI system (bear in mind I don't have a strong mathematical background at all - thanks lackluster school system ...). In it, I was playing around and wanted to make functional gears, but I couldn't find any useful information on generating gear meshes, so I ended up just coding something that could generate an N-toothed gear with a given radius that was visibly passable as a gear instead. Life ended up happening, and I haven't really revisited that project for a while. After watching this video just now, however I had an idea to help me generate better looking (and hopefully better working) gears: take an arbitrary shape and make it orbit around a circle (using [Math.atan2(y, x) * -2], removing pixels from the circle where the shape overlaps (this part should prove challenging for me lol). I think that ought to result in a shape that was 'traced out' with the outline of the original starting shape, no? I'll admit I'm just throwing stuff together to see if it works lol, I know there's probably a much simpler and better way to programmatically tackle this problem.

So car wheels are kinda of gears in a way. As both mediums move consistently relative to eachother

I usally skip sponsors but bc u were so polite i didnt :)

Would it be cheating to work in polar coordinates instead?

Are there 3d gears? I mean this calculations can be extended to more dimensions and what they mean?

Pi

I wish I had this while I was doing my degree

Didn't the last video end with the statement that constant angular velocity is beyond the scope of the video? Now I'd like to see the development to constant torque. I was also hoping for the mirrored wheel/gear example leading to the triangular cutter that you showed last time but for this new condition.

The outside envelope may be usefull for gears meshing from inside for small form gearboxes, like cycloidal ones Edit. Yeah i just got to that in video😅

Hey, man could you please design a gear for a circle?

23:08 I disagree with the character, watching the terms shuffle around and morph into other terms to produce a formula is simply amazing

27:01 Imagine trying to build that thing, immediate jam when the egg gets in the crevice. That's why it doesn't work lol.

Call them duplex not complex, I'm trying to make that a thing lol.

i thought dot product returned a scalar and cross product returned a vector

Watching things relating to machining has taught me years ago that a line (the road equivalent in these videos) can be thought as a circle with infinite diameter, so it is almost obvious you can scale "a road" back to a shape with less than infinite diameter and vice versa given that you can scale between harmonics.

to make it diverge, use all of the arrows and make it already infinite! so the other type of arrows doesn't do anything so u can use 'em too

You can get rolling without sliding with helicals, shaved for contact only at the pitch circle tangency

In order to navigate that minefield, you would need infinitely small feet, in which case you could just walk across the minefield via pretty much any path you like.

Will the alternating odd number series diverge if you place all the +ve terms ahead of the negative ones, or vice-versa?

Seems pretty obvious to me. The second series, truncated at any given finite length, will always have more positive terms than the first, ergo it will be larger.

Subscribed for the great animations and the humor included in the educational videos!