what light source do you use? been seeking for some point-ish light source - what hilden diaz used for their chandelier - for years :)

I wonder if you could you make one that can go trhough itself on both sides? So it can rotate 360 degrees? I wonder what shape it would trace out if you held one end fixed and let the rest rotate around? and how it would change based on how many segments you have

Super cool

Smegerman

Maybe it would be an interesting in a loom. The grey pieces could be holding warp threads because if you have the green gears fixed the grey gears just alternate between two positions

As long as you have an odd number of gears along each lil stick segment, you can make them as small as you want, meaning you could make it collapse smaller

In some sense I think the infinite trip knot can’t be untied the obvious way because the obvious way doesn’t actually change the knot-it would be like removing a single term from the front of an infinite series.

0:46 "they move"

I'd say it's still impossible because the underlying set theory still applies. It's just that now each object has two values attached (number and orientation). At the end of the day it's still a set, and just as it's impossible to turn (1, 2) into (2, 1) in an even number of swaps, it would still be impossible to reach half of the possible permutations in the modified puzzle. As for how to "solve anyway", I came up with a much simpler way: just target a known impossible permutation. If 0 represents the gap, then the states 0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15 and 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,0 are respectively of odd and even parity. So if you have an impossible puzzle, just target the one with the gap on the top left and call that a solve. If you get to change the rules by adding a wormhole to the bottom right then I get to change the rules, too.

"Can you make linkages act like a gear" In the sense of gearing things up/down, yes, pantographs are one example.

If you made the gears smaller, for instance each gear's diameter is the same as the width of the beam it is attached to, then you could use multiple gears on each straight segment to keep them parallel. As long as the number of gears is odd, it should work. Making the gears smaller would help it collapse to a space efficient profile. It will introduce other problems, though, such as added friction from more moving parts and greater forces being applied on the gears from a bigger reduction.

It would be interesting to exchange the middle gears for chains. That way the side gears can be small compared to the stick and it looks much more like half a scissor mechanism

I used to compete in robotics, and one of the main mechanisms we would use if we needed to lift things was called a 4 bar lift, which was basically the first 4 bars in a scissor linkage, with the first bar being anchored, creating a parallelogram. Sometimes, when we couldn't fit a full 4 bar lift, or needed more that 170 degrees of mobility, we used what we called a virtual 4bar, where the the first bar was linked to the output with just a single bar, and a chain and sprocket system that caused the third bar to stay parallel to the first, just like the linkage you have here. We used sprockets instead of gears because using an excess of gears would have induced a lot of slop in the mechanical design

What shape does the end trace?

Fascinating! ...yes it's possible to building with lego kzbin.info0fWSGFlLcnY?si=SG4qGJWT710ehABo

Geneva drive? Closest i can say is a linkage acting as a gear. But no, can't really say

John Dee was a renowned mathematician and Mercator frequenter. The scrying tools seem to use projective geometry, and the elemental tables refer to the carnot cycle and the collapse of political regimes. It seems that someone was using these processes to decipher the soyga tables. Abraham Abulafia's combinatorial methods also seem to relate to this.

Using one gear you cannot expand it all the way straight and stop right?

I made a standard scissor linkage out of Legos, and one out of laminated paper (with printed squares) and little fasteners.

This is actually useful for me, I've been trying to design an adjustable height table that would need a scissor mechanism, but I don't like the look of scissor mechanisms, when one side has to move and the other remains still

you could probably make it able to retract further by doing a larger number of inner gears, all being smaller

I'm not sure, but I think the error in the positioning of the models may be due to changes in perspective when the camera moves. The difference is quite noticeable after the flash of light. I also am not sure that a lighting setup could be found that would create exactly the same effect for both models, either practically or in principle. A projection may be "perspective-y", i.e., look similar to a perspective projection, but the perspective projection is a specific thing. It depends on a "focus" with a position, a direction of view, an "up" direction, and the distance to the plane of projection. The position is a dimensionless point, the directions are vectors and the distance to the plane of projection is a scalar value. I think the term "lines of sight" isn't really ideal for the lines from the focus to points in a scene. They are lines from those points to the focus and their intersections with the plane of projection are their projections onto the latter. However, the only "line of sight", to my way of thinking, is the line specified by the position and direction of view of the focus. If the direction is changed, so is the plane of projection, which is always perpendicular to that line. The projection for a given focus can be expressed as a 4x4 transformation matrix, which may then be applied to points with 4 "homogeneous" coordinates, conventionally named x, y, z and w. Under "normal" circumstances, the w-coordinate will always be 1. When projected using the perspective projection, it is very likely to be not equal to 1. For example, let a focus be defined like this: set f with_position (0, 10, -10) with_direction (0, 10, 10) with_distance 10 and assume that the "up" direction is calculated automatically and points in the positive y direction (i.e., straight up). Then, the transformation matrix will look like this: 1.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.1 0.0 0.0 0.0 1.0 By contrast, the "identity" matrix, which has the amazing property that, when applied to a point, it leaves the latter unchanged, looks like this: 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 A possible implementation of a routine in C++ that performs the magic of applying the transformation to the point (leaving out all error handling) looks like this: for(int i = 0; i < 4; i++) { for(int j = 0; j < 4; j++) { projective_coordinates[i] += temp_coordinates[j] * f.get_persp_element(j, i); } } The values of `temp_coordinates[n]' for n = 0, 1, 2, 3 start off simply as the coordinates of the point. `f' is the focus and `get_persp_element' simply returns the specified element of the transformation matrix.

This would make a much better Go-Go-Gadget Boxing glove than the original

What about as pulleys/capstan instead of gears? Given the purpose of the centre gears is to reciprocate the force/motion thus constraining the DOF, then having the belt/string cross over the centre point of each link should achieve the same effect. It should also enable closer packing and the full range of motion like the geared version.

5:18 could you instead of having solid bars on the lower rack, have diamonds instead that allow both directions of movement?

what would happen if you inserted the green gears while the grey bars are not parallel? will it keep the same angle?

So cool

Now the same without gears

When attaching the green gears, you had to be careful to align the sticks correctly. But what would happen if you were to mount these at some other angles? That would likely be another thing a regular scissor linkage cannot do

If the gears changed size from one end to the other would it "reach out" faster at the distal end?

This was interesting. I'd be very interested in seeing more. I've been doing some work on linkages lately with computer graphics and paper models. My main source of information has been Cundy and Rollett's _Mathematical Models_ but by chance I found a book at a used book store on mechanical computing machines from shortly after 1945 with a lot of information on linkages. It's not so easy, especially for a non-mathematician such as myself.

Would love a collab with Arglin Kampling on how to replace gears with linkages!

What happens if you put only half of the gears ?

hello, the link seems dead, is there a way to get a 3d model for printing?

I think one of the causes for difference might be the lens distortion, it's much more visible with a fisheye lens, but even a normal lens slightly deforms the picture compared to the ideal.

You'd be able to close it tighter if it had 5 on an arm instead of 3...

Yes, I have made it out of Lego Technic almost 2 decades ago, I also found no use for it other than as a toy

I'm fascinated by Oskar van Deventer's Tailspin mechanism. I think it can be used as an example to help explain to children the expansion of the universe and how the farther away you observe, the faster it's epanding.

Oh, I think I just made a linkage that acts like a Gear.

Very interesting!

interesting! What would happen if you offset the grey geared linkages by one tooth each when assembling? They should then stay all at a slight angle to each other instead of staying parallel, so if I am not mistaken you should be able to make a shrinking/expanding circle then.

i was wondering if you had also made a version which used 3 intermediate gears per leg. it wouldn't fundamentally change how it functions at all, but it would allow it to fold in tighter. i also thought it might look pretty cool

sigh, gotta power up the 3d printer again

wise assembly of several sets of Cardan gears!

Can the geared scissor mechanism bend slightly so it forms an iris which expands and contracts?

would be good for puppetry or animation

I wonder if this could be useful in driving a scissor lift without an actuator Could gear a motor right on