Talk:Straight-line mechanism

Cardan Gear

I propose another mechanism. I do not really have enough information to write an article (I am not even sure "Cardan Gear" is the correct name). [1], [2], [3]

Cardan Gear

Greetings --Jahobr (talk) 19:47, 28 May 2018 (UTC)

Linkage Diagrams Are Unclear

They show the resulting straight (or nearly straight) line, but not how the linkage is powered by a rotary source.

74.119.231.16 (talk) 16:18, 21 October 2019 (UTC)captcrisis

Linkage aren't really machines (they don't do work) - they're more a set of constraints made into physical form. All they do is limit how their parts move. Determining why the parts move isn't the topic of the linkage. If a linkage is useful, it can be incorporated into a more complex machine, like a crane or steam engine, and the responsibility for explaining how the machine is powered is part of the article about that machine. Often the power can be delivered to a different part of the linkage, depending on what task the machine is trying to achieve. So, for Watt's linkage for example, if you apply force to the cylinder (the linear moving part) L2, it produces rotating force at the two fulcra - which you can use to turn a wheel, and thus drive a locomotive. But apply force at a fulcrum, the linkage works to push the linear part back and forward, giving you a pump, or a crane, or a steam hammer. The job of explaining that belongs in the articles about steam engines or pumps. The linkage only constrains the geometry, and so the article about the linkage only talks about geometry. -- Finlay McWalter··–·Talk 16:58, 21 October 2019 (UTC)

Not responsive. The diagram should show the rotary motion as well as the resulting straight line. 74.119.231.16 (talk) 17:49, 23 October 2019 (UTC)captcrisis

New Linkages and Standardizing the Diagrams

Just before I go along, I do want to say that I greatly respect everyone who put in their work in creating many of the mechanisms used for this page. I've come to this page more times than I count for referencing on things. However, as I delved further into linkages as an amateur kinematician, I've noticed that this page is... much more outdated than I had first thought. So I went ahead and added a few new linkages to the list.

Categorization of the Kumara-Kampling linkage

Kumara-Kampling Inversor
Links of the same color are the same length.

One of the things that I've added is the Kumara-Kampling linkage. The linkage was originally created by a japanese person, Fumio Imai, just two years ago, and I made a few revisions to it to make it function in a more practical setting.

What I'm not entirely sure of, however, is where it should be categorized. Is it a quadruplanar inversor?

In terms of semantics, it shouldn't be: as the name 'quadruplanar' implies 'four planes', but all of the parts that make up the Kumara-Kampling inversor are links/bars, rather than planes. In terms of what's written in the article, it also shouldn't be, as it states that the point is "displaced sideways off the sides." However, it would technically count as quadruplanar as you could see it as just a triangle with its third point displaced along the links, making it essentially a triangle of zero height.

I'd like to hear people's thoughts on this on whether it should be grouped with them or if should just be kept standalone.

Continuing on...

Standardization of mechanisms

As I said above, I appreciate everyone's work in creating many of the diagrams, however what has never quite sat in me has been that the style of diagram for all of them is a bit... 'varying,' you could say.

Some of the diagrams are too small.

• The former Peacuellier-Lipkin linkage gif was a pretty heavy inspiration for how I standardized my gifs, though good lord it's tiny compared to the other mechanical diagrams, haha.

Some of the diagrams had a rather low framerate. This isn't a big deal but it is nice to have a better viewability.

• The framerate for the former Hoekens linkage gif was alright, but due to how low it was compared to how fast the crank was moving, it resulted in a really low resolution locus being drawn.

Some of the diagrams had some of the dimensions incorrect.

• The former Watt's Parallel Motion offsetted itself probably to make links easier to see, though that ended up just confusing me more as it didn't line up with the existing descriptions.
• The first Quadruplanar Inversor linkage actually has its yellow triangle in the wrong orientation, as the new third point on all of the triangles should form a parallelogram.

And some of the mechanisms, of course, just straight up didn't have a diagram at all.

So over the course of the past month or so, I've been coming up with a fairly reasonable standardization.

1. All Diagrams are made in GeoGebra.
   • Links are set to size 13 (maximum width)
   • Joints are set to size 5. Colored black by default. Point type is the colored dot with a black outline.
   • Ground Joints are set to size 6. Colored black by default. Point type is the cross.
2. Size for diagrams are a 646 pixels by 646 pixels square by default. (There isn't actually a reason as to why this is the case. I could've chosen 500x500 or some other value, but 646 for some odd reason stuck with me.)
   • Sides at a minimum have to be at least 646 pixels.
   • If a mechanism is too wide or tall for a square, change it to a 1.5:1 or 1:1.5 ratio (969 x 646 px or 646 x 969 px).
   • I have yet to come across a mechanism that requires even wider or taller ratios, but if required, just go by multiples of 323, starting from 646.
3. Parts of the same color have the same dimensions. This is the color pallete priorities I'm using in RGB:
   • Cyan - 26, 187, 178 - Usually the power source.
   • Pink - 247, 181, 236 - Indicates a bar that travels in a straight line, or is a connecting bar between two unique straight line output.*
   • Magenta - 255, 0, 140 - Indicates an output if two unique straight lines are formed from a single mechanism.
   • Orange - 233, 102, 46 - Indicates an output if two unique straight lines are formed from a single mechanism.
   • Amethyst - 167, 31, 255 - Indicates a slide and slider.
   • Gold - 255, 193, 82 - Larger than green links.
   • Lime - 124, 191, 114 - Smaller than yellow links.
   • Indigo - 103, 104, 180 - If really necessary, which it rarely should be.
   • Sky Blue - 164, 195, 239 - Not used yet, but can be.
   • Red - 189, 52, 48 - Not used yet, but can be.
   • Brown - 109, 81, 72 - Not used yet, but can be.
   • Blue - 54, 57, 218 - Not used yet, but can be (hang on how many unique links does your linkage have?!)
4. Most have the output animated in a sinusoidal motion. The only exception to this is the Sylvester-Kempe Inversor 3 (cyan crank rotates regularly) and Sarrus linkage the yellow links go WAY too fast if the output travelled sinusoidally, so I made it follow the function $1-\sin \left(x\right)^{4}$ which runs a lot more smoothly.
5. Framerate is 20 FPS.
6. Links that are planes rather than lines should be shaded in. (Refer to the Quadruplanar Inversor diagrams for an example.)

* This is still a bit inconsistent. I'll have to create a proper standard for this.

It's a pretty long list, and I'm curious to hear about thoughts on this as well. I'm open to suggestions! I'm also, of course, willing to make new linkages upon request from people, being this is quite a lot to follow, haha.

For now, I will be keeping Bryllig's gifs, as I think they are fantastic animations and it would take quite a long time for me to figured out how I can recreate them in GeoGebra. I may do it one day, but for now I am going to take a break, haha.

Most importantly, no hard feelings to everyone who made the previous diagrams. After all, I would've not been able to animate the majority of these without your help. I simply believed it was about time to give them all a unified update.

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Edit 1: Arglin Kampling (talk) 16:04, 11 April 2022 (UTC)

Additional note that Roberts linkage will be updated to match the style of the Quadruplanar Inversor, as I realized people were mistaking the triangular link as three separate links. It's not an issue in terms of its function, but it does also break the consistency. Will be fixed later.

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Edit 2: Arglin Kampling (talk) 06:04, 16 April 2022 (UTC)

I've also realized the Kumara-Kampling linkage should have the contraparallelogram part shaded in solid. Adding to queue.

One more thing that is not related to the diagrams but rather the way I actually write out the dimensions. I've recently taken inspiration from a friend who's a retired mechanical engineer: Nguyễn Đức Thắng. He's known mainly for his videos showcasing thousands of mechanisms in Autodesk Inventor. He usually writes his dimensions for links like the following:

• If it is a solid link: Red Link = $8$

• If it is a solid link, but with a bend or joint in the middle of it: Red Link = $6+2$

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Edit 3: Arglin Kampling (talk) 08:31, 30 April 2022 (UTC) Noticed a few errors I made while typing this, oops.

--Arglin Kampling (talk) 00:55, 11 April 2022 (UTC)

Natural fundamental first primitive: sweep function

It's about sweep here that "integers to unit interval" with "constant monotonic strictly increasing", it's about the first one there. (It's the first one.) 97.113.48.144 (talk) 09:17, 11 October 2022 (UTC)