Mathematical Model: Modified 4-Bar Lift

Ok guys, we need to make an algebraic equation to model the lifting path of a modified 4 bar, what do you think?

It might not be possible, but I’m thinking you insert the value of 4 constants, each of which represent the length of a certain bar in the 4 bar and then the value of a single variable that represents the degree of a certain bar relative to a certain bar that we have already set a length for. The function then would hopefully graph the path of the lift on a coordinate plane. I have little to no Idea how this would work, but I think we could do it.

I think we can do it guys.

Edit: and it would probably be easiest to base it off of Desmos


Math is my worst subject. Dont make me write an equation unless you want your robot to randomly start breakdancing.


Don’t worry, you’ll only make a virtual modified 4 bar start to break dance

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Hey! I wrote a report on this (it’s not super complete, I wrote it the night before it was due, it was a mess), but I think it talks a bit about what you’re trying to achieve. If you want, you can take a look over and see if there’s anything usable for you guys.

Yes, this was a school assignment that I did for marks. (IB HL math IA).

Anthony Luo IA.pdf (422.1 KB)


Since both bars are traveling along a circle you can just constrain two lines to the circumference of two circles with the radius of the lengths of the arms.

Here is a quick model i made, descriptions of each variable used in it should tell you what they change and by using the sliders you should be able to get the model you are looking for. Hope this helps.

edit: oops, used the wrong variable for one part, fixed now


Oh wow that’s really cool, I’ll have to look into that a bit further (still need to study/write 2 essays for English XD)

But I can’t help myself, I think I have figured out a way to do this. Going off of a line segment creator already available on the Desmos user (library)? I would be able to limit the points of each line based off of the radius of a circle, as @Zach_929U said, and then set the distance between the center of each circle as the length of the fixed bar. I would then just have to constrain the end of each of the lift bars to either end of the end bar. Then I could set the degree of one of the lifting bars using sin and cos.

Thankfully I’ve messed with circles before so I should be good.

It will still be difficult but since Desmos covers most of the back end we should be good.

I think I can get this done tomorrow after my Anguish English exam.

I guess I didn’t make this very clear in my first post, but I want to be able to change the length of individual bars. This is with the goal of being able to model the movement of a non-parallel 4 bar(probably incorrect term, but essentially a 4 bar with “uneven” sides) for various applications.

How about this one? You can change the lengths of the vertical and horizontal bars.

It doesn’t go below the x-axis, but if you want to imagine the lift mounted on a tower pointing down, you could multiply f1 and f2 by (-1).


I need to change the lengths of the horizontal bars independently as well as the vertical bars independently. It will be easy enough once I have some time to myself, but right now I have an exam to study for XD.



How about this? I mainly designed this to see what heights I can get from lifts of various settings. See the parameters folder for explanations of all the variables. Note that this only really works when L1 and L3 (the lengths of the parallel bars on each four bar) are the same. You can also animate a (by pressing the play button) to see how the lift looks when moving

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I made this one to model a regular 4-bar.

I just used linear functions and trig. I want to do one with more definite constraints later

Broooooo that is an insane IA… I just might do something like this now…

lol yeah do it! My IA got an IB grade of 5?

If you started not-the-night-before and went through the calculations slowly, and included a few more variables for center-of-hole and perhaps a midsection distance then you could get (probably) a(some) proper looking graph(s)!


Ok here’s an update with what I’ve got so far. I have the two moving bars ready. I just need to set a fixed length to the right most bar and find a way to set the rotation of the top bar, or alternatively set a fixed length to it w/out control over the rotation.

Here is the link:

If you have any tips for completing the final stretch of the project, please post them or even modify your copy of the project if you are up for it. Helpful criticism is also welcome.

Note: I’m going to take a break from this tonight and hopefully have it finished tomorrow with your guys help. I will still be available for response though.

Ok we are on the home stretch. I managed to set the rotation for the bars off of circles and then find the joint between the right and top bars using equations to find the intercepts of said circles. The only problem I’m encountering so far is that I am using way too many variables, but the deal is, I don’t think there is a way to shorten the equation.

Here is what I have so far:

I’ll try a few more things to hopefully get it working on my own, but again if there is any suggestion as to how we can get past this last hurdle, please post it, or if you know how to fix it, by all means fix it in your copy and post the link to your copy here.

Anyways, this will hopefully be the last update before it is complete!

They allowed that?!

The math dept in my sch thinks it is too easy to be an IA topic… sob…

Man I wish I could’ve picked this as my IA topic. We had ours preselected. Of course this was about 7-8 years ago…

Lol starting the night before is the worst fear from all my teachers…although my comp sci EE seems to take shape in that way. Thanks for the input, and I hope to not start the night before its due!

They did? As long as it deals with something commencorate to the difficulty of the course - mine was probably on the easier side though. Also canada education is not as op as singapore ;(

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