# 4 bar mechanism simulator

I'm trying to design a jewellery box, with a mirror in the lid. When open, the lid should rest at an angle of about 135 degrees from original closed position.

I've been learning about 4 bar mechanisms, they sound appropriate (frame = box, coupler = lid) BUT in my case, the crank won't go through a full 360 degrees.

I've been using a simulator with crank=150, coupler=160, rocker=frame=225 but I need a way to model the start / finish positions to ensure everything lines up right.

Is there an app, or even a page full of math, covering the use of 4 bar mechanisms as a hinge? (I'm new to the mechanical engineering field, any help appreciated)

EDIT: The techniques of designing joint positions are apparently what I'm looking for. Mechanism synthesis (2- or 3-position synthesis) is the term to look for. It would seem I'm also going to need a full-blown CAD program, as compared to simple web-based apps I've been using

• Welcome to Engineering! This looks like a resource-hunting question. Such questions are prone to becoming out-dated, and are therefore considered off-topic for this site.
– Wasabi
Commented Oct 5, 2016 at 2:58
• @Wasabi Well not quite, true the asker asks for a simulator. But in reality OP does not need one just one of the methods for designing the positions of the joints. Also the method hasnt changed in more than a hundred years, and easily fits an answer so i do not think it will become obsolete very soon. Commented Oct 5, 2016 at 6:09
• @Wasabi added answer. Alan You should change the quetion slightly so it more easily conforms to the rules of the board and dont hint needing external resources because you do not need ones. Commented Oct 5, 2016 at 8:43

Reading your question leads me to belive that you are not really after a simulator at all! Instead you are looking for a mechanism synthesis method, which allows you to design the mechanism. A simulator only shows how the thing would work given measurements but does not help you into placing the joints that you need.

In your case one of the simpler synthesis methods is probably going to suffice, although there are many I would suggest that you use either 2 position or 3 position synthesis which are easy to make on your own all you need is a ruler and a compass, or a suitable drawing application/CAD.

The 3 position synthesis is a special case of the 2 position synthesis. So by teaching the 3 position method i will in fact teach you both. I do suggest you draw this is some CAD application as it makes it easy for you to parametrise the values as you may want to fiddle with the joint positions a bit to get a better result (any MCAD can do this). Let get started*:

1. Draw a linear span of what connect the joints on the lid. (You may want to draw the lid also so you can see how the entire thing behaves). This will be your first position, i suggest you start with lid closed. Name the joints so you know whet connects where (I will name the joints B1 and C1 for first position. I start with B so they the designed joints will get the name be A and D)

Image 1: Draw the first position (lid closed). Name the joints and position.

2. Draw the second position, say where the lid rests in open position.

Image 2: Draw the second position (lid open)

3. Connect the joints with lines. B1 to B2, C1 to C2. Find the midpoint on the connecting line and draw a perpendicular line at the midpoint. The joint A now need to be on any point at the perpendicular line that hits midpoint B1 and B2 while the joint D needs to be on the other line.

Image 3: Joints should be anywhere on line A or line D, you pick.

4. Due to the set being over constrained and the fact that i can not control the descent direction. I can take a 3rd position and repeat the above method. This will give me an answer that is fully defined. Since i want the lid to approach quite vertically it would be best to position it close to B1. Due to practical considerations on where the joint can be I'm going to place this into a virtual position that happens before open. Repeat steps (2-3)

Image 4: The second constraint forces the joints A and B to be in the position where the 2 constraints cross.

You still need to check that you havent got a degenerate solution. That's it. After doing this a few times i'm sure you have the ultimate positions. Go search your own solution. There are more sophisticated methods, but ultimately there is no perfect way to choose. It is always a bit open to human intuition, there are more solutions possible (but that's good this makes them patenttable). But 3 points synthesis should suffice for you. Like i said this is the place where you crack open your CAD as it makes it easy for you to explore the space

* I am drawing in illustrator so i can not easily remake the positions but if you use a CAD then it would be easy to just drag things until your position is good enough.

• Feedback welcome. Espeically if there are soem hard parts to understand. Commented Oct 5, 2016 at 8:40
• A great starting point for my education - thanks! I was hoping a basic web app would solve this: I'm reluctant to select & learn a CAD app just to design a freakin' hinge but them's the breaks I guess. Commented Oct 6, 2016 at 4:22
• @AlanCampbell well you need a CAD anyway to make drawings. It is mostly assumed if you make mechanical designs then you have a CAD application at hand. If you do not use paper ruler and compass and now that you know its called syntesis im sure you can find an app yourself. Software recommendation/external resources not being on scope. Note that since the fourbar has 2 solutions that it is possible that the solutions are crossed so that the other position is in the other fourbar configuration. Commented Oct 6, 2016 at 4:33