# Rotation around an axis outside of the mechanism

I want to design a system of linkages that will allow me to rotate the green element around the blue point/axis without entering the red circle.

The green triangle to go fully around the blue point. I only need about 120 degrees.

I have seen examples of it being done (some provided below).

I don't want to build a robot arm :), so it has to be purely mechanical, preferably with only one rotating axis as an input.

What is this idea/mechanism/process called? I have trouble googling for it. Is there some kind of solver that would help me find relative lengths of all the linkages, etc.?

Some examples

Elephant Compliant Mechanism https://youtu.be/iAVV_7k79ZI?t=15

Six-bar linkage for stretch and turn https://www.youtube.com/watch?v=q8tVdjMo22E

• A free app, best on a tablet if you have one, or an Android emulator on a computer even youtu.be/by4-J-YeR9o – Jonathan R Swift Oct 13 '20 at 21:38
• Does the path need to be an exact circle around the blue pivot, or just travel generally 'around' the red object, with a slightly variable radius? – Jonathan R Swift Oct 14 '20 at 8:56

The design that you illustrated is pretty much correct. See below:

In order for the end to move along a circular path, you want a four-bar-linkage with equal length arms.

Note how the length of the medium grey linkages (60mm) is equal to the radius of the red circle (50mm), plus some clearance (10mm).

Note how the distance from the centre of the red circle to the upper fixed pivot is equal to the distance from tip ('green triangle') to the upper moving pivot. This means that when the arms are horizontal, the tip will be horizontal vs the red circle centre.

The vertical spacing between arms is not critical, but must be equal at each end - it will define the available range of motion if you have the arms on the same plane, as illustrated. This provides a convenient 'end stop' at the lower position.

• Wow, that is perfect. Thanks! – Allshar Oct 14 '20 at 19:36

This is a basic way of doing it. A rotating cam, attached to the triangle via a link through a bore in the reciprocating runner guide.

The runner guide goes back an force in a path made by 4 bearings and activated by an actuator. The sketch does not show some details for clarity.

It's just a starting point.

The program Solvespace may be of use to your project. The first example in a Solvespace video refers to the term 'mechanical linkage' and shows a circular path for one of the pivots of the linkage, while another part of the linkage describes a semicircular path.

As the 5/6 point travels on the semicircle, the 4/6 point travels in a circle.

You specify that you do not want the green triangle to enter the circle. Is it permitted to pass over the circle or under it?

Any set of links used to describe a circle will have to intersect the circle in some manner but the primary location would remain outside of that circle.

I suppose it's possible to modify the lengths of the links and add an extension to the "pointer" to keep it out of the red circle, but it would be necessary to experiment. I've spoken in the past with a mechanical engineer regarding the math involved in building a specific linkage and was told that the general method was try something, then try something else. Not particularly satisfying, that answer.

Solvespace is not particularly difficult to learn and other CAD-type programs may be able to perform similar manipulations for test purposes.

• That's for the software. I will look into it. Nothing should enter the circle. Same with going above or below. Crucial information I forgot to add is that I don't need the green triangle to go fully around the blue point. I only need about 120 degrees, so I don't need a huge "scissor" assembly that would extend around the whole thing. – Allshar Oct 13 '20 at 19:39
• With only 120 degrees, your objective becomes less challenging. – fred_dot_u Oct 13 '20 at 19:58

Another online resource you can try out is http://cadcam.eng.sunysb.edu/app/

• I think this should be a comment, rather than an answer :) – Jonathan R Swift Oct 14 '20 at 15:45