# How to trace a square with a reuleaux triangle

I am trying to trace a square (with rounded corners) using a reuleaux triangle and a single (circular rotation) motor. I've seen many animations (example) of this but do not understand how to make it.

A diagram or geogebra file in the answer would be extremely helpful. Thanks!

Now I'm not positive if I am correct with this but from the example and some thinking I have an educated guess of how this could be calculated.

Starting with your square with rounded corners, and an equilateral triangle with side lengths that are equal to the lengths of the square.

To calculate the arcs of the reulaeaux triangle I believe you would use the following formula.

r = (H/2) + [(W^2)/(8*H)]

H = [W sqrt(3)]/2


Where r is the radius of the arc of the reuleaux triangle. W is the length of the square edges.
H is going the be the radius of the corners of the square.

I'm not 100% positive yet but if someone could check this out for me I would be grateful.

Hopefully this helps!

EDIT: Under further review of this I've noticed that the relationship between a reuleaux triangle and a square with rounded corners is very specific (only 1 square will work with a specific triangle). I've updated my above formula and believe that this is the correct correlation between the two.

• Hi I am trying to recreate this mechanically, in other words i have a releaux triangle and i'm trying to make it trace a square. – Ankit Sep 28 '20 at 23:22
• So you're looking for what the center path of reuleaux triangle would be? – JoshL Sep 29 '20 at 13:35
• No I am looking for how to use a reuleaux triangle to trace a square. Please look at the animation I included to understand what I need. – Ankit Sep 29 '20 at 13:42
• So you mean yes then to the center path of the triangle. Because without that or the outer edge of the square you would not be able to trace the square. – JoshL Sep 29 '20 at 13:52
• oh ok I understand what you mean now, yes that is what I am looking for. – Ankit Sep 29 '20 at 17:38