Reuleaux Triangle

A closed plane curve, not actually a triangle, that consists of three arcs, each of which joins two vertices of an equilateral triangle and is part of a circle centered at the remaining vertex.


History of (Reuleaux Triangle)

Franz Reuleaux is the father of kinematics machine. He wanted to see how many constraints would it take to prevent a planar from moving. Reuleaux defined the constraints as lower and higher pairs. Lower pair is where the surface contact and in this case is the cylindrical bearing. The higher pair have line or point contacts between parts in this case it is the gear teeth. He found out that a three point constraints was not enough to prevent rotation of the object. He created an equilateral triangle in a square hole, and the object rotates perfectly in a circular motion.

Application of (Reuleaux Triangle)

The united Kingdom fifty pence and twenty pence coins have constant width. This helps reduce the problems associated with them becoming stuck in slot machines.
Another application of the Reuleaux triangle is the rotary rotor. In a traditional engine the piston reciprocates but in a rotary engine, as the name implies, direct circular motion is generated. This is done by taking a Reuleaux rotor and from the centre drilling a large hole to created an internal gear. This then rotates on a fixed gear. By symmetry it is clear that the three vertices of the rotor all move along the same path, and the gaps left allow the fuel to be injected, compressed, ignited and for the combustion products to expand and finally be expelled.

Rotary Engine


2.Automotive Engines: James D. Halderman, Page: 31-32.
3. York Tech Libary (Book)
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