Model: B02 Curved Triangular Rotor in a Square Chamber

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Reuleaux called the line or point contact between machine components "higher order pairs" in contrast to bodies in surface contact constraint. Here he constructed a curved triangle from an equilateral triangle with circular arcs whose centers are at the three vertices of the triangle. This figure is known as a "curve of constant width". While one's intuition might lead one to conclude that three points of contact of a plane figure would constrain the motion of the curved triangle in the square chamber, Reuleaux showed that it was possible for the object to rotate and slide since the three contact normals always meet at a point.

Some mathematicians have called this constant breadth, curved triangle the 'Reuleaux triangle'. This area can rotate between two parallel surfaces while maintaining contact or rotate in a square (B2), or rhombus shaped bearing without losing contact. Applications of this principle can be found in the positive return cams of models L1-L6. Variations of the constant breadth triangle based on an odd sided polygon of equal sides can be found in Reuleaux's book. The seven sided British 20p and 50p coins are applications of this principle. They can roll in a coin machine as if they were circular yet have a distinctive shape between one's fingers. This model may have inspired the Wankel rotary engine used today in a popular sports car.

Some mathematicians have called this constant breadth, curved triangle the 'Reuleaux triangle'. This area can rotate between two parallel surfaces while maintaining contact or rotate in a square (B2), or rhombus shaped bearing without losing contact. Applications of this principle can be found in the positive return cams of models L1-L6. Variations of the constant breadth triangle based on an odd sided polygon of equal sides can be found in Reuleaux's book. The seven sided British 20p and 50p coins are applications of this principle. They can roll in a coin machine as if they were circular yet have a distinctive shape between one's fingers. This model may have inspired the Wankel rotary engine used today in a popular sports car.

Francis Moon 2003-05-29

#### Reference :

- Reuleaux, Kennedy : Kinematics of Machinery (p.116, Art.22., 1876)
- Henderson, Taimina : Experiencing Geometry (ch.21, 2005)

#### Resources :

- Biography : Reuleaux, Franz
- Biography : Wankel, Felix
- CAD Model : Reuleaux B.02 Curved Triangular Rotor in a Square Chamber ( 2D Laser-cut Version ) CAD Files and Instructions
- Movie : B02. Curved Triangular Rotor in a Square Chamber
- Movie : Reuleaux B.02 Curved Triangular Rotor in a Square Chamber ( 2D Laser-cut Version ) Movie
- Movie : Reuleaux b2 swf
- Still Image : Reuleaux B.02 Curved Triangular Rotor in a Square Chamber ( 2D Laser-cut Version ) Picture
- Tutorials and Descriptions : Reuleaux Triangle