Curved Triangle Variation in a Square
- Title:
- Curved Triangle Variation in a Square
- Title (German):
- Gleichschenkliges Bogendreieck im Quadrat
- Collection:
- Reuleaux Kinematic Mechanisms Collection
- Set:
- B. Higher Element Pairs
- Designer:
- Reuleaux, F. (Franz), 1829-1905
- Manufacturer:
- Gustav Voigt Werkstatt
- Date:
- 1882
- Country:
- Germany
- Voigt Catalog Model:
- B4
- File Name:
- B04.jpg
- Work Type:
- Mechanical model
- Materials/Techniques:
- cast iron and brass on wood pedestal
- Subject:
- Kinematics of Machinery
- Measurement:
- 239 x 247 (millimeters, width x depth)
239 x 262 x 471 (millimeters, width x depth x height) - Description:
- Higher Element Pairs; Reuleaux Triangle_Curve of Constant Width. 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. [Francis Moon 2001-00-00]
The 220 models in Cornell University’s Reuleaux Collection were built in the late 19th century to demonstrate the elements of machine motion, as theorized by the German engineer Franz Reuleaux. The University acquired the models in 1882 for use in teaching and research. The Reuleaux models are classified according to the alphanumeric schema employed in the catalog of the manufacturer, Gustav Voigt. The letter in a model's ID (e.g., B14 or S35) refers to a class of mechanism; the number is a specific instance of the class. This classification scheme is a simplified version of the taxonomy of machine elements elaborated in Reuleaux's work. - Repository:
- Sibley School of Mechanical and Aerospace Engineering, Cornell University
- Format:
- Image
- Rights:
- Photography credit: Jon Reis (www.jonreis.com). Jon Reis Photography grants Cornell University Libraries and the Cornell College of Engineering the rights to display copyrighted images of the Reuleux collection of kinetic machines on the Cornell University and National Science Digital Library web sites and for unlimited use in Cornell University Library publications for education purposes only. Rights for all other uses, including but not limited to, editorial, commercial, advertising, web use and display by third parties not affiliated with Cornell University are reserved by the photographer. The written permission of any copyright and other rights holders is required for distribution, reproduction, or other use that extends beyond what is authorized by fair use and other statutory exemptions. Responsibility for making an independent legal assessment of an item and securing any necessary permissions ultimately rests with persons desiring to use the item. For questions about this item or other items please contact the Physical Sciences Librarians at pslref@cornell.edu.