Background
Challenge

Peaucellier-Lipkin linkage

What is it?

Berlin's Franz Reuleaux (1829-1905) created the world's largest collection of kinematic models at the Technical University of Berlin with over 800 models. These models were used to teach inventors and engineers about machines. While many of the models were destroyed during WWII, Reuleaux had authorized and supervised the reproduction of approximately 360 mechanisms by the Berlin model maker Gustav Voigt. Cornell's first president, Andrew Dickson White, acquired a collection of 266 Voigt-Reuleaux models for the university in 1882. These models were used for teaching machine design up until the 1970’s.

Now, a new generation of academics has again found these models useful for teaching and research. Today, at Cornell, Reuleaux's models are used in the teaching of design, dynamics, robotics, art, and architecture, as well as in historical research.

In November 2002, the Reuleaux Collection of Mechanisms and Machines at Cornell University was designated a National Mechanical Engineering Historic Collection by the American Society of Mechanical Engineers History and Heritage Committee (http://www.asme.org/history/hhc.html).

For more about the Cornell Reuleaux Collection, see Francis C. Moon, "The Reuleaux Collection of Kinematic Mechanisms at Cornell University" (July 1999): http://kmoddl.library.cornell.edu/facets/moon61899.htm

Around 1875, Reuleaux identified six basic mechanical components from which machines are built:
  1. The eye-bar type of link, called crank in kinematics;
  2. The wheel, including gears;
  3. The cam
  4. The screw for communicating motion and force;
  5. The ratchet, an intermittent-motion device
  6. The tension-compression organs, or parts having "one way rigidity", as belts (chains) and hydraulic lines.


Kinematics became popular in the 19th century as machine inventors learned to transmit information and forces from one element in a machine to another. The challenge to create input-output kinematic devices that could convert circular motion into noncircular, complex, three-dimensional, intermittent motions attracted both practical inventors as well as mathematicians. Thousands of mechanisms were invented, designed, and built.

Reuleaux's mission was to codify, analyze, and synthesize kinematic mechanisms so that engineers could approach machine design in a rational way. He laid the foundation for a systematic study of machines by defining clearly the machine and mechanism, determining the basic building blocks, and developing a system for classifying known as mechanism types.

How to Draw a Straight Line

According to Euclid "a straight line is a line which lies evenly with the points on itself." When solving this problem, you might suggest using a straight-edge. But the challenge is how can you know that your straight-edge is straight? How can you check that something is straight? What does "straight" even mean?



S35.jpgThe Peaucellier-Lipkin linkage was the first precise solution to the question "How can you draw a straight line?" Cornell university's Reuleaux kinematic model collection includes the Peaucellier-Lipkin linkage S35.

There were several attempts to solve this problem before Peaucellier. The Peaucellier-Lipkin linkage is noteworthy because when it was invented, mathematicians were beginning to think that designing a linkage to convert circular to linear motion was impossible.


Other linkages in the Reuleaux collection are connected with some of the names of 19th century mathematicians who tried to solve the problem of how to draw a precise straight line. Reuleaux thought that these mechanisms were so important that he designed 39 straight line mechanisms for his collection, including those of Watt, Roberts, Evans, Chebyshev, Peuaucellier-Lipkin, Cartwright and some of his own design. See all models in the S-series.

To see how the Peaucellier straight-line linkage works:Peaucellier-Lipkin linkage

Some history about linkages and discussion of the Peaucellier-Lipkin linkage can be found here





Peaucellier Straight Line Linkage by member JonHollander

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