Inversor by Peaucellier

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The Peaucellier Inversor is a coupling gear for converting a circular movement into a straight line movement and vice versa. It is named after Charles-Nicolas Peaucellier , who invented it in 1864. Lipman Lipkin (1846–1876) discovered the same mechanism in 1871 independently of Peaucellier . Until the invention of this mechanism, there was no planar method of creating linear movements without using linear guides such as rail guides . The inverse z. B. in the construction of piston steam engines .

  • Animation of how the inverse works

  • The geometric basis of the inverse

functionality

Peaucellier's inverse is based on the inversion on the circle , which has the property of transforming circles into straight lines through the center of inversion. Because of this property, the Peaucellier inversor can also be used to construct a pixel under the inversion.

The inverse consists of two long rods (green, each with length a ) and four shorter ones (red, each with length b ), which are connected by joints. Here the joint where the two long green rods meet with O, the one where the blue one is connected to the two red ones with B and the one where only the two short red ones are connected with each other with D. Due to its construction, the joints B and D are inversely to each other, whereby the inversion circle has its center in O with a radius of . So if B moves on a circle through O (in the animation this is realized by the blue rod), point D moves on a straight line.

In practice, the joint B can only move on part of the circle, as the mechanism prevents it from coming as close as desired to the point O. Another problem in practice is the large number of joints.

literature

Web links

Commons : Inversor by Peaucellier  - collection of images, videos and audio files

Individual evidence

  1. ↑ Daina Taimina: How to Draw a Straight Line. Retrieved March 29, 2016.