Peaucellier Mechanism
Introduction

The Peaucellier–Lipkin linkage occupies a very important place in the history of kinematics of mechanics, it being the first planar linkage consisting only of revolute joints, that was capable of transforming rotary motion into perfect straight-line motion, and vice versa. It is named after its iventors,  Charles-Nicolas Peaucellier , a French army officer, and Yom Tov Lipman Lipkin, who came upon the idea indepent of each other. Lord Kelvin, upon seeing the mechanism, described it as "the most beautiful thing I have ever seen in my life".

The mathematics behind the Peaucellier–Lipkin linkage comes from the theory of inversion of a circle. The linkage is actually a combination of the same two four bar likages in with one in straight and another in crossed configuration and sharing a common link. A basic introduction to the theory of Inversion of a circle and its relation to the Peaucellier linkage follows.