Introduction

If you have a collection of straight sticks that are pinned (hinged) to one another, then you can say you have a linkage like in the windshield wipers in your car or in some desk lamps. Linkages can also be robot arms. It is possible that our own arms caused people to start to think about the use of linkages.

In this paper I will discuss how linkages and other historical mechanisms (that involve sliding in groove or rolling circles) can be used for drawing different curves and in engineering to design machine motion. This knowledge was very popular at the end of the 19th century, but much of it was forgotten during most of the 20th Century. Now there is, among mathematicians and engineers, renewed interest in these mechanisms and in kinematics — the geometry of pure motion. Study of these mechanisms can be used in classrooms as a way to show interconnections between mathematics and technology and provide a bridge to interesting history that can bring meaning into the classroom. For examples, Descartes considered only those curves that could be drawn with mechanical devices. Curves were constructed from geometrical actions, many of which were pictured as mechanical apparatuses. After curves had been drawn, Descartes introduced coordinates and then analyzed the curve-drawing actions in order to arrive at an equation that represented the curve. Equations did not create curves; curves gave rise to equations. [10]