Model: S01 Exact Slider Crank Ellipse and Straight-line Linkage
The use of linkages to draw mathematical curves has a long history. The double slider crank or 'Trammel' mechanism for example (Model S-2), has long been used to draw exact ellipses. What is not well known is that a special form of the slider crank mechanism (Model C-2) will also draw an ellipse as well as an exact straight-line when the connecting link between the crank and the slider have equal lengths. The straight line is then generated by an extension of the connecting link by the length of the crank as shown in the model S-1.

A working model of this mechanism may also found in the Deutsches Museum in Munich in the Mathematics section. The description attributes the invention to Benjamin Bramer (1588-1652) c. 1600. However there is also credit for an ellipse drawing mechanism given to Leonardo da Vinci by Reuleaux (See Models D-10, D-12) as well as to a Dutchman von Schooten around the same period. This suggests that the idea of an ellipse drawing device may have been common knowledge among artists and mathematics in the Renaissance. There was great interest among artists in the use of geometry (e.g. perspective) in representing exactly real world objects. [See also tutorial on "How to Draw an Ellipse']

The use of straight-line mechanisms found application to power machines in the Watt-Boulton steam engines of the late 18th century. Their function was to translate the linear motion of the oscillating piston into the rocking motion of the balance arm. However Machine Age applications of straight-line mechanisms relied on linkages with cylindrical joints and not slider-crank mechanisms. Some of these pure linkage straight-line mechanisms are described in models S-14, S-24, S-31 and S-35.

Francis Moon 2003-07-01

Resources :