Watt's Lemniscoidal Linkage

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Watt's linkage is a four-bar mechanical linkage with one degree of freedom. The linkage was developed to convert rotary motion into approximate rectilinear motion.


The linkage consists of a driver (left bar) and follower (right bar) linked by a coupler bar. While the driver and follower bars perform a reciprocating angular movement, a point on the coupler bar draws a lemniscoidal curve. This refers to a self-intersecting curve resembling a lemniscate. If the three bars have approximately equal lengths and the tracing point is the center of the coupler bar, the traced curve becomes an actual lemniscate with two almost rectilinear segments.

If you uncheck the "connect" box, the dots on the trace show the speed evolution of the coupler bar point with constant angular speed of the driver bar.

During the Industrial Revolution, Watt's linkage was used in the design of the first steam engines [1].


Contributed by: Erik Mahieu (September 2016)
Open content licensed under CC BY-NC-SA



Snapshot 1: if the three bars have similar lengths, the center of the coupler bar draws a lemniscate with two substantial, almost rectilinear parts


[1] Cornell University, Sibley School of Mechanical and Aerospace Engineering. "Model: S24 Lemniscoidal Linkage of the First Kind by Watt." (Sep 27, 2016) kmoddl.library.cornell.edu/model.php?m=145.

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