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Revisiting James Watt's Linkage with Implicit Functions and Modern Techniques

The engineer James Watt (1736–1819) was a pioneer of steam power in the United Kingdom. His practical work revolutionised the rather inefficient atmospheric engines of his predecessors such as Newcomen. He vastly improved these engines in a variety of ways so that steam power became the “prime mover” of his age. In doing so he accelerated the Industrial Revolution and helped to usher in the modern industrial era. In this article I want to re-examine a mechanism he invented to constrain the piston of a steam engine to move in a straight line. It consists of the simple linkage system illustrated in FIGURE 1. This may appear rather trivial to us now but with the rise of the importance of mechanical engineering during the Victorian period this, and related mechanisms, had many important applications. Such linkages still find many contemporary uses and modern research in robotics and flexible structures rely on the geometry which we are going to examine here.