design is the four-bar linkage consisting of , and and the base link is , both joints on the framework of the engine. As the beam rocks, point (which is drawn to aid this explanation, but is not a marked point on the machine itself) describes an elongated figure-eight (more precisely, a lemniscate of Bernoulli) in mid-air. Since the motion of the walking beam is constrained to a small angle, describes only a short section of the figure-eight, which is quite close to a vertical straight line. The figure-eight is symmetrical as long as arms and are equal in length, and straightest when the ratio of to matches that of to . If the stroke length (that is, the maximum travel of ) is , then the straight section is longest when is around and is . It would have been possible to connect directly to the piston rod (the "Watt's linkage" design), but this would have made the machine an awkward shape, with a long way from the end of the walking beam. To avoid this, Watt added the parallelogram linkage to form a pantograph. This guarantees that always lies on a straight line between and , and therefore that the motion of is a magnified version of the motion of . is therefore the point to which the piston rod is attached. The addition of the pantograph made the mechanism shorter and so the building containing the engine could be smaller. As already noted, the path of is not a perfect straight line, but merely an approximation. Watt's design produced a deviation of about one part in 4000 from a straight line. Later, in the 19th century, perfect straight-line linkages were invented, beginning with the Peaucellier–Lipkin linkage of 1864. See also Pantograph, part of what the Parallel motion linkage uses. Straight line mechanism Watt's linkage, the core of how the Parallel motion linkage works. References General Linkages article in Encyclopædia Britannica, 1958. Parallel Motion article in Encyclopædia Britannica, 1911. Robert Stuart, A Descriptive History of the Steam Engine, London, J. Knight and H. Lacey, 1824. Further reading How Round Is Your Circle? (Bryant and Sangwin, 2008) contains a chapter about James Watt's parallel motion mechanism Beam engines Technical drawing Scottish inventions Linkages (mechanical) Straight line mechanisms