in the mid-1700s the steam engine was of growing importance, and james watt realized that efficiency could be increased by using different cylinders for expansion and condensation of the steam. this drove his search for a linkage that could transform rotation of a crank into a linear slide, and resulted in his discovery of what is called watt's linkage. this led to the study of linkages that could generate straight lines, even if only approximately; and inspired the mathematician j. j. sylvester, who lectured on the peaucellier linkage, which generates an exact straight line from a rotating crank.