Mechanisms and Robotics Editor

As we move into the adolescent years of the 21st century, allow e to discuss where research in mechanisms and robotics has een as a prelude to considering where it is going. Polynomials Mechanisms have been characterized by the curves that they race since the time of Archimedes 1. In the 1800s, Reuleaux, ennedy, and Burmester formalized this by applying the descrip-ive geometry of Gaspard Monge to the analysis and synthesis of achines 2. Watt invented a straight-line linkage to convert the inear expansion of steam into the rotation of the great beam, aking the steam engine practical Fig. 1, and captured the magination of the mathematician Chebyshev, who introduced the athematical analysis and synthesis of linkages. About the same ime, Sylvester, who introduced the Sylvester resultant for the olution of polynomial equations, went on to lecture about the mportance of the Peaucellier linkage, which generates a pure lin-ar movement from a rotating link 3. Influenced by Sylvester, empe developed a method for designing a linkage that traces a iven algebraic curve 4 that even now inspires research at the ntersection of geometry 5,6 and computation. In the mid-1950s, Denavit and Hartenberg introduced a matrix ormulation of the loop equations of a mechanism to obtain poly-omials that defined its movement 7. During a speech in 1972, reudenstein famously used the phrase “Mount Everest of kine-atics ” to describe the solution of these polynomials for the 7Rom