Linkages have a long history ranging back to the 18th century in the quest for mechanical conversion between circular motion and linear motion, as needed in say a steam engine. In 1877, Kempe wrote an entire book of such mechanisms for "drawing a straight line". (In mathematical circles, Kempe is famous for an attempted proof of the Four-Color Theorem, whose main ideas persist in the current, correct proofs.) Kempe designed many linkages which, after solidification by modern mathematicians Kapovich, Millson, and Thurston, establish an impressively strong result: there is a linkage that signs your name by simply turning a crank. Over the years, mathematicians have revealed a deep mathematical structure in linkages. A surge of results over the past few years have intriguing applications to robotics, graphics, and protein folding. More details