Robert Hooke's ‘universal joint’ and its application to sundials and the sundial-clock

Abstract

Robert Hooke is commonly thought of as the inventor of ‘Hooke's joint’ or the ‘universal joint’. However, it is shown that this flexible coupling (based on a four-armed cross pivoted between semicircular yokes attached to two shafts) was in fact known long before Hooke's time but was always assumed to give an output exactly matching that of the input shaft. Hooke carefully measured the relative displacements of the two axes, and found that if one were inclined to the other, uniform rotation of the input produced a varying rate of rotation of the output. He also recognized that this variable rate exactly corresponded to the movement of the shadow of a gnomon across the face of a sundial, as generated by the projection of the uniform motion of the Sun around an inclined polar axis. He therefore proposed that a ‘mechanical sundial’ might be made by coupling a 24-hour clock movement (with its hour shaft at the appropriate inclination) to a pointer via a universal joint. This proposal has been investigated both practically and mathematically, and shown to be valid. Hooke's studies of the universal joint caused it to be identified with his name, and it has ultimately proved far more important as a rotary coupling than as a sundial analogue. More complex versions subsequently designed by Hooke included provision for two basic couplings to be linked by an intermediate shaft. With appropriate setting of phase and shaft angles this ‘double Hooke's joint’ could annul the variable output velocity characteristic of the single universal. It has proved invaluable for modern automotive transmissions.