A landmark in the history of non-circular gears design: The mechanical masterpiece of Dondi's astrarium

The paper focuses on the contribution of the Italian clockmaker Giovanni Dondi (1330-1388). He authored the manuscript Tractatus Astrarii documenting, with text and drawings, the design and manufacturing phases of a very sophisticated astronomical clock. In particular, the manuscript contains one of the earliest documented procedures for the design of non-circular gears. Hence, the purpose of this paper is twofold: to call the attention of the mechanism community about these historically meaningful procedures and to offer insights on the kinematic structure of some relevant parts of Dondi's astronomical clock. In fact, detailed descriptions of the gear trains for tracking the motions of the Mercury planet and of the Moon are herein presented. In these gear trains non-circular gears have been used to account for the apparent irregular motion of the planets. Finally, it has been observed the correspondence between the average angular speeds of the gear wheels and those of the Ptolemaic model.