Tractional Motion Machines extend GPAC-generable functions

In late 17th century there appeared the Tractional Motion instruments, mechanical devices which plot the curves solving differential equations by the management of the tangent. In early 20th century Vannevar Bush’s Differential Analyzer got the same aim: in this paper we’ll compare the Differential Analyzer mathematical model (the Shannon’s General Purpose Analog Computer, or GPAC) with the Tractional Motion Machine potentials. Even if we will not arrive in defining the class of the functions generated by Tractional Motion Machines, we’ll see how this class will strictly extend the GPAC-generable functions.