The first (relatively) large scale analog computer was the
'differential analyzer' invented and constructed at MIT by Vannevar Bush
(1890-1974) in the early 1930's. The machine was a completely
mechanical assembly of gears and shafts driven by
electric motors. The top picture shows Bush and his differential
analyzer in a U.S. Army laboratory during World War II.
The Bush differential analyzer is pictured in the science fiction movie Earth vs. the Flying Saucers (Columbia Pictures 1956), shown below. Click the control to see and hear the Bush DA working. It is a very short take, only a few seconds, and I doubt whether the machine was really capable of producing handwriting....
An even better take (in colour) of the differential analyzer appears in When Worlds Collide (George Pal 1951):
The still pictures were reproduced from IEEE Spectrum, July 1995. November, 2015