It was reportedly designed by a couple of Westingouse Research Lab employees "during a long lunch hour", though improved, and actually built, by engineers at its Pittsbugh plant.
The Nimatron was not the giant robot used as an illustration on some web pages! This was actually Elektro, the "amazing Westinghouse Moto-Man", in the same pavilion. [The Christmas 08/09 issue of NewScientist has an interesting article on Elektro's story. That article also mentions a YouTube video of Elektro performing at the World's Fair]
Image reproduced, under Fair Use Copyringht provisions, from
The American Mathematical Monthly vol 49 (1942).
[Sorry about the quality of reproduction, but this is the only actual
photo of the machine I've been able to find.]