That's an interesting machine but I don't think anyone would have guessed it.
I found this about the Uni-horse. From what I can tell these machines were manufactured for a short time in the early 1960's in Great Britain....so jmurray01.....this one had your name on it as it was manufactured just a few hundred miles from Scotland.
I'm pretty sure there aren't any in this country, everything I found was in the UK. I figured it was of European design, but I was unable to find anything. I'm guessing there were only a few hundred produced.
As far as the engine goes it is rather large and by the sound of it had, a long stroke so maybe the piston was not all that large. Here's a good video.
Uni-horse Garden Tractor - YouTube
The Uni-Horse Tractor Company was, at least, at the end of its life, based in Droitwich in Worcestershire. The company was owned by the private family company Edward Williams Holdings, but was closed down in the 1970's. I am not sure if the Lee Francis Company designed the original, certainly I was not aware of this fact. The unit I just got going yesterday has a BSA engine and hydraulic actuation of the implement attachment.