Ah, no more suffering school ponies teaching kids how to post the trot! A mechanical horse is just what we needed!
This device, pictured in a 1916 issue of Popular Science Monthly, was being used to train British cavalry men. The caption says: "English cavalryman Astride 'Back Ache.' " I haven't heard of any recent use of such things - except mechanical bulls for training bull riders. But perhaps there are other mechanical horses still in use somewhere.