This is a novel that I think I remember reading somewhere in the 1990s courtesy of my brother (who does not remember the book). Only a few details are coming to mind at the moment. It's a male protagonist. Something was not quite right with his legs, which led to him being nicknamed Frog or Leapfrog due to his usual method of locomotion, which consisted of pushing off from his legs to his hands and vice versa. Something happens and he winds up moving between a number of worlds. There was a part which stuck with me where he's in a bottomless hole and finds he keeps falling faster and faster without end.

I will try to remember more details, but that's what is in my head.