@Nicolas_Sassoon I have a uunitek idraw (cheaper than axidraw) and I've really liked it. Functional, easy, and you're not spending all your time on calibration. That said if money is no object just get an axi/nextdraw.
@maxflowminclout If you want to derive the algorithms yourself, read Richard Hofstadter's March 1981 Scientific America column Magic Cubology. (Also available now in the book Metamagical Themas.) It gives the group theory concepts and some notation without giving a full solution.