  We propose a new method for constructing rational spatial Pythagorean
Hodograph (PH) curves based on determining a suitable rational framing motion.
While the spherical component of the framing motion is arbitrary, the
translation part is determined be a modestly sized and nicely structured system
of linear equations. Rather surprisingly, generic input data will only result
in polynomial PH curves. We provide a complete characterization of all cases
that admit truly rational (non-polynomial) solutions. Examples illustrate our
ideas and relate them to existing literature.
