I've unsuccessfully been looking for a decent proof of Chasles' Theorem which states that any rigid body displacement whatsoever can be decomposed into a screw motion. In other words, no matter what the displacement is, you can consider it the result of the partiles having moved to their positions by following a circular helixical path about a common axis, with a common angular speed. I suppose I'm mostly looking for a (linear) algebraic type proof. Most proofs I've encountered have been fairly loose and unconvincing. Does anyone know of a solid proof of this theorem? Awkwardly, this theorem is also variously known as Mozzi's or Cauchy's screw theorem.