Abstract: A controlled relative motion system comprising a base support, a manipulable support, a group of link end constrainers each having a first portion movably connected to a second portion thereof so that ends of the first and second portions can be selectively separated from one another in a selected direction so as to have a selected distance therebetween, and two groups of pivoting links. With at least four link end constrainers in the group thereof, the first group of pivoting links has corresponding links each rotatably coupled to force imparting means or to the base support so as to be rotatable about a corresponding base link axis where each of said base link axes extend into regions between adjacent ones of said first group of pivoting links into which regions said base link axes of said adjacent ones also extend, and each coupled to a first portion end of a corresponding one of the group of link end constrainers.