When the leg rods of a fully in-parallel manipulator are fixed in their lengths, it is usual that the device can be assembled in several distinct ways. Sometimes it happens that motion between such assemblies can take place such that the linkage is never at a special configuration; that is, a configuration where the moving-platform body acquires uncontrollable freedom relative to the base. The possibility of such motion has implications for control. Focusing on 3–3 devices, we present a geometric explanation of how these motions arise, and give a sufficient condition for their existence. For the 3–3 planar-motion device, we show that never-special assembly changing motions can be excluded by making platform and base triangles similar, and we conjecture that appropriate, perhaps identical, specialization for the octahedral manipulator has the same effect.