This paper addresses automatic assembly with passive rather than active compliant devices. Previous work has shown that in an ideal manufacturing environment three assembly primitives (prismatic insertions, threaded fits and general path insertions) exhibit a high level of difficulty. None of these are reliably assemblable under sensor-based force control or with an ordinary remote center compliance (RCC) device. In this paper, we extend the science of part mating and apply dexterity theory to synthesize a passive assembly device for precision fits of three-dimensional prismatic parts. This Spatial Remote Center Compliance (SRCC) obviates sensor-based and force control approaches to precision assembly of nonaxisymmetric parts.