This paper presents a three-dimensional (3D) extension of our previous work on the synthesis of assemblies whose dimensional integrity is insensitive to the dimensional variations of individual parts. Assuming that assemblies can be built in the reverse sequence of decomposition, the method recursively decomposes a given product geometry into two subassemblies until parts become manufacturable. At each recursion, joints are assigned to the interfaces between two subassemblies to ensure the two criteria for robust dimensional integrity, in-process dimensional adjustability, and proper part constraints. Screw theory is utilized as a unified 3D representation of the two criteria. A case study on an automotive space frame is presented to demonstrate the method.