One of the roadblocks to the rapid penetration of nanotechnology into new areas of commercialization is the dearth of existing design engineering tools that are applicable to nano-scale mechanical systems. While it is well known that nanosystems are governed by the laws of quantum mechanics, one needs more than the Schr�dinger equation for design engineering of nanosystems; one needs thoroughly vetted procedures that incorporate correct quantum mechanics. We seek to develop theoretical techniques for the design of mechanical molecular devices based on interlocked macromolecular complexes. A [3]rotaxane is such a complex that contains a long dumbbell-shaped molecule, (called the shaft) that threads two ring molecules. The three components are therefore chemically independent yet mechanically linked. If the shaft contains three or more potential binding sites for the rings, multiple co-conformations are possible, a molecular topological equivalent to an abacus. We address the question, how does strength of ring-binding to the shaft vary with respect to position on the shaft? Previous studies have found that a shaft with three binding sites exhibits strongest ring binding at the center site. Here a five-binding-site shaft is studied. We employ a novel method to partition the total energy of the system into contributions from inter-component binding and intra-component strain. The method uses the output of quantum mechanical electronic structure calculations to determine fitting parameters in a set of coupled equations. The solutions of the equations yield the energy partitioning. It is found that co-conformational preference is a compromise of ring strain and inter-component binding.