Network Models of Mechanical Assemblies
Last modified: May 11, 2006
Mechanical assemblies can have as many as several hundred parts connected to each other in complex ways. A network representation makes parts into nodes and solid connections between parts into bilateral links. The average nodal degree of such networks almost never exceeds 4 and averages 3. The reason for this can be traced directly to the need to avoid kinematic over-constraint. A closed-form expression for average nodal degree based on kinematics bears this out. The assemblies studied also have negative degree correlation. The reason for this can be traced to the presence of a few highly-connected parts that bear the main mechanical loads, while the rest of the parts have low nodal degree conforming to the limitation imposed by avoiding mechanical over-constraint. These circumstances bias the degree sequence and force the degree correlation to be negative. In fact, for some assemblies, the bias is so strong that no degree-preserving rewiring can create a network with positive degree sequence.
Many network analyses of complex systems seek to identify clusters or modules and associate them with important functions of the system. For most mechanical assemblies, clusters may relate to subfunctions but the high level functions are associated with closed loops. These loops typically span or join the communities. They express the main kinematic or load-bearing functions of the system.
Thus, while these assemblies fit the description of “technological” networks and have the expected negative degree correlation, other features or motifs of their structure are more important in understanding their function.