Compliant mechanisms for rigid part mating exist for prismatic geometries. A few instances are known of mechanisms to assemble screw threads. A comprehensive solution to this essentially geometric problem comprises at least three parts: parametric equations for nut and bolt contact in the critical starting phase of assembly, the possible space of motions between these parts during this phase, and the design space of compliant devices which accomplish the desired motions in the presence of friction and positional uncertainty. This work concentrates on the second part in which the threaded pair is modeled numerically, and contact tests are automated through software. Tessellated solid models were used during three-dimensional collision analysis to enumerate the approximate location of the initial contact point. The advent of a second contact point presented a more constrained contact state. Thus, the bolt is rotated about a vector defined by the initial two contact points until a third contact location was found. By analyzing the depth of intersection of the bolt into the nut as well as the vertical movement of the origin of the bolt reference frame, we determined that there are three types of contacts states present: unstable two-point, quasi-stable two-point, stable three point. The space of possible motions is bounded by these end conditions which will differ in detail depending upon the starting orientations. We investigated all potential orientations which obtain from a discretization of the roll, pitch, and yaw uncertainties, each of which has its own set of contact points. From this exhaustive examination, a full contact state history was determined, which lays the foundation for the design space of either compliant mechanisms or intelligent sensor-rich controls.
A Discretized Model for Three-dimensional Compliant Mechanisms in Dynamic Problems