Publications

Fixtures are tools used to hold parts in specific positions and orientations so that certain manufacturing steps can be carried out within required accuracies. Despite the importance of fixtures in the production of expensive devices at Sandia National Laboratories, there is little in-house expertise in mathematical design issues associated with fixtures. As a result, fixtures typically do not work as intended when they are first manufactured. Thus, an inefficient and expensive trial-and-error approach must be utilized. This design methodology adversely impacts important mission duties of Sandia National Laboratories, such as the production of neutron generators. The work performed under the support of this LDRD project took steps toward providing mechanical designers with software tools based on rigorous analytical techniques for dealing with fixture stability and tolerance stack-up.

Consider a system of rigid bodies with multiple concurrent contacts. The multi-rigid-body contact problem is to predict the accelerations of the bodies and the normal friction loads acting at the contacts. This paper presents theoretical results for the multi-rigid-body contact problem under the assumptions that one or more contacts occur over locally planar, finite regions and that friction forces are consistent with the maximum work inequality. Existence and uniqueness results are presented for this problem under mild assumptions on the system inputs. In addition, the performance of two different time-stepping methods for integrating the dynamics are compared on two simple multi-body systems.

This paper formally introduces several stability characterizations of fixtured three-dimensional rigid bodies initially at rest and in unilateral contact with Coulomb friction. These characterizations, weak stability and strong stability, arise naturally from the dynamic model of the system, formulated as a complementarity problem. Using the tools of complementarity theory, these characterizations are studied in detail to understand their properties and to develop techniques to identify the stability classifications of general systems subjected to known external loads.

In this paper a new time-stepping method for simulating systems of rigid bodies is given. Unlike methods which take an instantaneous point of view, the method is based on impulse-momentum equations, and so does not need to explicitly resolve impulsive forces. On the other hand, the method is distinct from previous impulsive methods in that it does not require explicit collision checking and it can handle simultaneous impacts. Numerical results are given for one planar and one three-dimensional example, which demonstrate the practicality of the method, and its convergence as the step size becomes small.