Automatic Design of Practical Fixtures

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

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Dexterous manipulation planning can be defined as the process of determining the joint trajectories for an articulated mechanical hand, such that, if executed, the hand would reconfigure the grasp into one known to be more desirable than the initial one. In this paper, we present a general methodology based on Desai's concept of contact formations [4] combined with a model of contact mechanics to solve the dexterous manipulation planning problem. If the model of contact mechanics supports the analysis of contact situations with multiple sliding contacts, then the method (in theory) can exploit this fact to solve problems not solvable if only rolling contacts are allowed. To highlight this feature, the method is used successfully to solve a frictionless planar example problem. 1

An implicit time-stepping scheme for rigid body dynamics with Coulomb friction

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

Stability characterizations of fixtured rigid bodies with Coulomb friction

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

Dynamic Multi-Rigid-Body Systems with Concurrent Distributed Contacts

. Consider a system of bodies with multiple concurrent contacts. The multi-rigid-body contact problem is to predict the accelerations of the bodies and the normal and 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 friction forces are consistent with the maximum work inequality. We present an existence and uniqueness result for this problem under some mild assumptions on the system inputs. The application of our results to three examples is discussed. Key Words. Multi-rigid-body contact problem, friction limit surface, maximum work inequality, linear complementarity, quasi-variational inequality. Any findings, conclusions, or recommendations expressed herein are those of the authors and do not necessarily reflect the views of the funding agencies. y The research of this author was based on work supported by the Nationa..

Complementarity Formulations and Existence of Solutions of Dynamic Multi-Rigid-Body Contact Problems with Coulomb Friction

. In this paper, we study the problem of predicting the acceleration of a set of rigid, 3-dimensional bodies in contact with Coulomb friction. The nonlinearity of Coulomb's law leads to a nonlinear complementarity formulation of the system model. This model is used in conjunction with the theory of quasi-variational inequalities to prove for the first time that multi-rigid-body systems with all contacts rolling always has a solution under a feasibility-type condition. The analysis of the more general problem with sliding and rolling contacts presents difficulties that motivate our consideration of a relaxed friction law. The corresponding complementarity formulations of the multi-rigid-body contact problem are derived and existence of solutions of these models is established. Key Words. Rigid-body contact problem, Coulomb friction, linear complementarity, quasi-variational inequality, set-valued mappings. 1 Introduction One of the main goals of the robotics research community is to a..

Dynamic Multi-Rigid-Body Systems with Concurrent Distributed Contacts: Theory and Examples

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

Performance of a Method for Formulating Geometrically Exact Complementarity Constraints in Multibody Dynamic Simulation

Contemporary problem formulation methods used in the dynamic simulation of rigid bodies suffer from problems in accuracy, performance, and robustness. Significant allowances for parameter tuning, coupled with careful implementation of a broad-phase collision detection scheme are required to make dynamic simulation useful for practical applications. A constraint formulation method is presented herein that is more robust, and not dependent on broad-phase collision detection or system tuning for its behavior. Several uncomplicated benchmark examples are presented to give an analysis and make a comparison of the new polyhedral exact geometry (PEG) method with the well-known Stewart-Trinkle method. The behavior and performance for the two methods are discussed. This includes specific cases where contemporary methods fail to match theorized and observed system states in simulation, and how they are ameliorated by the new method presented here. The goal of this work is to complete the groundwork for further research into high performance simulation