Fixture Synthesis Research Articles

Declining neighborhood simulated annealing algorithm to robust fixture synthesis in a point-set domain

Fixture synthesis addresses the problem of fixture-elements placement on the workpiece surfaces. This article presents a novel variant of the simulated annealing (SA) algorithm called declining neighborhood simulated annealing (DNSA) specifically developed for the problem of fixture synthesis. The objective is to minimize measurement errors in the machined features induced by the misalignment at locators-workpiece contact points. The algorithm systematically evaluates different fixture layouts to reach a sufficient approximation of the most robust layout. For each iteration, a set of previously accepted candidates are exploited to direct the search toward the optimal region. Throughout the progress of the algorithm, the search space is reduced and the new candidates are designated according to a declining probability density function (PDF). To assure best performance, the DNSA parameters are configured using the Technique for Order Preference by Similarity to Ideal Solution (TOPOSIS). Moreover, the parameters are set to auto-adapt the complexity of a given input based on a Shanon entropy index. The optimization process is carried out automatically in the computer-aided design (CAD) environment NX; a computer code was developed for this purpose using the application programming interface (API) NXOpen. Benchmark examples from industrial partner and literature demonstrate satisfactory results.

Multi-Objective Approach to Automated Fixture Synthesis Incorporating Deep Neural Network for Deformation Evaluation

Multi-Objective Approach to Automated Fixture Synthesis Incorporating Deep Neural Network for Deformation Evaluation

Recent developments on machining fixture layout design, analysis, and optimization using finite element method and evolutionary techniques

A review of the recent development of the machining fixture configuration/layout is presented in this paper. The literature review is mainly focused on the recently developed optimal fixture configuration under the dynamic conditions of the workpiece. In this review paper, the fixture design, fixture analysis, fixture synthesis, fixture layout design, optimization of fixture layout design, various optimization algorithms, and case studies of two- and three-dimensional workpiece geometries under dynamic conditions have been emphasized specially. The further scopes of the research are finally summarized.

Efficient Procedures for Form-Closure Grasp Planning and Fixture Layout Design

This paper presents an algorithm for optimal grasp planning and fixture synthesis. The object surface is depicted by a number of discrete points, which are used as the candidate contact points. This algorithm consists of two procedures. The first procedure selects a minimal subset of contacts from the candidates so as to construct a form-closure grasp or fixture, which is to determine a minimal subset of contact wrenches such that their convex hull forms a simplex containing the origin of the wrench space as an interior point. The second procedure adjusts the contact positions or alters the selected contact wrenches to maximize the minimum distance from the origin to the facets of the simplex, which enhances the capability of the grasp or fixture to immobilize and balance the object. As this algorithm does not employ any general optimization techniques and utilizes recursive formulas for most computations, it runs very fast. Its effectiveness and efficiency are demonstrated with illustrative examples.

A review of computer-aided fixture design with respect to information support requirements

This paper lays the foundation for an integrated representation for advanced computer-aided fixture design (CAFD) systems through a systematic comparative analysis of the existing CAFD systems. Significant work done in the CAFD field, the different methods used for each design phase, their working principles, and the information modeling requirements are presented. Information flows are developed through identification of CAFD phases (problem definition, fixture synthesis, and fixture analysis), of the effective methods for each, and of their input/output traffic. This survey is used to establish the representation and information requirements for integrated CAFD leading to a novel representation scheme. Specifically, the information types required include geometric information, locator information (number, type, orientation, and position), material properties, machining information (tool paths), applied forces, tolerance requirements, and displacement (errors).

A Polyhedral Bound on the Indeterminate Contact Forces in Planar Quasi-Rigid Fixturing and Grasping Arrangements

This paper considers multiple-contact arrangements where several bodies grasp, fixture, or support an object via frictional point contacts. Within a strictly rigid-body modeling paradigm, when an external wrench (i.e., force and torque) acts on the object, the reaction forces at the contacts are typically indeterminate and span an unbounded linear space. This paper analyzes the contact reaction forces within a generalized quasi-rigid-body framework that keeps the desirable geometric properties of rigid-body modeling, while also including more realistic physical effects. We describe two basic principles that govern the contact mechanics of quasi-rigid bodies. The main result is that for any given external wrench acting on a quasi-rigid object, the statically feasible contact reaction forces lie in a bounded Polyhedral set that depends on the external wrench, the grasp's geometry, and the preload forces. Moreover, the bound does not depend upon any detailed knowledge of the contact mechanics parameters. When some knowledge of the parameters is available, the bound can be sharpened. The polyhedral bound is useful for robust grasp and fixture synthesis. Given a set of external wrenches that may act upon an object, the grasp's geometry and preload forces can be chosen such that all of these external wrenches would be automatically supported by the contacts

Multi-objective optimal fixture layout design

This paper addresses a major issue in fixture layout design to determine and evaluate the acceptable fixture designs based on multiple quality criteria and to select an optimal fixture with appropriate trade-offs among multiple performance requirements. The performance objectives considered are related to the fundamental requirements of kinematic localization and total fixturing (form-closure). Three performance objectives are defined as the workpiece localization accuracy and the norm and dispersion of the locator contact forces. The paper focuses on multi-criteria optimal design with a hierarchical approach. An efficient interchange algorithm is extended and used for different practical cases, leading to proper trade-off strategies for performing fixture synthesis. Examples are given to illustrate empirical observations with respect to the proposed approach and its effectiveness.

Optimizing fixture layout in a point-set domain

This paper describes an approach to optimal design of a fixture layout with the minimum required number of elements, i.e., six locators and a clamp. The approach applies to parts with arbitrary 3D geometry and is restricted to be within a discrete domain of locations for placing the fixture elements of non-frictional contacts. The paper addresses two major issues: 1) to develop an efficient algorithm for fixture synthesis in the point set domain; and 2) to evaluate the acceptable fixture designs based on several performance criteria and to select the optimal fixture according to practical requirements. The performance objectives considered include the workpiece localization accuracy, and the norm and dispersion of the locator contact forces. An interchange algorithm with random initiation is developed. Also, the fixture performance characteristics are evaluated to understand their tradeoffs. The importance of the accurate localization and the contact force balance is discussed.

An optimum design for 3-D fixture synthesis in a point set domain

Addresses the problem of fixture synthesis for 3-D workpieces with a set of discrete locations on the workpiece surface as a point set of candidates for locator and clamp placement. A sequential optimization approach is presented in order to reduce the complexity associated with an exhaustive search. The approach is based on a concept of optimum experimental design, while the optimization focuses on the fixture performance of workpiece localization accuracy. In using the D-optimality criterion to minimize the workpiece positioning errors, two different greedy algorithms are developed for force-closure fixturing in the point set domain. Both 2-D and 3-D examples are presented to illustrate the effectiveness of the synthesis approach.