Bibliography Abstracts G through L
Home : Tolerancing Bibliography : G through L : Abstracts G through L

Garcia, Christopher J.
Automating GD&T Quality, June 1988, pp. 56-57.

Keywords: GD&T, Automation

Abstract: An excellent technique for manufacturing quality.

Garrett, R.E. and Allen S. Hall, Jr.
Effect of Tolerance and Clearance in Linkage Design Journal of Engineering for Industry, ASME, February 1969, pp. 198-202.

Keywords: Linkage Tolerances

Abstract: In designing a linkage transform one motion into another motion, consideration is given to the design sensitivity by analyzing the difference between the function generated by an ideal model of the mechanism and a model which incorporates manufacturing tolerances and clearances. The effects of these tolerances and clearances are presented in the form of mobility bands for the linkages.

Gauntet, Dominique
Vectorial Tolerancing Model Proceeding of 3rd CIRP Seminars on Computer Aided Tolerancing,Cachan,France,April 27-28,1993,pp. 25-50

Keywords: Dimensioning and tolerancing, Assembly, offsets, Stacks, Dimensions transfer, Technologically and Topologically Related Surfaces (TTRS), Minimum Geometric Datum Element (MGDE), Tolerancing Torsor

Abstract: In this paper we present a model for dimensioning and tolerancing mechanism parts. This work is based upon the Technologically and Topologically Related Surfaces and Minimum Geometric Datum Element concepts. We introduce the torsor tolerancing concept. Dimension transfer can be done with this model, for a part.
For a mechanism, the model gives a warranty about assembly and minimal defined stacks. Minimal and maximal offsets between mechanism parts can also be evaluated.

Gavankar, P., Bedworth, D.
Stacked Tolerance Analysis and Allocation Using Assembly Models 

Abstract: Allocation of appropriate tolerances is critical to ensure that components fit right and function satisfactorily in an assembly involving stacked components. There are numerous techniques available today to model assemblies on a computer. What is lacking is a common platform to make use of these computer models in order to perform tolerance analysis and allocation. This paper describes a technique to automate tolerance analysis and allocation of an assembly involving components stacked one on another represented in the boundary form. An algorithm is developed to track dimension loops in the stacked assembly. Statistical tolerance analysis and allocation is then performed on these interrelating dimensions and tolerances encompassed by a dimension loop. Advantages and limitations of this technique are compared against the manual method to conduct tolerance analysis and allocation.

Gavanker, Prasad, Henderson, Mark R.
Graph-Based Extraction of Protrusions and Depressions from Solid Models Graph-based Feature Extraction-CAD Journal Submission,Fri. Jul 28, 1989

Keywords: Solid Model, CAD, CAM

Abstract: Manufactured parts can be mathematically defined as solid models. The part definition data in the form of a solid model typically describes the geometry and topology of a part modeled on a CAD system in low level primitive boundary elements (faces, edges and vertices). These elements can be used to drive atuomated engineering analyses, but are typically at a level which is too low to be of use by the analysis procedures. Redefining the part in terms of its pertinent high level features can improve the efficiency of automated analysis. Automated recognition of the particular features of the part is a first step toward achieving CAD/CAM integration.The most complete computer representation of a part is a solid model. Three distinct classes of representing a solid model are: decomposition models, constructive models, and boundary represenation (MANT88). Decomposition models represent a point set as a collection of simple objects from a fixed collection of primitive object types, combined with a single "gluing" operation. Constructive models represent solid model as a collection of point sets, commonly known as primitives. Cylinders, cubes, tetrahedrons are examples of such primitives. In a boundary model, the solid is defined in terms of its boundary elements such as faces, edges, and vertices. This paper deals with the boundary representation (Brep) of a solid model.

Giesecke, F.E., Mitchell, A., Spencer, H.C., Hill, I.L., Loving, R.O.
Engineering Graphics, Second Edition Macmillan Publishing Co., Inc., Chapter 12 and appendix pp. 335-353, 822-829

Keywords: General Drafting Practices

Abstract: Chapter 12: Tolerancing

Giordano, Max, Duret, Daniel
Clearance Space and Deviation Space Proceeding of 3rd CIRP Seminars on Computer Aided Tolerancing, Cachan, France, April 27-28, 1993,pp. 179-196

Keywords: Clearances, Trouncing for function, Three-dimensional Trouncing

Abstract: The clearance between two assembled parts is represented by a volume in the small displacement space. The set of allowable deviation between a theoretical surface associated to a real part surface, and its nominal position, is also represented by a volume in the small displacement space. The composition of deviations and clearances in an assembly is translated into topological operations on these volumes. It is, in fact, an extension to the three-dimensional case of the notion of chains of dimenions, which consists of the composition of clearances and deviations. The method is illustrated by three examples. The requirement for assembly is verified for parts whose dimensions and geometric tolerances are known.

Gladman, C.A.
Manual for Geometric Analysis of Engineering Designs Australian Trade Publications,1966

Keywords: Tolerance examples

Abstract: This manual is concerned with that stage in the development of and engineering product where the functional design has been proved, the performance specification established and the design is to be made ready for production. This is the "design for production" stage where the function of each component part of the assembly is analyzed for size, form and geometric relation, where design modifications are made, where tolerances are determined, and where the objective is to secure the best compromise between the requirements of function, production, inspection, installation, use and service.

Gladman, C.A.
Techniques For Applying Probability to the Tolerancing of Machined Dimensions National Standards Laboratory Technical Paper No. 11, 1959 (Australia)

Keywords: Statistics, Tolerance

Abstract: Two general types of problems arising in the geometric analysis of engineering designs are discussed, one being concerned with chains of toleranced dimension and the other with toleranced products and quotients. The general method adopted involves calculating the probable maximum deviation for the dependent variable from the estimated standard deviations for the independent variables, assuming that the dependent frequency distribution is normal. A design factor is introduced which, when multiplied by the half-tolerance, enables an estimate to be made of the required standard deviation for a dimension. Values for the design factor are explored first in the case of machining a dimension with process variability less than the tolerance and with uniform tool wear across the field, and secondly in the case of machining a dimension with process variability greter than the tolerance.These two cases are used as a basis for recommending safe design factors for general use with the machined dimensions. The validity of the assumptions is discussed and three examples given to illustrate the application of the techniques.

Gladman, C.A.
Applying Probability in Tolerance Technology Transactions Institute Engineering Austral. Mech. Engr. Vol. ME5, No. 2, 1980, p. 82-88.

Abstract: A general approach to the geometric analysis of engineering designs is developed and presented in a form practicable for the application of probaility using design factors related to frequency distributions for the production processes. Design factors are established for three general types of design tolerance problems covering feature tolerances, geometry tolerances and the play between two assembled features. Simplified formulae are developed for use where appropriate; and the case is discussed where variables are not independent. The techniques are illustrated by application to a particular engineering product.

Gossard, D.C., Zuffante, R.P. and Sakurai, H.
Representing Dimensions, Tolerances, and Features in MCAE Systems Computer Graphics & Application, March 1988, pp. 51-59

Abstract: We present a method for explicitly representing dimensions, tolerances, and geometric features in solid models. The method combines CSG and boundary representations in a graph structure called an object graph Dimensions are represented by a relative position operator. The method can automatically translate changes in dimensional values into corresponding changes in geometry and topology. The representation provides an important foundation or higher level application programs to automate the redesign of assemblies and to automate tolerance analysis and synthesis. We implemented a prototype interactive polyhedral modeler based on this representation.

Greenhow, J.N. and Butterworth, N.A.
Tolerancing of Components for Assembly. Engineering Designer V.6, pp.26-29. March 1980

Abstract: In this article, the authors develop tolerance relationships based upon rectangularly distributed populaitons and compare them with existing relationships, which are in the main based upon statistical techniques. This work shows that, even when unlikely component distributions are considered, the tolerances on assemblies given by the relationships developed are less than those obtained using conventional 'safe' tolerancing techniques.

Greenwood, W. H. and Chase, K. W.
A New Tolerance Analysis Method for Designers and Manufacturers J. of Engineering for Industry, ASME, vol 109, May 1987, pp.112- 116

Greenwood, W. H. and Chase, K. W.
Worst Case Tolerance Analysis with Nonlinear Problems J. of Engineering for Industry, ASME, vol 110, Aug. 1988, pp. 232-235

Griffith, Gary
Tolerancing symbols Quality, June 1984, pp. 91-92

Keywords: Tolerance Symbols

Abstract: Some industrial drawings use American National Standards Institute Y14.5M tolerancing methods. This tolerancing method uses symbols for geometric control instead of worded notes. Thes symbols are easily learned because they generally take the shape of the geometric characteristic under consideration.

Grossman, D.D.
Monte Carlo Simulation of Tolerancing in Discrete Parts Manufacturing and Assembly. Stanford Artificial Intelligence Laboratory Memo AIM-280 Computer Science Department Report No. STAN-CS-76-555, May 1976

Keywords: Monte Carlo

Abstract: The assembly of discrete parts is strongly affected by imprecise components, imperfect fixtures and tools, and inexact measurements.

Guilford, James
GEOS Tolerance Analysis: Examples July 2, 1992

Abstract: This document describes several examples of tolerance analysis using GEOS. The examples chosen reflect several purposes: to illustrate how GEOS can be used in different situations, to show the range of capabilities of GEOS, and to list test cases than can be used to verify GEOS's operation.

Guilford, James, Sethi, Mani
Tolerance Analysis of CATIA Models Using the GEOS Key User's Guide for GEOS Version 1.4.0., March 11, 1992

Abstract: The GEOS tolerance analysis package is designed to be attached to a variety of solid modeling systems, which act as an interface to GEOS. This allows designers access to GEOS's capabilities while remaining in an environment with which they are familiar. One such system is CATIA.This report is a user's guide to CATIA interface to GEOS. It describes the concepts needed to effectively use GEOS, and then presents a tutorial example illustrating these ideas.

Guilford, James, Turner, Joshua
Advanced Tolerance Analysis and Synthesis for Geometric Tolerances CRTD-Vol. 27,International Forum on Dimensional Tolerancing and Metrology,ASME,Dearborn,Michigan,June 17-19,1993,pp. 187-198

Abstract: With the increasing trend towards replacing engineering drawings with solid modeling systems, a means is needed for integrating tolerances within the solid modeling framework. Before this can be done, however, a clear understanding is needed of what a tolerance is and how it can be analyzed.This paper compares parametric and geometric tolerances. It then describes the theory behind the GEOS tolerance analysis system, which is designed explicitly to handle geometric tolerances.
The GEOS system integrates a tolerance analysis capability within a solid modeler. The solid modeler actually defines a complete variational model; the tolerances become constraints on the geometric variations. This allows GEOS to derive relationships between the variational model and the tolerances, and between the variational model and the design function being analyzed. Using linear programming techniques, the numerical relationship between the design function and the tolerances can be derived.
Tolerance analysis is the process of taking known tolerances and computing their effect on a particular design function. Tolerance synthesis is the process of taking some desired behavior of the design function along with suitable models relating tolerances to manufacturing cost and computing a set of tolerances which minimize the cost. Instead of working from fixed limits on the design function, the GEOS system considers variations of the design function from nominal as a cost associated with a "quality loss" function from Taguchi. The tolerance synthesis algorithm then attempts to minimize the total cost, which is the sum of the manufacturing cost and the cost due to the quality loss.

Gutmann, Fredrick T.
Limits and Fits by The Numbers and Letters Mechanical Engineering, November 1987, pp. 68-72.

Keywords: Cylindrical Fits

Abstract: A standard system of dimensions and tolerances can ensure proper fits.

Hahn, G. J., and S. S. Shapiro
Statistical Models in Engineering John Wiley & Sons 1967

Abstract: Fundamental text on advanced statistical methods, describes use of Pearson & Johnson systems as well as random number algorithms by Monte Carlo simulation.

Hambleton, Fred
Extracting Data from Mainframe CAD Systems December 1988,Mechanical Engineering,pp. 60-61

Keywords: CAD, Data Structure

Abstract: Access software that runs on a PC has taken much of the pain out of a process that once could be compared to the pulling of teeth.

Hanka, W.
Equations Predict Chance of Misfit in Assembly Product Engineering, May 26, 1958, pp. 61-63.

Keywords: Tolerance, Assembly, Reject, Estimation

Abstract: Tight tolerances aren't always necessary-sometimes you can gamble on wider ones that save money and will often work satisfactorily. But before gambling, know the odds. Uniform distributions.

Harry, Mikel J. and Reigle Stewart
Six Sigma Mechanical Design Tolerancing Publication No. 6s-2-10/88, Motorola Corporation, 1988

Keywords: Statistical Tolerancing, Tolerance Synthesis, Process Capability

Hasofer, A.M., Lind, N.C.
Exact and Invariant Second-Moment Code Journal of the Engineering Mechanics Division, ASCE, Feb. 1974, pp. 111-121

Keywords: Advanced Statistics, (Other)

Heath, H.H.
Statistical Tolerancing of Engineering Components: Is it Worth It? Precision Engineering, 1979 p. 153-156.

Keywords: Tolerance, Statistics

Abstract: It is often claimed that if statistical methods were applied to engineering tolerances a worthwhile relaxation of accuracy would be possible. In this paper some typical cases are examined to show what advantages could result from the use of statistical tolerancing. A worthwhile gain can be obtained only in comparatively few situations.

Held, David O.
Assembly Variation Analysis: Liberty's Process Driven Design Tool for Quality SAE Technical Paper Series, 880606International Congress and Exposition, Detroit, MI, Feb 29 - Mar 4, 1988

Keywords: Monte Carlo Simulation

Abstract: The purpose of this paper is to describe the technical components that support the Assembly Variation Analysis group at the Liberty Development Center of Chrysler Motors. A short chronicle of these elements is presented, as well as a summary of the benefits afforded the user when these tools are properly utilized "up-front' in the advance engineering process.
This is followed by an example of a practical application of these tools to a major assembly process under development at Liberty. An analysis of the simluation results, and a brief outline of future developments is offered.

Also discussed is the development of a graphics program to enhance the simulation software presently used.

Henzold, Georg
Comparison of Vectorial Tolerancing and Conventional Tolerancing Michigan, June 17-19, 1993, CRTD-Vol. 27, International Forum on Dimensional Tolerancing and Metrology, ASME, pp. 147-160

Abstract: Coordinate measuring machines probe points of the workpiece surface. They store the coordinates of these points and evaluate the parameters of the workpiece geometry by calculation using appropriate computer programs.This method enables to achieve a new approach to assess the workpiece geometry called vectorial dimensioning and tolerancing which is dealt with in ISO TR 10- 360-1 (under preparation).
This new method is described. The differences between this method and the usual conventional method according to ISO 286, ISO 1947, ISO 5459, ISO 1101 etc. are shown. The advantages and disadvantages of each method are explained.
The vectorial method defines the components of size and geometry to be influenced in the manufacturing process in a clear and distinct way. It enables proper manufactruing control. The vectorial method separates form deviations from orientation deviations. Thereby it provides proper means to specify particular functional requirements, e.g. of kinematic linkages.

Hernla, Michael
Calculation of Measuring Uncertainty with CMMs under Industrial Conditions Proceeding fo 3rd CIRP Seminars on Computer Aided Tolerancing, Cachan, France, April 27-28, 1993, pp. 171-178

Keywords: Measuring Uncertainty, Principle of Propogation of Measuring Uncertainty, Admissible Uncertainty, Golden Rule of Production Measuring Technics, Measurable Tolerances.

Abstract: Every mathematically described geometric feature can be evaluated by CMMs. The results are including measuring deviations, which can be described by measuring uncertainty. Its size depends on uncertainty of measured points or features as well as on the geometric relations between them.The deviations of parameters are usually limited by tolerances. To assure measuring accuracy, the measuring uncertainty is not allowed to exceed the admissible one, which is a fixed share of tolerance. The ratio between them is always the same for all results. The equations of propagation of uncertainty can also be used to calculate measurable tolerances.
In this way it is possible to establish tolerances for various geometric features on complete workpieces with the same geometric accuracy not only based on experience, but also on mathematical principles.

Hillier, Frederick S. and Lieberman, Gerald J.
Introduction to Operations Research Holden-Day, Inc., 1986.

Hillyard, R.C.
The Build Group of Solid Modelers. IEEE Computer Graphics of Appl., March 1982, pp. 43-52

Keywords: Solid Model, B uild 2, Romulus Design

Abstract: Build 2, Design, and Romulus are solid modelers with evolutionary links. Consideration of their characteristics and histories yields some general insights into solid modeling.

Hillyard, R.C. and Braid, I.C.
Characterizing Non-Ideal Shapes in Terms fo Dimensions and Tolerances. ACM Computer Graphics,V. 12, W3, 1978, pp. 234-238

Abstract: A geometric model of a shape is extended so as to represent not only its nominal dimensions but also tolerance information and surface specifications. The data structure defining an object is visualised as a pin-jointed, infinitely elastic wire frame covered by elastic membranes. Constraints corresponding to the dimensions of technical drawings are applied to the structure, either by the designer or by an automatic dimensioning algorithm. The validity of the resultant scheme can be checked and then drawn using drawing office conventions. The data structure can handle dimensions fixing various types of curved surface; other types can easily be added by following the same rules. A method of changing the nominal shape of an object is demonstrated. These results provide a systematic and tolerancing, and should make the draughting process more amenable to computation.

Hillyard, R.C. and Braid, I.C.
Analysis of dimensions and tolerances in computer-aided mechanical design. Computer-Aided Design-Volume 10 number, 3 May 1978, pp. 161-166

Abstract: The paper sets forth a theory to explain how dimensions and views combine to specify the shape of a mechanical component. It provides a method to determine whether a component is under, over, or exactly defined by a given dimensioning scheme. Measures for assessing the quality of a scheme are proposed. A solution is offered to a problem of tolerancing: given a toleranced dimensioning scheme, find the resulting tolerances between undimensioned parts of a component.

Hochmuth, R.; Meerkamm, H.; Schweiger, W.
An Approach to a General View on Tolerances in Mechanical Engineering; 2nd International Workshop on Integrated Product Development IPD 98; Magdeburg; 1998; pp. 65 - 76.

Keywords: Compliant assemblies, flexible assemblies, variation management

Abstract: In this paper an approach will be made to a general view on tolerances in mechanical engineering, especially on tolerancing and optimising tolerance specifications by five major strategies.

To improve the quality of a product the tolerancing problem may not be seen isolated, also adjoining subjects have to be considered, as the stiffness and elastic deformation of machine parts, the construction structure, manufacturing processes, the assembly of components and the use of a product (multi-criterial optimisation). One of the possibilities is the use of tolerance controlled constraints.

These consequences of the product tolerancing will have to be investigated by the designer during the design process. Therefore, computer supported tools, which are integrated into an Engineering Workbench (overall architecture) to support the activities of the designer in each stage of the product development process, help to solve design conflicts.

Hocken, Robert J., Raja, (Jay)araman, Babu, Uppliappan
Sampling Issues in Coordinate Metrology CRTD-Vol. 27, International Forum on Dimensional Tolerancing and Metrology,Dearborn,Michigan,June 17-19,1993,ASME,pp. 97-112

Abstract: Coordinate measuring machines acquire data one point at a time on the surfaces of the parts being measured. These data must be analyzed in order to produce a substitute geometry to be compared to the design intent. Algorithms are used to analyze these data. The results obtained are strongly dependent upon measuring errors, the form error of the part, the sampling strategy, and the density of points sampled. In this paper we review these problems and discuss some of the progress addressing them during the past few years.

Hoeprich, Michael R.
Geometric Variation Effects on Rolling Element Bearing Life. Michigan, June 17-19, 1993, CRTD-Vol. 27, International Forum on Dimensional Toleranicng and Metrology, ASME, pp. 167-176

Abstract: Variations from the nominal geometry in bearing components, combined with those of housings and spindles, provide a variety of interactions affecting the fatigue life of bearings. While tapered rolling element bearings do not appear to be complex devices, determining bearing fatigue lives can be very involved. The large number of components in a bearing and the wide variety of application conditions result in numerous possibilities of internal load distribution. To avoid unfavorable stresses, minute modifications to the basic conical shapes of tapered rolling element bearing componenets must be made to accommodate the elastic deflections occuring in bearings and machinery components during operation. These modifications to the rolling surfaces are designed for the expected ranges of load and other application conditions. The calculation of contact stresses between the rolling elements and races is the basic starting point for determining bearing fatigue life. Since bearing fatigue life is related to contact stresses raised to the 6.66 power, chanes in contact stressesfrom desiredlevels and distributions can have a significant effect on life. Geometric variations in bearings, housing, and spindles can alter loads on bearing rolling elements and change the distribution of contact stresses along the lengths of the rolling elements. The degree to which these geometric variations influence fatigue life is affected by the elasic deflections in bearings, housing, and spindles when the machinery is being operated. Some geometric variations become less important and others become more important as load increases. Since machinery generally operates at a variety of load levels, the determination of tolerances may require the evaluation of their net effect over the entire load cycle.

Hoffmann, Peter
Analysis of tolerances and process inaccuracies in discrete part manufacturing. Computer-Aided Design, Volume 14 number 2 March 1982, pp. 83-ff.

Abstract: This paper discusses basic problems of tolerancing mechanical parts. The problem of part design analysis (determination of consistency, determinacy and stability) is reduced to the analysis of systemes of linear inequalities. It is shown that the calculation of resulting tolerances between components of parts can be easily solved by linear progamming. A method is provided for the construction of a system of inequalities which the working dimensions and inaccuracies of machining operations must satisfy if a given tolerance specification is to be met.

Hook, Richard
Keynote Address, Interaction of Dimensioning, Tolerancing, and Metrology CRTD-Vol. 27, International Forum on Dimensional Tolerancing and Metrology,ASME,Dearborn, Michigan, June 17-19, 1993

Abstract: This Forum is concerned with two activities that need to be better understood and integrated. They are specifying dimensions and tolerances for workpiece designs to capture and preserve design intent, and measuring actual workpieces to determine conformance with the specifications and design intent. The need for standards to govern dimensioning and tolerancing became apparent more than fifty years ago, but companion standards for measurement were not thought necessary until the 1980s, when coordinate measuring machines brought 'measurement divergence' to the force as a central problem. Work aimed at resolving measurement divergence and related matters accelerated after a 1988 Workshop brought the problems into public view, and new tolerancing and metrology standards are now emerging. This Forum will review the accomplishments to date, and consider what additional steps may be needed.

Hopp, Theodore H.
Computational Metrology CRTD-Vol. 27,International Forum on Dimensional Tolerancing and Metrology,ASME,Dearborn,Michigan,June 17-19,1993,pp. 207-218

Abstract: Coordinate measuring systems (CMSs) assess length-based characteristics of mechanical parts by measuring points on the part surface and analyzing the point data. Data analysis software can contribute significantly to the total measurement error of a CMS. Factors affecting software performance include the choice of analysis method, the quality of the software, and characteristics of the specific measurement uncertainty of a CMS.This paper describes research at NIST on computational metrology. Metrological questions fall into two categories: (1) the proper choice of data analysis objective for a particular application and (2) the performance of the implementation. Our research goal is to develop the basis for a national standard in the U.S. for CMS software performance evaluation. We are implementing a Special Test service to be offered through the NIST Measurement Services Program. The service is based on a black-box model of software, in which the internal structure of the software and the choice of solution methods are assumed to be unknown. The model identifies a number of error sources for data analysis software. We are designing test methods for identifying the methods for identifying the various components of the model and how those components relate to measurement uncetainty in inspection applications.

Humienny, Zbigniew
Language for Dimensional Analysis: The conception of a formal language for structure notiaon in selected, configurations of dimensional chains and system of this language's operational use Proceeding of 3rd CIRP Seminars on CAT, Cachan, France, April 1993, pp. 249-266

Keywords: Dimensioning, computer aided tolerancing, dimensional, chains, redimensioning, dependent dimension.

Abstract: The basic principles of a formal language for notation and analysis of the structure in configurations of simple dimensional chains and configurations of flat dimensional chains with common datum feature linear dimensioning are presented. Dimensions given on engineering drawing are coded in the matrix notation. Algorithms which can detect redundant dimensions and generate equations of any dependent dimensions are briefly described. In the conclusions the potential of the methods introduced are discussed as well as proposals for the future directions of investigations.

Hummel, K.E., Wolf, M.L.
Integrating Expert Systems With Solid Modeling Through Interprocess Communications and the Applications Interface Specification Computer in Engineering,ASME,Vol. one,1990,pp.355-360

Abstract: Arguably the most elusive problems to automate in engineering are those that require a large degree of spatial reasoning. One of the most significant reasons for this has been the lack of appropriate software tools with which to perform research and development. The optimal software environment should integrate the symbolic reasoning capabilitiess of a solid modeling system. This paper describes such an environment, developed using interprocess communications and a standardized solid modeling interface language. This integration has resulted in a seamless coupling that provides an exprt system with dynamic access to the full power of a solid modeling system. The details of the interprocess communications protocol, the solid modeling interface language, and the data dependency tracking technique are discussed.

Hura, C.M., Caron, N.O., Kanik, J.A. and Hunt, W.A.
SAE Technical Paper Series SAE Paper 881245

Hurt, James
Tolerance Analysis with a Variational Geometry System 

Abstract: This document outlines the theory used to design and develop the Tolerance and Sensitivity Analyis option for The Mechanical Advantage, a commercial Variation Geometry system. Its purpose is to describe what is computed in this option and to outline areas where further research is needed. No attempt is made to describe how anything is computed, but only what is computed and why.

Hurt, James
A Taxonomy of CAD/CAE Systems Manufacturing Review, ASME, Vol.2, No-3, September 1989, pp. 170-178

Abstract: This is a taxonomy of computer aided design (CAD) and engineering (CAE) systems thta are designed for use by mechanical, design and manufacturing engineers. This taxonomy looks at two characteristics of these systems: how the system handles geometric dimensionality; and how the system handles topology; and how each combination of these characteristics supports various types of engineering analysis. How a system handles geometric dimensionality considers the type of geometry that the system handles; where a system is in the range from two-dimensional to constructive solid geometry are stored (remembered by the system: where a system is in the range from fixed geometry to variational geometry. Geometry is where the objects are located, and topology is why they are located there.

Iannuzzi, Mark, Snadgren, Eric
Tolerance Optimization Using Genetic Algorithms: Benchmarking with Manual Analysis CIRP/JSPE/ASME Proceedings of the 4th CIRP Seminar on Computer Aided Tolerancing,The University of Tokyo,Tokyo,Japan,April 5-6,1995,pp.245-262

Keywords: Genetic Optimization, Tolerance analysis, Simultaneous engineering

Abstract: A computational design methodology is presented which permits the optimal allocation of tolerances for mechanical assemblies. A nontraditional genetic optimization method is coupled to a Monte Carlo based tolerance analysis. The objective is to determine the maximum tolerance zone value fo reach nominal feature while simultaneously meeting all critical dimensional and functional constraints imposed upon the design. A discretization of possible tolerance zone values is performed and a global search is conducted using a genetic algorithm. The goal is to develop a comprehensive software tool which can support dimensional variation decisions from concept through design, manufacturing, assembly and inspection. Three industrial problems are considered and the best solution generated by a manual method for each problem is compared to the solution generated by the optimizer. The results demonstrate the current capability of the approach and provide direction for future development.

Inui, Masatomo, Miura, Masahiro
Configuration Space Based Analysis of Position Uncertainties of Parts in An Assembly CIRP/JSPE/ASME Proceedings of the 4th CIRP Seminar on Computer Aided Tolerancing,The University of Tokyo,Tokyo,Japan,April 5-6,1995,pp. 155-172

Keywords: Tolerance modeling, Tolerance analysis, Configuration space

Abstract: A configuration space based method for analyzing position uncertainties of two parts in an assembly is proposed if certain shape variations of individual parts are allowed by tolerances. Proposed method is applicable to 2 dimensional polygon models of machine parts, for example sections of polyhedron parts in an assembly. The analysis is achieved by calculating a variation bound of the configuration of the parts if nonnominal parts allowed by the tolerance satisfy the positioning condition in an assembly. Different from the prior approach, our method does not assume any specific deviation types of the nonnominal part. An algorithm for computing the variation bound is developed and the configuration uncertainty of some sliding joints in the positioning mechanism is analyzed. Computational experiments suggest that the visualized image of the bound is developed and the configuration uncertainty of some sliding joints in the positioning mechanism is analyzed. Computational experiments suggest that the visualized image of the bound of the configuration variation is helpful for understanding the positioning characteristic of the joint.

Inui, Masatomo, Otto, Harald, Kimura, Fumihiko
Algebraic Interpretation of Geometric Tolerances for Evaluating Geometric Uncertainties in Solid Modeling 2nd ACM Solid Modeling, 1993-5

Abstract: Geometric tolerances specify the allowable limit of manufacturing imperfectness from the ideal design geometry. An actual feature is acceptable if it can be contained within the spatial tolerance zone. An unambiguous representation of the possible variation of the allowed actual feature is required for the development of computer-aided tolerancing sytems. A general definition of the geometric tolerance is used as our basis, which includes the form, orientation, and position tolerances in the standards. Based on geometric characteristics of machined surfaces, and actual feature model is initiated as small position and orientation variations of boundary faces of the nominal solid. The spatial constraint imposed on the acceptable feature is interpreted as a containment condition of the actual feature model by its corresponding portion of the tolerance zone. This condition is systemically derived in terms of linear inequalties based on the polyhedral approximation of the tolerance zone boundary. This paper discussed theoretical aspects of the method. Implementation of the system and evaluation of its applicability for analyzing machine parts with complex tolerance specifications are considered as following steps in our future work.

Ioannou, Yiannakis A. and Eyada, Osama K.
A Diagnostic Tolerance System Computers Ind. Engng Vol. 17, Nos 1-4, pp. 27-30, 1989.

Abstract: This paper describes a Diagnostic Tolerance System (DTS) designed to allow users to interactively select the appropriate class of fit and perform tolerance analysis for an assembly. The DTS is written in C programming language for a micro-computer and can be interfaced with CAD software, such as AutoCAD and CADkey. With the DTS, the productivity of designers is enhanced and design for manufacturability is easier to achieve.

Jablokow, Andrei G., Uicker, John J. Jr., Turcic, David A.
Topological and Geometric Consistency in Boundary Representations of Solid Models Advances in Design Automation-1990,Vol. 1,ASME Publication No. DE-Vol. 23-1, Proceedings of ASME Design Automation Conference, Chicago, IL Sept. 16-19, 1990,pp. 59066

Keywords: Solid model

Abstract: This paper describes a method of verifying the consistency between the topology and geometry of boundary representation (B-rep) of solid models. This verification is well suited for implementation as an algorithm and has been implemented as such in a polyhedral boundary representation solid modeling system (Jablokow 1989). Information regarding boundary representations is typically divided into the geometry and topology. It is important that the two are consistent for a valid solid model. In this work the genus of an object is calculated topologically and geometrically and then compared to verify the consistency of the solid model. The genus of an object gives insight as to the geometric complexity of the object. This is equivalent to verifying the Gauss-Bonnet Theorem for the model, and is discussed in the paper.

Jamieson, Archibald
Introduction to Quality Control Reston, Reston,VA. 1982

Keywords: Process tolerance data

Abstract: Cost of process tolerance, Chap. 1

Jensen, C., Helsel, J.
Engineering Drawing and Design McGraw-Hill Book Co., Second Edition, pp. 70-84, Chapter 5.

Keywords: True position tolerancing, GDT, Cylindrical fits, Machine tolerances

Abstract: Limits and Tolerances

Johnson, N.L., and J. O. Kitchen
Biometrical Tables for Statisticians Cambridge University Press, 1976

Keywords: Empirical Distributions

Johnson, R.H.
How to Evaluate Assembly Tolerances Product Engineering, Jan. 1953, pp. 179-181.

Keywords: Basic Assembly Analysis

Abstract: General rules and examples of how to evaluate the effects of component tolerances on their overall assembly and thus assign more realistic limits. The cases discussed include those of components which are combined into assemblies by simple addition, multiplication and non-linear functions.

Kanai, Satoshi, Onozuka, Mamoru, Takahashi, Hidetomo
Optimal Tolerance Synthesis by Genetic Algorithm under the Machining and Assembling Constraints CIRP/JSPE/ASME Proceedings of the 4th CIRP Seminar on Computer Aided Tolerancing,The University of Tokyo,Tokyo,Japan,April 5-6,1995,pp.263-282

Keywords: Tolerance synthesis, tolerance optimization, genetic algorithms, geometrical dimensioning & tolerancing, differential coordinate transformation, CAD, cost-tolerance model

Abstract: The designing of tolerance greatly affects the functions and manufacturing cost of mechanical assemblies. The purpose of this research is to develop a computer aided method of three dimensional tolerance synthesis. The assembly was represented by solid model, and dimensional and geometrical tolerances were formulated as a set of inequalitites constraining substitute features. Differential coordinate transformation and linear programming were used to analyze the dimensional features, tolerance ranges, machining and set-up costs. Tolerance synthesis was represented as the applied to solve the problem. The coding method and genetic operators were discussed. The algorithm was evaluated through the tolerance synthesis for the gear box.

Kanayama, Sunshine
Taguchi Rules in some Japanese Standardizations of Tolerancing CIRP/JSPE/ASME Proceedings of the 4th CIRP Seminar on Computer Aided Tolerancing,The University of Tokyo,Tokyo,Japan,April 5-6,1995,pp.229-244

Keywords: Tolerancing, Taguchi loss function, Taguchi method, Taguchi quality engineering, Plastic part tolerance, calibration, measurement, Japanese Industrial Standard

Abstract: Three Japanese Industrial Standards and a Standard Draft are issued on tolerancing, incorporating Taguchi rules. Reference Table of the standard JIS K 7109-1986 tabulates thirty-nine operation tolerances for plastic parts in field as compared to the tolerance by the standard. Careful review proves that Taguchi quadratic loss function shall be modified to a higher-order one to meet with the actual cases, as well as proves that Taguchi tolerance is independent of the part population but guarantees the part quality not enough. The supplier's expense for care of the customer's objection, the dole, and the customer's duty depend on the population strongly. The population shall be more centered and more narrow compared to the tolerance. The Standard Draft is to extend this standard to any part value other than dimensions, yet no actual data available. The other two standards, JIS K 0971-1989 for microvolumeter and JIS Z 9090-1991 for measurement system, describe commonly known principles such as that of mean square errors sum or so, incorporating Taguchi rules only auxiliarily. Incorporation of the rules or the way in standards being promoted strongly, but the profound thought and the fine mathematics shall be reviewed more accurately and more precisely, and restated concisely and legibly.

Kane, Victor E.
Process Capability Indices Journal of Quality Technology, Vo. 18, No 1, January 1986, pp. 41-52

Keywords: SPC, Process capability

Abstract: The capability indices Cp, CUP, CPL, k and Cpk are presented and related to process parameters. These indices are shown to form a complementary system of measures of process performance, and can be used with bilateral and unilateral tolerances, with or without target values. A number of Japanese industries currently use the five indices and the US automotive industry has started using these measures in a number of areas. Various applications of the indices are discussed along with statistical sampling considerations.

Kase, Kiwamu
An Evaluation of Geometrical Errors by Segmentation with Fitting Form Error Features. CIRP/JSPE/ASME Proceedings of the 4th CIRP Seminar on CAT, Japan, April 5-6, 1995, pp. 357-365

Keywords: Geometrical Error Evaluation, Segmentation and Fitting for Scattered Data, Bezier Template, Simulated Annealing Method

Abstract: Geometrical errors after manufacturing processes are conventionally evaluated by maximum width of tolerance zones which envelop actual features. Details of error shapes within such zones should however be investigated when the designer studies relation between errors and functionality of a product, or when he wants to compare and examine manufacturing methods in quest of high accuracy of machined surfaces.We propose a new method for the evaluation of form errors from a series of points data such as measuring points form product surfaces. This evaluation consists of two parts: 1. Form error features which consists of error models (Bezier Template) and error conditions 2. Segmentation by fitting of form error features are realized by the Simulated Annealing Method, a statistical optimization method which can search for the global minimum combinational solution. Using our method, the designer fitting Form Error Features as a substitute. This leads to functional tolerancing.

Kececioglu, D., Lamarre, G.
Mechanical Reliability Confidence Limit Journal of Mechanical Design, 1978,pp. 607-612

Keywords: Probabilistic Design, Reliability

Abstract: Charts are presented relating the lower one-sided limit on the reliability, R (L1), to the effective sample size, n (e) calculated from the sample size used to estimate the failure governing stress and strength distributions, or f(s) and f(S) respectively, and a factor K which is a function of the estimated means and standard deviations of f(s) and f(S). These graphs cover an n(e) range of 5 to 2000, confidence levels of 0.80, 0.90, 0.95, and 0.99, and lower one-sided limits on the reliability of 0.85 to 0.9(14)5. The equations used to develop these charts are derived and two examples of their applications are given.

Kennedy, Clifford W. and Andrews, Donald E.
Inspection and Gaging M.F. Spotts in 3 books

Abstract: A training manual and reference work that discusses the place of inspection in industry; describes the types of automatic and manual gaging and measuring devices employed; shows the proper techniques of using inspection equipment; and outlines the various duties of inspection personnel.

Kim, S H, Lee, K
An Assembly Modelling System for Dynamic and Kinematic Analysis Computer-Aided Design,v.21,N1,Jan/Feb 89, pp.2-12

Keywords: Assembly Modelling, Dynamic Analysis, Kinematic Analysis

Abstract: An assembly modelling system, with which a designer can interactively create an assembly of components ready for dynamic analysis, has been developed. In this system, an assembly model is created from the mating conditions between the components in the assembly, and then most of the information required for the dynamic or kinematic analysis packags is derived. For this development, the following problems have been solved: creation of assembly data structure, structuring of assembly data, derivation of joint information, inference of each component's position, and creation of joint coordinate systems. Through this work, the designer can easily model an assembly by assigning mating conditions, and check the dynamic or kinematic performance with the automatic creation of inputs for the assembly analysis packages.

Kline, W.A., DeVor, R.E. and Shareef, I.A.
The Prediction of Surface Accuracy in End Milling. ASME Paper

Abstract: In the end milling process, the cutting forces during machining produce deflection of the cutter and work piece which result in dimensional inaccuracies or surface error on the finished component. A previously developed mathematical model for the cutting force system in end milling is combined with models for cutter deflection and workpiece deflection so that the surface error profile may be predicted from the machining conditions and geometry and material properties of the cutter and workpiece. Machining experiments are performed on rigid and flexible workpieces of 7075 aluminum to verify the ability of the models to predict surface error. The model predicted surface error profiles are accurate both in magnitude and shape with the difference between measured and predicted surface errors raging from 5 to 15 percent. This approach for the prediction of surface errors provides a useful aid for the analysis of a variety of end milling process design and optimization problems.

Knauer, Karl and Hans-Jörg Pfleiderer
Yield enhancement realised for analogue integrated filters by design techniques IEE Proc., Vol. 129, Pt. G, No. 4, August 1982, p. 122-126

Keywords: Electronics fabrication

Abstract: The fabrication of analogue integrated circuits to yield depends on the tolerances and defect density in mask generation and device fabrication. Yield optimization, therefore, has to resolve two conflicting requirements. Whereas to reduce the influence of tolerances the device area has to be large, the larger the device area chosen, the higher will be the possible defect number. To determine the optimum device area with respect to yield in the fabrication of CCD transversal filters, the tolerances in mask generation and fabrication have first to be analyzed. Tolerances that are constant in a device can be eliminated by 'design cleverness'. The way in which the influence of statistical tolerances can be reduced by design centering will be demonstrated with reference to an implemented device. To determine the total yield it is further necessary to take into account the influence of defects. The optimum device area, considering yield, can then be determined as a function of both tolerance and defect density.

Koplewicz, Danielle
Specification by tolerances zone-Current situation and evolutions Proceeding of 3rd CIRP Seminars on CAT, Cachan, France, April 1993, pp. 213-222

Keywords: Product specification, toleranceing, geometrical tolerancing, tolerance zone.

Abstract: This paper gives an overview of the international standardization dealing with geometrical tolerancing of products. This tolerancing is based on feature specification through tolerance zone. The evolutions already agreed and to be studied in the (near) future, are presented: they are inteded to impove the definition, to avoid contradictions, and to fill the gaps.

Kuntze, Robert
The Toleranced Design of the Model 520 Computer Hewlett-Packard Journal May 1984

Latta, Lester W.
Least-Cost tolerancing Product Engineering September 16, 1963

Abstract: How do you split the functional tolerances between mating surfaces? It depends on how they're to be made sometimes on the specific machine used.

Laurance, Neal
A High Level View of Step- A Formal Specification of the Information Content of a Product Design. Michigan, June 17-19, 1993, CRTD-Vol. 27, International Forum on Dimensional Tolerancing and Metrology, ASME, pp. 37-48

Abstract: This talk provides a brief introduction to STEP, an emerging International Standard covering all the requirements of an enterprise for information about a product from the time the product is first conceived until it is obsolescent. This standard is intended to replace IGES as a medium of interchange for geometrical data, and to include all the other types of data about a product in an industry. The standard is a blend of CAD/CAM models and advanced database concepts. In general, STEP draws its information models from appropriate technological domains and recasts them in a common information schema.While the early use of STEP will be for exchange between proprietary CAD systems, there is already evidence that next generation systems will have a native mode conceptually equivalent to the data base formulation prescribed by STEP. Examples of the use of STEP for relatively simple geometrical items are given. The current status and the work in progress of this standard is summarized.
STEP today handles only nominal geometry, i.e. ideal form. However, future versions of STEP will incorporate a tolerance model based on Y 14.5.1. That work is just now beginning, and the first results will not be available until next year. Standardization is similarly several years away.

Law, Averill M.
How To Build Valid, Credible and Appropriately Detailed Simulation Models. Industrial Engineering, pp. 16-17, April 1990

Lee, Kunwoo and Andrews, Guy
Inference of the positions of components in an assembly: part 2 Computer-aided design, Vol 17, no.1 Jan/Feb 1985, pp. 20-24

Abstract: A method is dirived to compute the location and orientation of each component from the spatial relationships imposed on the component in an assembly. With this method, any assembly can be represented by the spatial relationship between its components instead of by the transformation matrices of each component.

Lee, Woo Jong, and Tony C. Woo
Tolerancing: Its Distribution, Analysis, and Synthesis Technical Report No. 86-30, University of Michigan, Dept of Industrial and Operations Engineering, December 1986

Keywords: Tolerance, Analysis, Synthesis

Abstract: Tolerance, representing a permissible variation of a dimension in an engineering drawing, is synthesized by considering assembly stack-up conditions based on manufacturing cost minimization. A random variable and its standard deviation are associated with a dimension and its tolerance. This probabilistic approach makes it possible to perform trade-off between performance and tolerance rather than worst case analysis as it is commonly practiced. Tolerance (stack-up) analysis, as an inner loop in the overall algorithm for tolerance synthesis, is performed by approximating the volume under the multivariate probability density function constrained by nonlinear stack-up conditions with a convex polytope. This approximation makes use of the notion of reliability index [10] in structural safety. Consequently, the probabilistic optimization problem for tolerance synthesis is simplified into a deterministic nonlinear programming problem. An algorithm is then developed and is proven to converge to the global optimum through an investigation of the monotonic relations among tolerance, the reliability index, and cost. Examples from the implementation of the algorithm are given.

Lee, Woo-Jong and Tony C. Woo
Optimum Selection of Discrete Tolerances Technical Report No. 87-34, University of Michigan, Dept of Industrial and Operations Engineering, Dec. 1987

Keywords: Tolerance synthesis, Cost optimization, Branch and Bound

Abstract: Tolerance determination involves considerations from manufacturing, design, and assembly. Along with minimum cost and maximum functionality and interchangeability, the practice of tolerancing urges a process engineer to choose an appropriate manufacturing process as well. This situation is formalized by using a discret model. For an optimum selection of tolerances from given tolerances of various manufacturing processes, minimization of manufacturing cost is achieved under the constraints of tolerance stack-ups.
A random variable and its standard deviation are assigned to a dimension and its tolerance. This probabilistic approach enables trade-off between performance and tolerance but it also suggests stochastic optimization. With the aid of a notion called the reliability index [8], tolerance selection is formulated as an integer programming problem. A branch and bound algorithm for ensuring an optimum selection is developed by exploiting the special structure of the constraints. To make the enumeration tree small, monotonic relations among the reliability index, cost, and tolerances are examined. The algorithm is tested with examples.

Lee, Woo-Jong, Woo, T.C.
Tolerances: Their Analysis and Synthesis Journal of Engineering for Industry. Vol. 112/113, May 1990

Abstract: Tolerance, representing a permissible variation of a dimension in an engineering drawing, is synthesized by considering assembly stack-up conditions based on manufacturing cost minimization. A random variable and its standard deviation are associated with a dimension and its tolerance. This probalistic approach makes it possible to perform trade-off between performance and tolerance rather than the worst case analysis as it is commonly practiced. Tolerance (stack-up) analysis, as an inner loop in the overall algorithm for tolerance sythesis, is performed by approximating the volume under the multivariate probability density function constrained by nonlinear stack-up conditions with a convex polytope. This approximation makes use of the notion of reliability index [10] in structural safety. Consequently, the probalistic optimization problem for tolerance sythesis is simplified into a deterministic nonlinear programming problen. An algorithm is then developed and is proven to converge to the global optimum through an investigation of the monotonic relations among tolerance, the reliablilty index, and cost. Examples from the implementation of the algorithm are given.

Lehtihet, E.A. and Dindelli, B.A.
TOLCON: Microcomputer-Based Module for Simulation of Tolerances. Manuf. Ref. Vol.2, Num.3, Sept 1989. pp.179-188.

Abstract: One of the fundamental aspects of design and maufacture is the transformation of product functional requirements into tolerances or dimentional bounds on the individual components which make up the product. Tolerance problems in design and manufacturing often require the solution to linear or nonlinear combinations of stochastic variables. This paper describes progress towards the development of integrated computer modules for the solution of statistical tolerancing problems. A software package for the automatic generation fo Monte Carlo simulation for combinations of stachastic variables has been designed and implemented. The structure and capabilities of this package are described. Its usefulness in the analysis of tolerances is illustrated by a position tolerance application.

Lehtihet, E.A. and N.U. Gunasena
Models for the Position and Size Tolerance of a Single Hole Manufacturing Metrology, ASME Publication No PED-Vol 29, 1988, pp. 49-63.

Keywords: Geometric form, Tolerance Hole

Abstract: True position tolerancing enables designers to convey a concise statement of design intent to both production and inspection. The position tolerance of a feature can be specified as a static quantity by using the Regardless of Feature Size (RFS) modifier or as a dynamic quantity by using the Maximum Material condition (MMC) modifier. However, the constraints imposed on production errors are not evident from the tolerance frame. This paper develops several models relating position and size tolerance of a feature to inherent production errors. Performance under different models is evaluated by computing the probability of an acceptable feature with respect to position and size requirements.

Lenz, R.G.
Roundness Measurement, Part Three-Applying the Standard Mechanical Engineering, Dec. 1969, pp. 30-36.

Keywords: GDT, Inspection, Roundess

Abstract: The roundness standard currently being developed by a U.S.A. Standards Committee proposes methods for assessing the circular geometry of parts with a rotatable precision spindle measuring machine. This article describes how such a machine has been used to evaluate the geometry and improve the operation of automotive components.

Leveaux, Florence, Bourdet, Pierre, Lartique, Claire
Geometrical validation of Dimensioning and tolerancing specifications Proceeding of 3rd CIRP Seminars on CAT, Cachan, France, April 1993, pp. 233-248

Keywords: Dimensioning and Tolerancing, CAD models (Computer Aided Design). geometrical control, CMM (Coordinate Measuring Machine).

Abstract: A complete and sytaxically consistent data model of Dimensioning and Tolerancing specifications is elaborated following STEP project concepts (Standard for Exachange of Product Data.)With this conceptual data representation, a Dimensioning and Tolerancing specifications validation method is proposed. This method, illustrated thanks to a specification example, is based on the algorithmic simulation of a high level geometric control process.
This approach uses coordinate measuring principles and is independent form the inspection process and the dimensional measuring equipments. Variations on specified geometric features location and orientation are quantitatively estimated and are used to validate the Dimensioning and Tolerancing specifications a priori and during the design phase.
This validation method could be a contribution to automatic tolerancing for concurrent engineering.

Levy, S.J.
Applied Geometric Tolerancing TAD Products Corp., 1974

Keywords: True Position, GDT

Liggett, J.V.
The Boundary Concept of Position Tolerance Society of Automotive Engineers, SAE Paper No. 680489

Keywords: True Position, Tolerancing, GDT

Abstract: Current position tolerance standards treat noncircular shapes (square holes, slots, keyways) either as special applications, or in a different manner than round features are treated. The Boundary Concept enables position tolerance to be applied in a consistent manner to all feature shapes by defining position tolerance as the interaction of a surface (the feature) and a boundary. Good correlation with the functional gaging practices of the automotive and aircraft industries is achieved. Drastic changes in current standards have been avoided. The Boundary Concept is the result of a project of the SAE Drawing Standards Committee.

Light, Robert and David Gossard
Modification of Geometric Models Through Variational Geometry Computer-Aided Design, Vol. 14, No. 4, July 1982, p. 209-214

Keywords: Computer-Aided Design, Geometric Model, Variational Geometry

Abstract: Systems for computer-aided mechanical design use geometric models for drafting, analysis and programming of NC machines. Because design is iterative in nature, the topology, geometry or dimensioning of a geometric model must be modified many times during the design cycle. The effectiveness of future CAD systems will depend in large part upon the ease wiht which geometric models can be created and modified.
This paper represents the results of a research effort to develop flexible procedures for the definition and modification of geometric models. A central idea of this effort is that dimensions, such as appear on a mechanicla drawing, are a natural descriptor of geometry and provide the most appropriate means for altering a geometric model.

A procedure is described by which geometry is determined from a set of dimensions. The gemetry corresponding to an altered dimension is found through the simultaneous solution of the set of contraint equations. Presented in this paper are the basic approach to modifications of gemetric models, a procedure for significant reduction of the number of constraint equaions to be solved, and the effect of sparse matrix methods in reducing the time required to solve the equations.

Lin, Chin-Wen
A Statistical Analysis Tool for Variation Simulation Modeling Computers & Industrial Engineering, Vol. 13, Nos. 1-4, pp. 386-391, 1987

Keywords: Monte Carlo Simulation

Abstract: The analysis of an assembly process in the discrete part manufacturing industry usually involves a large number of dimensions. Each dimension tolerance influences the dimension variation of the final product, which is the so-called "quality". Furthermore, there are many random factors (noise) present during the assembly operations (tool wear, loose fixture, etc.). Few mathematical models can represent the assembly process. By applying a geometric standard and simulating the physical operations, the statistics of the final product dimensions can be predicted. With the simulation results, statistical anlysis is essential to identifying the critical factors (component dimensions). The traditional experimental designs, such as full factorial design, however, are not practical since the number of factors is too large. Taguchi method, which explores a special subset of factor combinations (called the orthogonal array) is able to examine a large number of factors (and interactions) in a much smaller number of experiments. With this unified tool, engineering understanding and judgement become more effective in product and process design.

Lin, V.C., Gossard, D.C., and Light, R.A.
Variational Geometry in Computer -Aided Design Computer Graphics, vol. 15, Num. 3, Aug. 1981, pp. 171-177

Abstract: Abstract: A system has been developed which utilizes variational geometry in the design and modification of mechanical parts. Three-dimensional constraints between characteristic points are used to define an object's geometry. Modification of geometry is accomplished by alteration of one or more constraints. A matrix method is used to determine the shape of the part by simultaneous solution of constraint equations. A method for increasing the speed and efficiency of the solution procedure is described. The method uses the relationships between the geometry and constraints to minimize the number of equations and variables to be solved.

Linares, Jean Marc, Marty, Claude
Tolerancing by functional group Proceeding of 3rd CIRP Seminars on CAT, Cachan, France, April 1993, pp. 267-277

Keywords: Tolerancing, small displacements, functional, spacial, clearance

Abstract: In the concept of analytical model conception of tolerancing an essential stage of the process is the model conception of functional groups, these are constituted by all surfaces which take part at the realization of functional conditions.The model, obtained from the connection graph and described by small displacements representing the difference of postition and orientation; permits to define the internal and external dimensioning and tolerancing.
This analytical process, very useful to approach the automatic tolerancing on CAD, CAM, proposes minimal and sufficient conditions. The surface errors, in a functional group, influence the assembly or the functional conditions and the choice of clearance between functional groups.
The assignment of specifications must stay compatible with the potentialities of production methods and control.

Little, R.E.
Statistical Tolerance Limits for Censored Log-Normal Data Journal of Testing and Evaluation, Vol. 8, No. 2, March 1980, pp. 80-84

Keywords: Reliability, Log-Normal Distribution

Abstract: A-basis and B-basis statistical tolerance limit computations are given for Type sII failure censored log-normal data. The statistical tolerance limits are established by using factors given by Nelson and Schmee in conjunction with the best linear unbiased estimates for hte normal distribution based on the coefficients tabulated by Sarhan and Greenberg. Thes tolerance limit computations complement analogous computations based on the Weibull distribution which have been illustrated in recent tutorial paper by Little.

Liu, S., Dong, Z.
A Solid Boundary Based Tolerance Representation Model Advances in Design Automation - DE-Vol. 44-2, ASME 1992

Abstract: An ambiguous representation of design geometry and its allowed variation is essential to design and manufacturing analysis tools using geometric modeling. In this paper, a new approach for modeling and representing mechanical tolerances, using information embedded in the solid model, is introduced. THe work focuses on mathematical mapping between the nominal and variant configurations of design geometry, using boundary face-based model variables. The method identifies the realtion between the errors of part geometry, represented by a solid model and measured using acoordinate measureing machine, and the tolerances, specified by dimensioning and tolerancing standards. The work is of benefit in understanding of the fundamental nature of geometric errors and tolerances; it guides the specification of dimensional and geometric tolerances; and, contributes to automated mechanical tolerancing in a solid modeling based system.

Loewen, E.G..
Microinch Accuracy...Really? American Machinist, Vol. 111, Number 12, June 5, 1967, pp. 135-141

Keywords: Gaging

Abstract: A metrologist does not believe all that he hears and sees about claims that gages can actually measure to millionths. Here are his arguments supporting his views.

Lorenz, G.
Dimensional Analysis of Production Processes National Standards Laboratory Technical Paper No.13, 1960 Australia

Keywords: Tolerance, Production Process Cost

Abstract: The aims of the dimensional analysis of production processes, together with the significances of the analysis in economical production, are described. The terms process variability, process capability, process tolerance, mean process displacement, and safety margin are defined, and their application illustrated by practical examples.

Lu, Stephen C-Y., Wilhelm, Robert G.
Automating Tolerance Synthesis: A Framework and Tools Journal of Manufacturing Systems. Vol. 10, N4, pp. 279-296.

Abstract: This paper describes CASCADE-T - a new approach to tolerance synthesis that uses a complete representation of the conditional tolerance relations that exist between features of a part under design. Conditional tolerances are automatically determined from functional requirements and shape information. Tolerance primitives based on the virtual boundary requirements approach to tolerance representation are composed to form more complex tolerance relationships. Artificial intelligence techniques, including a constraint network, frame-based system, and dependency tracking are used to support flexible and detailed computation for tolerance analysis and synthesis.

Luby, S.C., Dixon, J.R., Simmons, M.K.
Designing With Features: Creating and Using a Features Data Base for Evaluation of Manufacturability of Castings. Computers in Engineering Conference Proceedings. Vol. 1, pp. 285-292, 1986 ASME

Keywords: Feature Design, Casting, Manufacturability

Abstract: This paper describes a working research prototype features based design aid for aluminum castings. The program, called Casper, employs macro-features (such as boxes or L-brackets) together with co-features (such as holes, bosses. or ribs) for use by the designer in creating parts. An add-modify-delete menu allows the designer considerable scope and flexibility. As the design proceeds the program develops and updates a representation of the design in terms of the features used and also in terms of faces, edges, and points, which are readily derived from the feature. This representation is used to provide the designer with a visual display in an interactive graphics environment.Manufacturability evaluation, when requested by the designer, occurs in two steps. First, process limits (such as section thickness and overall dimensions) are checked. Then a directional solidification analysis is done and interpreted. Both steps identify the location ot the program's operation are shown and discussed.

Luzadder, P.E.
Graphics for Engineers Prentice-Hall, Inc., Englewood Cliffs, N.J., 1957, pp. 424-435, Chapter 16.

Keywords: True Position Tolerancing, GDT

Abstract: Size Dimension, Limit Dimension, Basic Shaft System, Square Tolerances, True Position Dimensioning, Surface Quality

Luzadder, W.J. P.E.
Fundamentals of Engineering Drawing Fourth Edition, Prentice-Hall, Inc. pp. 354-365, Ch. 15

Keywords: General, Drafting Practices

Abstract: Chapter 15: Dimensioning

Lynch, A.F., Vanderploeg, M.J.
A Symbolic Formulation for Linearization of Multibody Equations of Motion. Computer in Engineering,ASME,Vol. one,1990, pp. 201-207

Keywords: Linearization, Kinematics, Loop constraint, Mathematics

Abstract: This paper presents as method for obtaining linearized state space representations of open or closed loop miltibody dynamic systems. The paper develops a symbolic formulation for multibody dynamic systems which result in an explicit set of symbolic equations of motion. The symbolic equations are then used to perform synbolic linearizations. The resulting syumbolic, linear equations are in terms of the system parameters and the equilibrium point. Finally, a method is developed for reducing a linearized, constrained multibody system consisting of a mixed set of alegraic-differential equations to a reduced set of differential equations in terms of an independent coordinate set. An example is used to demonstrate the technique.