Identification and Minimization of Deviations of Real Gear Tooth Surfaces

The authors propose an approach that uses coordinate measurements of the real surface to: (i) determine the real applied machine-tool settings, (ii) determine the deviations of the real surface from the theoretical one, (iii) minimize the deviations by correction of the machine-tool settings, and (iv) represent the real surface analytically in the same Gaussian coordinates as the theoretical one.

Position Tolerance Verification Using Simulated Gaging

One of the routine manual tasks in dimensional inspection is the assembly verification of circular features by mechanical gaging. With the aid of coordinate measuring machines or vision systems, this task can be performed more efficiently through simulation or soft-gaging. A formulation is presented for interpretation of 2D position tolerance specifications. Simulated gages are constructed from datum features as a set of constraint relationships. The measure of perfect-form position-imperfection is determined as the distance between the measured and the nominal feature positions subject to datum constraint requirements. The derived formulation is applied to an example part with a hole-slot datum-priority-frame. This formulation results in a three-variable optimization problem which is solved by an Augmented Lagrange Multipliers technique. The extension of the formulation to 3D is also discussed, but without reference to a specific representation.

A Simple Practical Criterion to Guarantee Second Order Smoothness of Blend Surfaces

Computer Aided Geometric Design of surfaces sometimes presents problems that were not envisioned by mathematicians in differential geometry. This paper presents mathematical results that pertain to the design of second order smooth blending surfaces. Second order smoothness normally requires that normal curvatures agree along all tangent directions at all points of the common boundary of two patches, called the linkage curve. The Linkage Curve Theorem proved here shows that, for the blend to be second order smooth when it is already first order smooth, it is sufficient that normal curvatures agree in one direction other than the tangent to a first order continuous linkage curve. This result is significant for it substantiates earlier works in computer aided geometric design. It also offers simple practical means of generating second order blends for it reduces the dimensionality of the problem to that of curve fairing, and is well adapted to a formulation of the blend surface using sweeps. From a theoretical viewpoint, it is remarkable that one can generate second order smooth blends with the assumption that the linkage curve is only first order smooth. This property may be helpful to the designer since linkage curves can be constructed from low order piecewise continuous curves.

Pattern Matching Synthesis As an Automated Approach to Mechanism Design

A new knowledge-based approach for the synthesis of mechanisms, referred to as Pattern Matching Synthesis, has been developed based on committee machine and Hopfield neural network models of pattern matching applied to coupler curves. Computational tests performed on a dimensionally parameterized four bar mechanism have yielded 15 distinct coupler curve groups (patterns) from a total of 356 generated coupler curves. This innovative approach represents a first step toward the automation of mapping structure-to-function in mechanism design based on the application of artificial intelligence programming techniques.

The Evaluation of Moments of Regions With Piecewise-Linearly Approximated Boundaries via Line Integration

The subject of this paper is the computation of the first three moments of bounded regions imbedded in the three-dimensional Euclidean space. The method adopted here is based upon a repeated application of Gauss’s Divergence Theorem to reduce the computation of the said moments — volume, vector first moment and inertia tensor — to line integration. Explicit, readily implementable formulae are developed to evaluate the said moments for arbitrary solids, given their piecewise-linearly approximated boundary. An example is included that illustrates the applicability of the formulae.

Design Quality and Reliability Through Technology Readiness

This paper discusses the relationship between the growth of reliability in the early stages of a product delivery process and Technology Readiness, and describes the importance of ‘ready’ technologies if product launch schedules are to be achieved. Technology Readiness itself is defined and the enablers for it are identified. A process which has been developed is described, and some proposals for tracking and managing progress are made. Finally, the importance of critical design parameters both in the development of technologies and in understanding technology capabilities are described fully.

Synthesis of Systems From Specifications Containing Orientations and Positions Associated With Flow Variables

A class of systems can be specified by a set of constant input-output power variables with generalized flow variables having associated orientations and positions. This paper presents a method for generating conceptual parametric designs. A quasi-decoupled approach is taken to solve the problem. A hierarchy of considerations of magnitude, orientation and position transforms is established. Orientation and position transformers are introduced in each domain. A solution to the “vector” problem is obtained by augmenting the “scalar” solution using vector transformers.

Application of Variational Geometry to the Analysis of Mechanical Tolerances

The proper selection of tolerances is an important part of mechanical design that can have a significant impact on the cost and quality of the final product. Yet, despite their importance, current techniques for tolerance design are rather primitive and often based on experience and trial and error. Better tolerance design methods have been proposed but are seldom used because of the difficulty in formulating the necessary design equations for practical problems. In this paper we propose a technique for the automatic formulation of the design equations, or design functions, which is based on the use of solid models and variational geometry. A prototype system has been developed which can model conventional and statistical tolernaces, and a limited set of geometric tolerances. The prototype system is limited to the modeling of single parts, but can perform both a worst case analysis and a statistical analysis. Results on several simple parts with known characteristics are presented which demonstrate the accuracy of the system and the types of analysis it can perform. The paper concludes with a discussion of extensions to the prototype system to a broader range of geometry and the handling of assemblies.

Computer Aided Tolerance Analysis of Parts and Assemblies

An exact constraint scheme based on the physical contacting constraints of real part mating features is used to represent the process of assembling the parts. To provide useful probability information about how assembly dimensions are distributed when the parts are assembled as intended, the real world constraints that would prevent interference are ignored. This work addresses some limitations in the area of three dimensional assembly tolerance analysis. As a result of this work, the following were demonstrated: 1. Assembly of parts whose assembly mating features are subjected to variation; 2. Assemble parts using a real world set of exact constraints; 3. Provide probability distributions of assembly dimensions.

A Structured Design Methodology and Metadesigner: A System Shell Concept for Computer Aided Creative Design

This paper discusses the concept of managing the design process using Objected Oriented Programming Paradigm. A software system shell, called MetaDesigner is being developed for aiding the human designer to create new designs, based on the hierarchical nature of the design space. This system shell is intended to have the following capabilities: (1) interactive and system-guided design process to analyze design structure and to characterize design options, (2) to provide interactive and system-guided knowledge acquisition, classification, and retrieval to achieve machine learning, and (3) to build a flexible and forever expandable structure for knowledge-based system implementation.