Form Accuracy Analysis of Cylindrical Parts Produced by Rapid Prototyping

Solid Freeform fabrication processes are being considered for creating fit and assembly nature functional parts. It is extremely important that these parts are within allowable dimensional and geometric tolerance. The part accuracy produced by rapid prototyping process is greatly affected by the relative orientation of build and face normal directions. A systematic method is needed to find the reliability of the created product. This paper discusses the work done in this area and the effect of build orientation on the part form accuracy analysis of each specified tolerance like circularity and cylindricity. Feasible build direction that can be used to satisfy those tolerances is identified. It will help process engineer in selecting a build direction that can satisfy a mathematical model of form tolerance.Mechanical Engineerin

Robustness in solid modeling - a tolerance based, intuitionistic approach

Journal ArticleThis paper presents a new robustness method for geometric modeling operations. It computes geometric relations from the tolerances defined for geometric objects and dynamically updates the tolerances to preserve the properties of the relations, using an intuitionistic self-validation approach. Geometric algorithms using this approach are proved to be robust. A robust Boolean set operation algorithm using this robustness approach has been implemented and test examples are described in this paper as well

A new approach to tolerance analysis

Journal ArticleTolerance analysis is seen as part of a more general problem, namely handling data with uncertainty. Uncertain geometric data arises when interpreting measured data, but also in solid modeling where floating point approximations are common, when representing design tolerances, or when dealing with limited manufacturing precision. The common question is whether parts with uncertain shape fulfill certain functional specification. The question is expressed as geometrical relationship between toleranced objects. Unfortunately, tolerance based relations are often inconsistent, unlike relations between exactly represented objects. In this paper we survey current tolerance representation and analysis methods. We then derive our method of intuitionistic tolerance handling from a method developed for robust solid modeling. A new representational framework is proposed, which serves as the basis for robust geometric modeling and tolerance analysis. We illustrate the framework with examples of assembly design

The discretized polyhedra simplification (DPS): a framework for polyhedra simplification based on decomposition schemes

This work discusses simplification algorithms for the generation of a multiresolution family of solid representations from an initial polyhedral solid. We introduce the Discretized Polyhedra Simplification (DPS), a framework for polyhedra simplification using space decomposition models. The DPS is based on a new error measurement and provides a sound scheme for error-bounded, geometry and topology simplification while preserving the validity of the model. A method following this framework, Direct DPS, is presented and discussed. Direct DPS uses an octree for topology simplification and error control, and generates valid solid representations. Our method is also able to generate approximations which do not interpenetrate the original model, either being completely contained in the input solid or bounding it. Unlike most of the current methods, our algorithm can deal and also produces faces with arbitrary complexity. An extension of the Direct method for appearance preservation, called Hybrid DPS, is also discussed

Robustness in geometric modeling - an intuitionistic and tolerance-based approach

Journal ArticleAn intuitionistic geometry approach is taken to develop two tolerance-based methods for robust geometric computation. The so called analytic model method and the approximated model method are developed independently of a specific application or a geometric algorithm. Geometric robustness is formally defined. Geometric relations are computed based on tolerances defined for geometric objects. Dynamic tolerance updating rules are given to preserve properties of the geometric relations. The two methods differ in the definition of robustness and they use different tolerance updating rules, and hence, they preseve different properties and are suitable for different kinds of applications. To handle the possibly occuring ambiguities dynamic ambiguity handling methods are described as well

Robust boolean set operations for manifold solids bounded by planar and natural quadric surfaces

Journal ArticleThis paper describes our latest effort in robust solid modeling. An algorithm for set operations on solids bounded by planar and natural quadric surfaces, that handles all geometrically degenerate cases robustly, is described. We identify as the main reason for the lack of robustness in geometric modeling, that dependent relations are handled inconsistently by disregarding the dependencies. Instead of using explicit reasoning to make dependent decisions consistent, we show that redundant computation can be avoided by correctly ordering the operations, and redundant data can be eliminated in the set operation algorithm, so that the result is guaranteed to be a valid two-manifold solid