Showing papers in "Computer-aided Design in 1998"

Part orientation and build cost determination in layered manufacturing

Abstract: As more choices of materials and build processes become available in layered manufacturing (LM), it is increasingly important to identify fundamental problems that underlie the entire field. Determination of best build orientation and minimizing build cost of a part are two such issues that must be considered in any LM process. By decoupling the solution to these problems from a specific LM technology, not only can the solution be applied to a variety of processes, but more realistic cost comparisons of parts built on different machines become possible.

Current research in the conceptual design of mechanical products

Abstract: Decisions made at the conceptual design stage have significant influence on factors such as costs, performance, reliability, safety and environmental impact of a product. However, knowledge of all the design requirements and constraints during this early phase of a product's life cycle is usually imprecise, approximate or unknown. Faced with such complexity, individual designers have restricted themselves to narrow, well-defined sub-tasks and as a result, progress in this area has been patchy and spasmodic. The purpose of this survey is to document the current state of research and development in this crucial design activity and in doing so, to identify avenues of fruitful exploration. In this paper, we provide a comparison of the advantages/disadvantages and limitations between the various techniques/tools and, where applicable, suggest possible future research directions.

Automatic recognition of interacting machining features based on minimal condition subgraph

Abstract: This paper presents a methodology for efficiently recognizing both isolated and interacting features in a uniform way. The conventional, graph-based recognition method is combined with hint-based feature recognition to recognize and extract alternative interpretations of interacting features. First all isolated (non-intersecting) features are recognized based on a Manufacturing Face Adjacency Graph. Interacting features are then recognized based on the feature's minimal condition subgraph (MCSG) that is used as a feature hint. Unlike Previous hint-based recognition methods, the MCSGs of all features are defined, generated and completed in a uniform way, independent of the feature type. Hints are defined by an Extended Attributed Adjacency Graph, generated by graph decomposition and completed by adding virtual links, corresponding to entities lost by interactions. An efficient algorithm for generating virtual links is developed. A new classification of feature interactions is also presented.

DeWall: A fast divide and conquer Delaunay triangulation algorithm in Ed

Abstract: The paper deals with Delaunay Triangulations (DT) in Ed space. This classic computational geometry problem is studied from the point of view of the efficiency, extendibility to any dimensionality, and ease of implementation. A new solution to DT is proposed, based on an original interpretation of the well-known Divide and Conquer paradigm. One of the main characteristics of this new algorithm is its generality: it can be simply extended to triangulate point sets in any dimension. The technique adopted is very efficient and presents a subquadratic behaviour in real applications in E’, although its computational complexity does not improve the theoretical bounds reported in the literature. An evaluation of the performance on a number of datasets is reported, together with a comparison with other DT algorithms. 0 1998 Published by Elsevier Science Ltd. All rights reserved.

An object-oriented representation for product and design processes

Abstract: We report on the development of a knowledge representation model, which is based on the SHARED object model reported in Shared Workspaces for Computer-Aided Collaborative Engineering (Wong, A. and Sriram, D., Technical Report, IESL 93-06, Intelligent Engineering Systems Laboratory, Department of Civil Engineering, MIT, March, 1993) and Research in Engineering Design (Wong, A. and Sriram, D., SHARED: An Information Model for Cooperative Product Development, 1993, Fall, 21-39). Our current model is implemented as a layered scheme, that incorporates both an evolving artifact and its associated design process. To represent artifacts as they evolve, we define objects recursively without a pre-defined granularity on this recursive decomposition. This eliminates the need for translations between levels of abstraction in the design process. The SHARED model extends traditional OOP in three ways: 1. by allowing explicit relationship classes with inheritance hierarchies; 2. by permitting constraints to be associated with objects and relationships; and 3. by comparing `similar' objects at three different levels (form, function and behavior). Five primitive objects define the design process: goal, plan, specification, decision and context. Goal objects achieve function, introduce constraints, introduce new artifacts or modify existing ones, and create subgoals. Plan objects order goals and link a product hierarchy to a process hierarchy. Specification objects define user inputs as constraints. Decision objects relate goals to user decisions and context objects describe the design context. Operators that are applied to design objects collectively form a representation of the design process for a given context. The representation is robust enough to effectively model four design paradigms [described in Journal of CAD (Gorti, S. and Sriram, R. D., Symbol to Form Mapping: a Framework for Conceptual Design, 1996, 28 (11), 853–870)]: top-down decomposition, step-wise refinement, bottom-up composition and constraint propagation. To demonstrate this, we represent the designs of two TV remote controllers in the SHARED architecture. The example reveals that certain aspects of artifact knowledge are essentially context-independent and that this representation can be a foundation for robust knowledge-based systems in design.

Non-isoparametric tool path planning by machining strip evaluation for 5-axis sculptured surface machining

Abstract: Presented in this paper is a new approach to 5-axis NC tool path generation for sculptured surface machining. Techniques of feasible machining strip evaluation are used for non-isoparametric 5-axis tool path generation. A searching algorithm is proposed to find the parameter increments of adjacent cutter locations along orthogonal path intervals for optimal non-isoparametric path generation. Compared to the use of the smallest path interval by the traditional constant parametric path planning, the proposed methodology can generate efficient tool paths for sculptured surface machining by reducing the redundant overlapping between adjacent tool paths. The proposed methodology includes three steps: (1) evaluating feasible machining strip, (2) solving parameter increments (Δu, Δv) along orthogonal path intervals, and (3) searching for adjacent non-isoparametric cutter locations. The techniques presented in this paper can be used to improve 5-axis machined surface quality and to automate the non-isoparametric cutter path generation for CAD/CAM systems.

Distribution modeling and evaluation of product design problems

Abstract: This paper proposes a framework for the modeling and evaluation of product design problems in a computer network-oriented design environment. The framework is intended to integrate designer-specified mathematical models for multidisciplinary and multiobjective design problems. The goal is to provide the ability to rapidly construct integrated design problem models to facilitate collaborative design work, improve product quality and reduce development time. Ultimately, it should allow specialized engineering applications and design problem models to operate under a common design environment. A product design problem is modeled in terms of interacting objects, called modules, each representing a specific aspect of the problem. Modules interact with one another through services that allow the exchange of information. Modules can encapsulate engineering models and data or software applications. The method is extended using a standard network communication protocol to create a distributed object-based modeling and evaluation framework for design problems.

CAD and the product master model

Abstract: We develop an architecture for a product master model that federates CAD systems with downstream application processes for different feature views that are part of the design process. The architecture addresses especially the need to make persistent associations of design information with net shape elements. Moreover, the design respects the need of commercial CAD systems (and of downstream applications) to maintain proprietary information that must not be disclosed in the master model. Two case studies consider the requirements on the master model architecture for geometric dimensioning and tolerancing, and for manufacturing process planning using NC machining. We discuss how to reconcile the associated feature views and how to update them under net shape redesign. The case studies indicate that many design changes that arise from these downstream views can be formalized by a well-defined problem on dimensional and geometric constraints.

Variable-feedrate CNC interpolators for constant material removal rates along Pythagorean-hodograph curves

Abstract: An NC system that machines a curved shape at fixed depth of cut experiences time-varying cutting forces due to the ‘curvature effect’—the material removal rate is higher than nominal in concave regions, and lower in convex regions. A curvature-dependent feedrate function that automatically compensates for this effect is formulated, and it is shown that, for Pythagorean-hodograph (PH) curves, the periodic real time computation of reference points in accordance with this function can be analytically reduced to a sequence of root-finding problems for simple monotone functions. Empirical results from an implementation of this variable-feedrate interpolators on an open-architecture CNC milling machine are presented and compared with results from fixed-feedrate interpolators. The curvature-compensated feedrate scheme has important potential applications in ensuring part accuracy and in optimizing part programs consistent with a prescribed accuracy.

Design and engineering process integration through a multiple view intermediate modeller in a distributed object-oriented system environment

Abstract: Feature-based modelling is the emerging technology to integrate design and engineering activities. It enriches product data representation with semantic information, that allows more efficient and direct communication between engineering processes. Nevertheless, major industrial problems arise from the fact that the communication between these processes is still not based on sharing the same information within a computer-internal product model. The lack of industrial product data exchange between various CAD/CAE applications is owing to the fact that there are diverse data formats and standards, giving rise to conversion problems. The ISO standard STEP provides a unique, comprehensive technology to solve most of the industrial problems in data exchange. However, it still does not provide all the resources needed to achieve a high-level, semantic data communication between engineering processes. In this article, we propose a solution to link the design process (CAD) with downstream engineering processes (CAE) based on an integrated feature-based modelling approach that supports both design-by-features and feature recognition. Integration is thereby achieved through a homogeneous, multiple view feature-based representation of the part model, called intermediate model, which is shared among the various applications. A distributed, object-oriented feature-based system architecture is described. Herein, the intermediate modeller server acts as a service provider to network-based distributed applications. These share the intermediate model and are able to extract their specific view from the semantic data of the product. A prototype implementation of the integrated feature-based modelling kernel and its integration into the distributed environment is also outlined.

Representation and management of feature information in a cellular model

Abstract: Many limitations in current feature modelling systems are inherited from the geometric representation they use for the product model. Both a very rigid and a very extensive representation are unsuitable for feature applications, at least if no convenient support is provided to manage the data. This paper describes a cellular representation for feature models that contains all the relevant information to effectively solve a variety of current problems in feature modelling. Much benefit is gained from a coherent integration between shapes of a feature model and cells in the cellular model. Every feature shape has an explicit volumetric representation in terms of cells. Specific subsets of its boundary are also distinguished in terms of cell faces and edges. Feature interactions are maintained in attributes of cells, cell faces and cell edges. Methods for modifying and querying the cellular model are presented, and their application is illustrated for feature validity maintenance, feature interaction management, feature conversion between multiple views, and feature visualization.

Generation of 3D building models from 2D architectural plans

Abstract: A robust, semi-automatic way is presented to create 3D polyhedral building models from computer-drawn floor plans, requiring minimal user interaction. The models adhere to a consistent solids representation and can be used for computer rendering, visualization in interactive walkthroughs, and in various simulation and analysis programs. The output of our prototype program is directly compatible with the Berkeley WALKTHRU system and with the NIST CFAST fire simulator. A consistent model of a seven-storey building with more than 300 rooms has been generated in the time span of a few days from original AutoCAD floor plans drawn by architects.

Voronoi diagrams and offset curves of curvilinear polygons

Abstract: This paper studies the practical generation of Voronoi diagrams and offset curves of simply-connected planar areas bounded by straight lines and circular arcs. We present and analyze a wavefront-propagation algorithm for the generation of Voronoi diagrams and compare it experimentally to a tuned version of Lee's divide-and-conquer algorithm. Key performance parameters of these two algorithms are compared based on machine-generated test data. We conclude that the wavefront-propagation algorithm can be expected to outperform the divide-and-conquer algorithm for all, but pathological test data. In particular, its practical running time seems to grow only linearly. We also used our implementation in order to gather statistics on the CPU-consumption of offsetting based on Voronoi diagrams. All tests clearly showed the practical suitability of using Voronoi diagrams for the offsetting of curvilinear polygons. The CPU-time consumptions recorded also compare very favorably with other published codes for computing Voronoi diagrams.

An adaptive method for the automatic triangulation of 3D parametric surfaces

Abstract: We have developed automatic mesh generation procedures based on advancing front methods and featuring a priori nodal density calculations. A crucial step in the overall method consists of discretizing the edges and surfaces of an input B-Rep structure with the ability to respect as closely as possible this nodal density function across the part, which is highly interesting for analysis or representation purposes. The work presented here focuses on the discretization of three-dimensional parametric surfaces with strong variations of curvature with respect to a nodal density function with steep gradients. This algorithm is particularly suitable for FE mesh generation purposes and also in many engineering applications for which a 3D model has to be triangulated. We will tackle, in this context, the use of the technique in order to mesh parametric surfaces with a specified discretization tolerance. In this paper, we also present a new quality indicator for triangular and tetrahedral meshes in the context of a priori nodal density constraints.

A Simulated Annealing-Based Algorithm Using Hierarchical Models for General Three Dimensional Component Layout

Abstract: An efficient simulated annealing-based algorithm which optimizes component layout is presented. The efficiency comes in the algorithm's ability to calculate component overlap quickly by taking advantage of a hierarchical decomposition of the model's geometry. The result is an algorithm able to optimize the placement of components of arbitrary geometry inside an arbitrarily shaped container over multiple design goals and subject to inter-component spatial and performance constraints. The algorithm is demonstrated on test problems of known solution, and a variety of industrial problems of a priori unknown solution.

Modelling generic product structures in STEP

Abstract: Industrial companies need powerful data modelling mechanisms, e.g. classification, for the description of their products. The companies that adapt their products to the needs of individual customers in a routine manner have perhaps the most urgent needs. They must efficiently describe large numbers of product variants. STEP Application Protocol 214 (AP 214) for the automotive industry also addresses the modelling of product variants, i.e. generic product structure modelling. In addition to AP 214, the same mechanisms are needed in other standardization efforts as well, e.g. STEPlib of AP 221 and PLIB. STEP, however, does not include a mechanism for using classification and inheritance for modelling products of an individual company. These facilities are included in EXPRESS, but EXPRESS can only be used for describing the data schema to be standardized. The fundamental structure of STEP, therefore, prohibits a company from modelling its products in an object-oriented manner. This is an issue that may seriously affect the future of STEP as a general product-modelling methodology. The problems and possibilities of extending STEP in this direction within its current structure are discussed and a new mechanism is outlined as an alternative solution.

Automatic generation of NC cutter path from massive data points

Abstract: This paper proposes methodologies and algorithms through which a three-axis NC cutter path can be directly generated from massive data points obtained with contact or non-contact measuring devices. At the beginning, a Z-map model is employed to set up mesh points in order to economize on the use of computer memory. Rough-cut paths are produced by machining volumes of material in a slice-by-slice manner: firstly cutting the raw material into several slices on the basis of depth of cut, next judging from intersection information the cut and non-cut areas, and then generating roughcut paths of slices. Fine-cut paths are achieved by the height correction method, which by degrees examines mesh points within the cutters' projection areas. Any interference between the cutting tool and the data points is taken into account during the correction of the cutter height. Aside from a theoretical discussion, this research develops a computer-aided engraving system to prove the applicability of the proposed methods. In contrast to traditional copy milling, computer-aided engraving provides users with much more flexibility, reduces machining time, and adapts the workpiece forms to different circumstances so as to manufacture male or female dies.

Modeling the surface swept by a generalized cutter for NC verification

Abstract: Presented in this article is a procedure for representing the cutter-swept surface (CSS) of a generalized cutter in a single-valued form, z = f(x, y). The key idea is that the z-value of the CSS at a 2D point (x, y) is expressed as the sum of 1) the z-value at a point on the silhouette curve of the cutter bottom surface and 2) the incremental z-value along the cutter movement direction. Thus, the main part of the modeling method is to obtain the silhouette curve equations, which becomes a root finding problem for a quartic polynomial (when the cutter bottom surface contains a toroidal surface). The proposed method not only renders a single-valued representation for the CSS of a generalized cutter (which was not possible with the existing methods) including rounded endmill but also results in a computational scheme that is faster than the existing schemes for ball- and flat endmills.

Solving geometric constraint systems. II. A symbolic approach and decision of Rc-constructibility

Abstract: This paper reports a geometric constraint-solving approach based on symbolic computation. With this approach, we can compute robust numerical solutions for a set of equations and give complete methods of deciding whether the constraints are independent and whether a constraint system is over-constraint. Based on symbolic computation, we also have a decision procedure for the problem of deciding whether a constrained diagram can be constructed with ruler and compass (rc-constructibility).

Rational motion design—a survey

Abstract: In the last years many efforts have been made to transfer geometric CAD methods to motion design: The generation of a (one-parametric) motion with given properties. An object (arm of a robot…) is moved with respect to a fixed system. Methods from freeform curve design provide powerful tools to handle such problems. Some of these methods and results shall be presented in this survey. Here one can find a (geometric) approach including solutions of interpolation problems. First attempts are studied. Then we state two principal demands on the result of such a design process: The motions should be rational and invariant with respect to changes of coordinates in fixed and moving frame, respectively. We use quaternions to describe displacements and motions and give an overview on rational spline motions. Some known results on interpolating motions are reviewed. Then a third demand is presented: The design process should be ‘repeatable’ in the following sense: If a solution is computed the algorithm should give the same solution (including parametrisation), if we start with new input data generated by our first solution. The paper includes suggestions for further research.

A geometric algorithm for single selective disassembly using the wave propagation abstraction

Abstract: Disassembling a selected component from an assembly, defined as selective disassembly, is important for applications such as maintenance, recycling and reuse. This paper presents a geometric algorithm to solve the following selective disassembly problem: given an assembly and a selected component to be disassembled, determine the disassembly sequence with minimum component removals (motions), defined as an optimum sequence. We propose an abstraction “wave propagation” that analyzes the assembly from the selected component outwards, and orders the components for selective disassembly. The main contributions of this research are: (1) determining an optimal disassembly sequence; (2) reducing the search space by analyzing a subset of components in the assembly; and (3) providing a polynomial average complexity algorithm. The proposed selective disassembly approach applies to both two dimensional and three-dimensional assemblies.

On user-defined features

Abstract: Feature-based design is becoming one of the fundamental design paradigms of CAD systems. In this paradigm, the basic unit is a feature and parts are constructed by a sequence of feature attachment operations. The type and number of possible features involved depend upon product type, the application reasoning process and the level of abstraction. Therefore to provide CAD systems with a basic mechanism to define features that fit the end-user needs seems more appropriate than trying to provide a large repertoire of features covering every possible application.A procedural mechanism is proposed for generating and deploying user-defined features in a feature-based design paradigm. The usefulness of the mechanism relies on two functional capabilities. First the shape and size of the user-defined features are instantiated according to parameter values given by the end-user. Second the end-user positions and orients the feature in the part being designed by means of geometric gestures on geometric references.

Geometry-based triangulation of trimmed NURBS surfaces

Abstract: An algorithm for obtaining a piecewise triangular approximation of a trimmed NURBS surface is presented. The algorithm is geometry based, i.e. the surface is subdivided into triangular facets based on its geometric characteristics and not on its parametrization. No assumption is made about the surface's parametrical representation; it does not have to be continuously differentiable, only Co continuity is assumed. The surface subdivision is performed in model space, however, the triangulation is carried out in parameter space using the parametric vertices of subdivision rectangles. Along with computing the triangulation, the method produces a compact database for browsing in the triangular irregular network, e.g. finding all neighbors of a given triangle.

A feature-based approach to extracting machining features

Abstract: Feature-based modeling has been considered an indispensable tool for integrating design and manufacturing processes. In this paper, we propose a new approach to extracting machining features from a feature-based design model, based on an integrated geometric modeling system that supports both feature-based modeling and feature recognition. Feature recognition is achieved through an incremental feature converter. The incremental feature converter not only keeps the design model consistent, but also incrementally extracts machining features from design features as a design evolves. By combining the strength of feature-based design and feature recognition, the proposed approach can handle feature interactions and protrusion features effectively so that it deals with a large set of complex design models. Moreoever, the incremental nature makes it possible for the design process to be an ongoing negotiation between the design and the manufacturing planner at the initial design stage.

Representation and interpretation of geometric tolerances for polyhedral objects—I. Form tolerances

Abstract: This paper presents a scheme for representing form tolerances for polyhedral objects in solid modelers. This includes the development of a complete form tolerance zone definition based on a rigorous mathematical formulation in which derived algebraic constraints define the model variations. The paper also presents a procedure for the representation of the variant boundary surfaces that approximate the real world form variations and simulate the variations by planar surfaces (for tolerance analysis). The proposed scheme has been implemented in an object-oriented programming environment.

Interpolation schemes for rigid body motions

Abstract: This paper investigates methods for computing a smooth motion that interpolates a given set of positions and orientations. The position and orientation of a rigid body can be described with an element of the group of spatial rigid body displacements, SE(3). To find a smooth motion that interpolates a given set of positions and orientations is therefore the same as finding an interpolating curve between the corresponding elements of SE(3). To make the interpolation on SE(3) independent of the representation of the group, we use the coordinate-free framework of differential geometry. It is necessary to choose inertial and body-fixed reference frames to describe the position and orientation of the rigid body. We first show that trajectories that are independent of the choice of these frames can be obtained by using the exponential map on SE(3). However, these trajectories may exhibit rapid changes in the velocity or higher derivatives. The second contribution of the paper is a method for finding the maximally smooth interpolating curve. By adapting the techniques of the calculus of variations to SE(3), necessary conditions are derived for motions that are equivalent to cubic splines in the Euclidean space. These necessary conditions result in a boundary value problem with interior-point constraints. A simple and efficient numerical method for finding a solution is then described. Finally, we discuss the dependence of the computed trajectories on the metric on SE(3) and show that independence of the trajectories from the choice of the reference frames can be achieved by using a suitable metric.

Parametric kinematic tolerance analysis of general planar systems

Abstract: We present an algorithm for functional kinematic tolerance analysis of general planar mechanical systems with parametric tolerances. The algorithm performs worst-case analysis of systems of curved parts with contact changes, including open and closed kinematic chains. It computes quantitative variations and helps designers detect qualitative variations, such as blocking and under-cutting. The algorithm constructs a variation model for each interacting pair of parts: a mapping from the part tolerances and configurations to the kinematic variation of the pair. These models generalize the configuration space representation of nominal kinematics to toleranced parts. They are composed via sensitivity analysis and linear programming to derive the system variation at a given configuration. The variation relative to the nominal system function is computed by sampling the system variation. We demonstrate the algorithm on detailed parametric models of a movie camera film advance and of a micro-mechanical gear discriminator.

Real time motion fairing with unit quaternions

Abstract: Though it may be tempting to smooth orientation data by filtering the Euler angles directly, it is noted that smoothed Euler angles do not necessarily yield a smooth motion. This is caused by the difference between the metric in the rotation group and that in the Euclidean space. The quaternions, which Hamilton discovered in 1853, provide a means for representing rotation. A unit quaternion, represented as a hypersphere in R 4, has the same local topology and geometry as the rotation group. It thus provides a means for interpolating orientations. It is possible to achieve smooth rotation by filtering in quaternions the resulting quaternion may no longer be unitized. Fortunately, a unit quaternion curve, which represents the rotation path, can be derived by integrating the exponential map of the angular velocity. Unity of quaternions is thus maintained by filtering angular velocities. A lowpass filter coupled with an adaptive, mediative filter are employed to achieve smooth rotation motion in real time.

Solving geometric constraint systems. I. A global propagation approach

Abstract: We describe a geometric constraint solving method/system that takes the declarative description of geometric diagrams or engineering drawings as input and outputs a sequence of steps to construct the diagram with ruler and compass if it succeeds. We extend the local propagation to a global one. Like the local propagation, the global propagation tries to determine the position of a geometric object from the set of geometric objects whose positions are already known. However, our global propagation uses not only the constraints involving this object but also implicit information derived from other constraints. The algorithm can be used to build intelligent CAD and interactive computer graphic systems.

Fast 3D solid model reconstruction from orthographic views

Abstract: As the number of applications that use 3D solid models increases, there is a need to devise an efficient method of constructing a solid model. One approach is reconstruction from orthographic projections. With this method input of geometric information is easy. However, it requires combinatorial searches and complicated geometric operations because of the loss of semantic information during projection. In this paper, we propose an efficient algorithm for reconstructing solid models using geometric properties and the topology of geometric primitives. The experimental results show that the algorithm can reconstruct 3D models much faster than previous algorithms.