Complete swept volume generation, Part I: Swept volume of a piecewise C1-continuous cutter at five-axis milling via Gauss map

Lee, Seok Won; Nestler, Andreas

doi:10.1016/j.cad.2010.12.010

Cited by 45 publications

(18 citation statements)

References 27 publications

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“…Some considered the representation of the workpiece [4,5]. Other works, considered the generation of the tool swept volume [6][7][8]. The difficulty at this level is related to the kinematics of the 05-axis machine where the tool translates and rotates simultaneously.…”

Section: Macroscopic Scalementioning

confidence: 99%

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Survey on Simulation Methods in Multi-axis Machining

Bouhadja

Bey

2015

Transactions on Engineering Technologies

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In industry, the evolution of productivity and quality of mechanical manufacture of complex shape parts (mold, automobile, form : : : ) is marked by the development of several machining simulation techniques for modeling and predicting the manufacturing process to represent the most realistic cut phenomenon. There exist several machining simulation techniques and touch various levels. Thus, this chapter summarizes the literature review and presents the techniques in a simplified scheme for the rapid exploration in this area, and in order to direct the reader to select an appropriate approach linked to a geometric or physical problem at a given scales in Part-Tool-Machine system. Particular attention is given to geometric simulation methods of the macroscopic scale; completed by brief comparison between models of workpiece representation for material removal process (Dexel, Voxel, Triple-Dexel).

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Section: Macroscopic Scalementioning

confidence: 99%

“…The recent works are focused on the generation of the tool swept volume for 05-axis machining [6][7][8] where the difficulty is increased by the kinematics of the machine since the tool translates and rotates simultaneously ( Fig. 25.8).…”

Section: Geometric Model Of Swept Volumementioning

confidence: 99%

Survey on Simulation Methods in Multi-axis Machining

Bouhadja

Bey

2015

Transactions on Engineering Technologies

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“…The curve of contact is referred to as the characteristic curve in [PPSZ05]. The normals of contact at t are referred to as the contact map in [LN11a].…”

Section: Mathematical Structure Of the General Sweepmentioning

confidence: 99%

“…Sweeping has several applications, viz. CNC‐machining verification [LN11a, LN11b], collision detection, motion planning [AMBJ06] and packaging [Kin].…”

Section: Introductionmentioning

confidence: 99%

Incorporating Sharp Features in the General Solid Sweep Framework

Adsul

Machchhar

Sohoni

2016

Computer Graphics Forum

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This paper extends a recently proposed robust computational framework for constructing the boundary representation (brep) of the volume swept by a given smooth solid moving along a one parameter family h of rigid motions. Our extension allows the input solid to have sharp features, i.e., to be of class G0 wherein, the unit outward normal to the solid may be discontinuous. In the earlier framework, the solid to be swept was restricted to be G1, and thus this is a significant and useful extension of that work.This naturally requires a precise description of the geometry of the surface generated by the sweep of a sharp edge supported by two intersecting smooth faces. We uncover the geometry along with the related issues like parametrization, self-intersection and singularities via a novel mathematical analysis. Correct trimming of such a surface is achieved by a delicate analysis of the interplay between the cone of normals at a sharp point and its trajectory under h. The overall topology is explicated by a key lifting theorem which allows us to compute the adjacency relations amongst entities in the swept volume by relating them to corresponding adjacencies in the input solid. Moreover, global issues related to body-check such as orientation are efficiently resolved. Many examples from a pilot implementation illustrate the efficiency and effectiveness of our framework.

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“…A special case of this, viz., blends is already an important operation and used extensively. Prospective uses for the sweep are in NCmachining verification [1], [5], [8], [9], collision detection, assembly planning [1] and in packaging [7].…”

Section: Introductionmentioning

confidence: 99%

A Computational Framework for Boundary Representation of Solid Sweeps

Adsul

Machchhar

Sohoni

2014

Computer-Aided Design and Applications

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This paper proposes a robust algorithmic and computational framework to address the problem of modeling the volume obtained by sweeping a solid along a trajectory of rigid motions. The boundary representation (simply brep) of the input solid naturally induces a brep of the swept volume. We show that it is locally similar to the input brep and this serves as the basis of the framework. All the same, it admits several intricacies: (i) geometric, in terms of parametrizations and, (ii) topological, in terms of orientations. We provide a novel analysis for their resolution. More specifically, we prove a non-trivial lifting theorem which allows to locally orient the output using the orientation of the input. We illustrate the framework by providing many examples from a pilot implementation.Keywords: Solid sweep, swept volume, solid modeling, boundary representation, parametric curves and surfaces. INTRODUCTIONThis paper is about the theory and implementation of the solid sweep as a primitive solid modeling operation. A special case of this, viz., blends is already an important operation and used extensively. [7]. The solid sweep is the envelope surface of the swept volume generated by a given solid moving along a oneparameter family of rigid motions in . We use the industry standard boundary representation (brep) format to input the solid and to output the envelope . The brep of course is the topological data of vertices, edges and co-edges, loops bounding the faces and orientation of these, and the underlying geometric data of the surfaces and curves. As we show, the brep of , while intimately connected to that of , has several intricate issues of orientation and parametrization which need resolution.Much of the mathematics of self-intersection, of passing body-check and of overall geometry have been described in the earlier work [4]. This paper uncovers the topological aspects of the solid sweep and its construction as a solid model. Here, we restrict ourselves to the simple generic case, i.e., smooth and a smooth which is free from self-intersections. This serves to illustrate our approach and its implementation. The general case is also implemented and a sample sweep appears in Fig. 1.Our main contributions are (i) a clear topological description of the sweep, and (ii) an architectural framework for its construction. This, coupled with [4], which constructs the geometry/parametrizations of the surfaces, was used to build a pilot implementation of the solid sweep using the popular ACIS solid modeling kernel [3]. We give several illustrative 1

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Complete swept volume generation, Part I: Swept volume of a piecewise C1-continuous cutter at five-axis milling via Gauss map

Cited by 45 publications

References 27 publications

Survey on Simulation Methods in Multi-axis Machining

Survey on Simulation Methods in Multi-axis Machining

Incorporating Sharp Features in the General Solid Sweep Framework

A Computational Framework for Boundary Representation of Solid Sweeps

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