The sweep-envelope differential equation algorithm and its application to NC machining verification

Blackmore, Denis; Leu, Ming C.; Wang, Liping P.

doi:10.1016/s0010-4485(96)00101-7

Cited by 143 publications

(70 citation statements)

References 7 publications

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“…where n 1 and n 2 are the outward normal of the adjacent lines and V 1 is the velocity vector of P 1 . By using this criterion, the boundary of swept volume can be determined in this study.…”

Section: Journal Of Advanced Mechanical Design Systems and Manufactmentioning

confidence: 99%

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Collision Distance Detection Based on Swept Volume Strategy for Optimal Motion Plan

Huang

2009

JAMDSM

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A swept volume strategy to detect the collision distances between obstacles is presented in this paper for robot motion planning based on optimization technique. The strategy utilizes the recursive quadratic programming optimization method to perform the motion planning problem. This paper is based on segmental swept volume for convenient distance-to-contact calculation. Hermite interpolation is presented to approach the envelope bounding the swept volume. The new method is capable of handling a modestly non-convex swept volume and it has yielded accurate answers in distance calculations. Also, examples would be presented to illustrate and demonstrate this approach in the paper.

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Section: Journal Of Advanced Mechanical Design Systems and Manufactmentioning

confidence: 99%

“…Following the developed method by Wang and Wang (10) , lots of works were followed trying to build up on the Envelope Theory. A differential sweep-envelope equation algorithm proposed by Blackmore et al (1) was one of well defined swept volume theory for machine tools. Most of the following works were based on their studies.…”

Section: Introductionmentioning

confidence: 99%

Collision Distance Detection Based on Swept Volume Strategy for Optimal Motion Plan

Huang

2009

JAMDSM

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“…These Brep sweep solids lacked a robust mathematical foundation, selfintersecting sweeps were simply invalid. Recent work on the more general problem of sweeping a 3D volume has produced several general swept-volume envelope computation techniques which employ either the sweep-envelope differential equation [Blackmore et al 1997] or Jacobian rank-deficiency conditions [Abdel-Malek and Yeh 1997]. Applications of these techniques are explored in a recent survey [Abdel-Malek et al 2000a].…”

Section: Implicit Sweep Surfacesmentioning

confidence: 99%

Generalized sweep templates for implicit modeling

Schmidt

Wyvill

2005

Proceedings of the 3rd International Conference on Computer Graphics and Interactive Techniques in Australasia and South East A

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A technique is presented for generating implicit sweep objects that support direct specification and manipulation of the surface with no topological limitations on the 2D sweep template. The novelty of this method is that the underlying scalar field has global properties which are desirable for interactive implicit solid modeling, allowing multiple sweep objects to be composed. A simple method for converting distance fields to bounded fields is described, allowing implicit sweep templates to be generated from any set of closed 2D contours (including "holes"). To avoid blending issues arising from gradient discontinuities, a general distance field approximation technique is presented which preserves sharp creases on the contour but is otherwise C 2 smooth. Flat endcaps are introduced into the 3D sweep formulation, which is implemented in the context of an interactive hierarchical implicit volume modeling tool.

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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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The sweep-envelope differential equation algorithm and its application to NC machining verification

Cited by 143 publications

References 7 publications

Collision Distance Detection Based on Swept Volume Strategy for Optimal Motion Plan

Collision Distance Detection Based on Swept Volume Strategy for Optimal Motion Plan

Generalized sweep templates for implicit modeling

A Computational Framework for Boundary Representation of Solid Sweeps

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