Research Papers

Contact Prediction Between Moving Objects Bounded by Curved Surfaces

[+] Author and Article Information
Abdulmohsen Al Bedah, John J. Uicker

 King Saud University, Ridya, Saudi Arabia e-mail: albedah@ksu.edu.sa University of Wisconsin, Madison, WI 53706 e-mail: uicker@engr.wisc.edu

For further information on the use of transformation matrices for the representation of motion see Ref. [23].

We say theoretically because, in reality, sharp edges and corners are usually rounded; if this is the situation, then we will have only the face-face case.

Divergence is declared when the number of iterations exceeds a prescribed number before satisfying Eqs. 27.

J. Comput. Inf. Sci. Eng 12(1), 011003 (Dec 21, 2011) (9 pages) doi:10.1115/1.4005453 History: Received October 04, 2011; Revised October 09, 2011; Published December 21, 2011; Online December 21, 2011

This paper presents an algorithm for exact contact prediction between moving objects bounded by curved surfaces. The algorithm uses hierarchies of oriented bounding boxes (HOBBs) and local numerical methods for finding contact. Objects need not be convex and are described using the B-rep scheme. The bounding faces are represented by nonuniform rational B-splines (NURBS). The collision time is sought in short time intervals during the motion, during which time is one of the problem variables. HOBBs are based on curvature regions of the surfaces. This criterion ensures that local numerical methods will converge to the contact points if they exist. The patches enclosed in overlapping leaf nodes are tested for contact by solving a system of nonlinear equations, based on the type of collision expected. The types of collision studied are cusp–cusp, cusp–ridge, cusp– face, ridge–ridge, ridge–face, and face–face collisions. The current algorithm is implemented and compared to an efficient polyhedral collision package, and results appear promising.

Copyright © 2012 by American Society of Mechanical Engineers
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Figure 6

Efficiency comparison between current algorithm and rapid software

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Figure 7

The light gray area is where rapid was more efficient. rapid was always more efficient in discovering first intersection only when the number of triangles was≤ 70 or equal 1218, or when the objects were disjoint.

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Figure 9

Example 3. Initial position of the objects: perspective view (left) and front view (right). Lower view shows objects at the time of contact with the contact point highlighted by a circle.

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Figure 1

Types of contact between curved surfaces: (a) cusp–cusp, (b) cusp–ridge, (c) cusp–face, (d) ridge–ridge, (e) ridge–face, and (f) face–face

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Figure 2

Geometric interpretation of Newton method

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Figure 3

Chord length to radius of curvature relationship

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Figure 4

Estimation of angles in the u and v directions

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Figure 5

(a) Using only minimum distance as the merging criterion. BV4 which encloses both BV1 and BV3 contains a lot of empty space. (b) Using minimum distance and adjacency as merging criteria produces BV4 with less empty space.



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