On Shaping With Motion

[+] Author and Article Information
Horea T. Ilieş, Vadim Shapiro

Spatial Automation Laboratory, Department of Mechanical Engineering, 1513 University Avenue, University of Wisconsin-Madison, WI 53706

J. Mech. Des 122(4), 567-574 (Feb 01, 1999) (8 pages) doi:10.1115/1.1319319 History: Received February 01, 1999
Copyright © 2000 by ASME
Topics: Motion
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A translating disk sweeping a 2-dimensional set
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The largest set that remains inside a square that rotates around O by an angle of 45° in the clockwise direction
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Space partition induced by the operation of unsweep and the standard set operations. All points of each of the four sets behave the same relative to X under motion M: either all remain inside X (Ω1), go outside X (Ω2), collide with X (Ω3) or do not collide with X (Ω4).
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Some of the four sets might be empty, depending on the motion: in (a) Ω2 and Ω3 are empty sets, while in (b) Ω1 is an empty set
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The moving part S has to fit within the given containing set E
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Any stationary object B that maintains contact with the moving A must be a subset of Ω4∪∂Ω4. If we assume that A is the follower, then the bounded set may be the cam that would move relative to A according to the given relative motion M.
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Object A, which moves relative to B as shown, induces a partitioning of the space in which it moves. Set Ω4 can be used to detect collision and eliminate it by changing the shape of B.
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The largest secondary hood latch (d) is obtained from a Boolean intersection of the largest shape satisfying the containment constraint (b) and the largest shape satisfying the contact constraints (c). This largest latch remains inside the specified containing set, and hence it does not collide with the neighboring parts, and it also satisfies the kinematic functionality.




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