Computing All Immobilizing Grasps of a Simple Polygon with Few Contacts

被引：0

作者：

Jae-Sook Cheong

Herman J. Haverkort

A. Frank van der Stappen

机构：

[1] Department of Information and Computing Sciences,

[2] Utrecht University,undefined

[3] P.O. Box 80089,undefined

[4] 3508 TB Utrecht,undefined

[5] Department of Mathematics and Computing Science,undefined

[6] Eindhoven University of Technology,undefined

[7] P.O. Box 513,undefined

[8] 5600 MB Eindhoven,undefined

来源：

Algorithmica | 2006年 / 44卷

关键词：

Immobility; Grasp; Fixturing; Wrench; Form closure; Second-order immobility; Positive basis;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

We study the output-sensitive computation of all the combinations of edges and concave vertices of a simple polygon that allow an immobilizing grasp with less than four frictionless point contacts. More specifically, if n is the number of edges, and m is the number of concave vertices of the polygon, we show how to compute: in O(m4/3 log1/3 m + K) time, all K combinations that allow a form-closure grasp with two contacts; in O(n2 log4 m + K) time, all K combinations that allow a form-closure grasp with three contacts; in O(n log4 m + (nm)2/3 log2+ε m + K) time (for any constant ε > 0), all K combinations of one concave vertex and one edge that allow a grasp with one contact on the vertex and one contact on the interior of the edge, satisfying Czyzowicz's weaker conditions for immobilization; in O(n2 log3 n + K) time, all K combinations of three edges that allow a grasp with one contact on the interior of each edge, satisfying Czyzowicz's weaker conditions for immobilization.

引用

页码：117 / 136

页数：19