### 抜粋

The problem of designing a k-link robot arm confined in a convex polygon that can reach any point in the polygon starting from a fixed initial configuration is considered. The links of an arm are assumed to be all of the same length. We present a necessary condition and a sufficient condition on the shape of the given polygon for the existence of such a k-link arm for various values of k, as well as necessary and sufficient conditions for rectangles, triangles and diamonds to have such an arm. We then study the case k = 2, and show that, for an arbitrary n-sided convex polygon, in O(n^{2}) time we can decide whether there exists a 2-link arm that can reach all inside points, and construct such an arm if it exists. Finally, we prove a lower bound and an upper bound on the number of links needed to construct an arm that can reach every point in a general n-sided convex polygon, and show that the two bounds can differ by at most one. The constructive proof of the upper bound thus provides a simple method for designing a desired arm having at most k+1 links when a minimum of k links are necessary, for any k ≥ 3. The method can be implemented to run in O(n^{2}) time.

元の言語 | 英語 |
---|---|

ページ（範囲） | 461-486 |

ページ数 | 26 |

ジャーナル | International Journal of Computational Geometry and Applications |

巻 | 6 |

発行部数 | 4 |

DOI | |

出版物ステータス | 出版済み - 1 1 1996 |

### フィンガープリント

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Geometry and Topology
- Computational Theory and Mathematics
- Computational Mathematics
- Applied Mathematics

### これを引用

*International Journal of Computational Geometry and Applications*,

*6*(4), 461-486. https://doi.org/10.1142/S0218195996000290