Designing multi-link robot arms in a convex polygon

Ichiro Suzuki, Masafumi Yamashita

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


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(n2) 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(n2) time.

Original languageEnglish
Pages (from-to)461-486
Number of pages26
JournalInternational Journal of Computational Geometry and Applications
Issue number4
Publication statusPublished - Jan 1 1996

All Science Journal Classification (ASJC) codes

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


Dive into the research topics of 'Designing multi-link robot arms in a convex polygon'. Together they form a unique fingerprint.

Cite this