TY - JOUR

T1 - Designing multi-link robot arms in a convex polygon

AU - Suzuki, Ichiro

AU - Yamashita, Masafumi

PY - 1996/1/1

Y1 - 1996/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0030353246&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0030353246&partnerID=8YFLogxK

U2 - 10.1142/S0218195996000290

DO - 10.1142/S0218195996000290

M3 - Article

AN - SCOPUS:0030353246

VL - 6

SP - 461

EP - 486

JO - International Journal of Computational Geometry and Applications

JF - International Journal of Computational Geometry and Applications

SN - 0218-1959

IS - 4

ER -