Reaching a Point with an Unanchored Robot Arm in a Square

Abstract

This paper considers an unanchored n-link robot arm in a square with side length at least as long as the longest arm link. The main result is a necessary and sufficient condition for a point in the square region to be reachable by a specified end of the arm. The condition takes O(n) time to determine. This result represents a continuation of previous work published by Hopcroft, Joseph, and Whitesides, by Kantabutra and Kosaraju, and by Kantabutra.