Robots and topology

Topology and topological invariants can be used to give insight into engineering problems. In the case at hand we consider a robot arm constructed out of links serially attached. Each link can move only by rotating about an axis through the previous link´s point of contact with the link at hand. The problem is to devise an algorithm so that the end effector at the end of the arm can follow the motion of any frame through its workspace. The difficulty is that there are positions of the arm from which it cannot move instantaneously in the correct direction. These singular positions can be explained through topology. They can never be eliminated but they can be avoided.