Topology and the robot arm
A robot arm is in effect a smooth function from the space of positions of the arm to the space of positions of a coordinate frame attached to the end of the arm. For the most common robots built today, this means a map f: \(T^ n\to {\mathbb{R}}^ 3\times SO_ 3\). We describe the singularities of this map. The set of rotational singularities is the set of arm positions where the axes of the links are parallel to a plane. Thus, it is always two-dimensional. Also, we show that f is homotopic to a map which factors through a circle, and represents the generator of \(\pi_ 1(SO_ 3)\). The engineering implications of these statements are discussed.
space of positions of a coordinate frame
scientific article; zbMATH DE number 4064074