Robotic Workspaces after a Free-Swinging Failure

A robotic manipulator can fail in many diierent ways, and its capabilities after a failure are a major concern, especially for manipulators used in hazardous and remote environments, where the cost of repair or replacement is high. This article presents a study of the workspaces of robotic arms after a free-swinging failure, deened as a hardware or software failure that prevents the application of actuator torque on a joint. Two analytical methods are discussed. The rst is for planar arms only and is based on a positional inverse-kinematic algorithm that uses polynomial roots, guaranteeing that all solutions, and therefore the postfailure workspace, can be found. The second method has no such guarantee, but is applicable to general spatial manipulators. It is based on a diierential technique for tracing the postfailure workspace boundary.