bled back on itself. There might be, but is not always, a wrist joint that can flex likethe elbow and/or twist around and around.A 90-degree-elevation revolute robot arm can reach any point within a half sphere.The radius of the half sphere is the length of the arm when its elbow and wrist (if any)are straightened out. A 180-degree-elevation revolute arm can be designed that willreach any point within a fully defined sphere, with the exception of the small obstructedregion around the base.Robotic hearing and visionMachine hearing involves more than just the picking up of sound (done with a mi-crophone) and the amplification of the resulting audio signals (done with an ampli-fier). A sophisticated robot can tell from which direction the sound is coming andperhaps deduce the nature of the source: human voice, gasoline engine, fire, or bark-ing dog.652 Robotics and artificial intelligencexyTelescoping armSliding androtating movementReference axiszReference plane34-4Cylindrical coordinate geometry in three dimensions. Variable xrepresents reach; y represents elevation; z represents rotation.