One Robot, Multiple Coordinate Systems

Because a robot arm is simply a chain of revolute joints, any movement in the task space – often called cartesian space – can only be realised thanks to the magic of inverse kinematics. When we refer to the cartesian coordinates of a waypoint in space, they must be defined relative to a coordinate system that often takes its origin at the centre of the base of the robot. But this origin, often called the Base coordinate system, is only ever an arbitrary origin that has no physical reality besides being defined as a point located at the base of the robot. Similarly there is another arbitrary coordinate system, often called the Tool coordinate system, that defines a translation and orientation offset from the tool flange, and that can be considered as a particular point of interest when working with various tools. By using these together they allow the robot controller to make complex movements easily, without being restricted by the natural mechanics of a machine like a 3D printer that can only ever move alongside its fixed axes. In robotics, coordinate systems are commonly referred to as frames.