On the position density of planar two-link manipulators

Every manipulator exhibits a discrete resolution in its joint actuation due to the use of angular encoders as the sensing device for joint actuation. Hence, one obtains a manipulator that is limited to movement within discrete positions in its reachable workspace. This corresponds to the fact that the absolute accuracy of the end effector depends on the resolution of the actuated joints. In this work we present a thorough analysis of this discretization process and its mathematical foundations for a two-link planar manipulator. We show how to compute an underlying accuracy function for the end effector position of arbitrary two-link manipulators. This allows us to formulate a metric to compare possible variations of these robots in terms of end effector precision. Despite the simplicity of our robot model, a two-link planar robot, we obtain viable results as the two-link mechanism is widely applied in so called SCARA's. We therefore demonstrate our analysis to selected industrial SCARA type robots.