Machine efficiency determined using graph and screw theories with application in robotics

Abstract A new method to determine the efficiency of complex machines, including parallel robots, based on graph and screw theories is presented. The method can be used with any arbitrary set of joints connected in any possible way. Graph theory is used to describe the topology and screw theory, the joints geometric features. It is an extension of the Davies’ Method in which active coupling is used to model power entering and leaving a kinematic chain. An increase in accuracy is obtained by splitting up prismatic joints, which results in a more realistic model. The slider-crank linkage and the 3-UPU spatial manipulator are used as examples and details on modelling prismatic, revolute and universal joints are presented.