A fundamental study of the effect of gravity on the static and dynamic behavior of robots.

Abstract

The gravity induced force on revolute robot links is generally comparable to the dynamic induced forces at high operational speeds. At low speeds this force dominates over the dynamic forces. In the process of study of the static and dynamic behaviour of manipulators through the overall measures such as the force ellipsoid, the dynamic manipulability ellipsoid, and the generalized ellipsoid of inertia the effect of gravity is ignored due to the complexity that the inclusion of this force brings to the analysis. This study presents a method to include the effect of gravity in the static and dynamic analysis of robot arms. Using the concept of fields, the gravity induced forces acting on individual links are replaced by a single force, called here the generalized weight of the arm. The generalized weight is a force that acts at the end effector and its magnitude and direction are functions of the configuration of the manipulator. Since the system is conservative, the generalized weight is considered to be the gradient of a potential field that will be called here the generalized gravitational field (GGF). This field alone can illustrate the overall effect of gravity on the manipulator throughout its work volume. The generalized weight field is then integrated with the force ellipsoid to display the true force that a manipulator can apply to its environment. Based on the generalized weight field and the generalized inertia tensor the generalized gravitational acceleration field is introduced. The dynamic manipulability ellipsoid is then superimposed on this field to demonstrate the true acceleration capability of the end effector. The relation between the generalized weight and the generalized ellipsoid of inertia is investigated. Effect of change of physical parameters of the arm are also discussed. It is shown that for a particular design of manipulators the generalized gravitational field is absolutely flat, and in general the manipulators's physical parameters may be used to tailor the GGF for a particular application.