On the dynamic analysis of a manipulator and its end effector interacting with the environment

Dynamic behavior of a manipulator arm and its end effector that interact with the environment is analyzed. Inertial properties of the arm and the end effector are represented with respect to a point of contact between the end effector and the environment. Virtual mass is then defined to be the equivalent mass of the arm and the end effector reflected to the point of contact, and is given by the ratio of a force acting on the point to the acceleration caused by the force at the point. Unlike a real mass, the virtual mass varies depending on the direction of the applied force and the location of the contact point. The maximum and minimum values of the virtual mass are then obtained and the physical meanings are discussed. Next, the rotational motion of the end effector is considered. A single rigid body possesses a centroid; a particular point at which rotation and translation of the rigid body are separated. The concept of the centroid is extended to the one for a system of rigid bodies such as arm links and the members of the end effector. The point is referred to as the generalized centroid, at which a linear force causes only a linear acceleration and a pure moment causes only an angular acceleration, hence separated. The virtual mass and the generalized centroid are then applied to task planning for chipping, hard surface contact, and dynamic insertion operations. The orientation of a tool and the configuration of the manipulator arm are optimized so that a desired dynamic behavior can be accomplished by having an appropriate virtual mass and the generalized centroid at an appropriate point.