Simulation of Manipulator Dynamics and Adjusting to Functional Movements

Abstract

The methods for computer-aided formation and solution of the mathematical models of active mechanisms (described in Chapter II and in [1–15]) have served as a basis for the development of the algorithm for the simulation of manipulator dynamics. We shall first indicate the main ideas and problems, and then describe the general algorithm for the simulation of dynamics [16, 17]. Later, we shall adjust this algorithm to some classes of practical tasks, i.e., to functional movements, particularly because of the efficiency of handling the algorithm. At the same time we shall analyse the need for a certain number of degrees of freedom of the manipulator as well as their use in the various categories task [18]. Something more should be said about the number of manipulator d.o.f. and about the number of d.o.f. necessary for performing a particular manipulation task. At first, we note the difference between the number of d.o.f. of the whole manipulator (considered as a dynamical system), and the number of d.o.f. of the gripper (considered as the last rigid body in the chain). These two numbers need not be equal. The number of manipulator d.o.f. depends on the number of joints and the number of d.o.f. in each joint. For instance, if a manipulator represents an open chain without branching and consists of n segments and n one-d.o.f. joints, then it has n degrees of freedom.