China
Africa
Explore chapters and articles related to this topic
Stochastic Processes, Estimation, and Control
Published in Gregory S. Chirikjian, Alexander B. Kyatkin, Engineering Applications of Noncommutative Harmonic Analysis, 2021
Gregory S. Chirikjian, Alexander B. Kyatkin
Here x(t) is the actual state of the system at time t. For a purely mechanical system, the state can be viewed as the set of all generalized coordinates that describe the geometry of the system together with the rates of these generalized coordinates. u(t) is the control input to the system. For a mechanical system this may be a set of generalized forces which alter the behavior of the system. w(t) is some kind of exteraal random disturbance acting on the system at time t. It is assumed within this model that the system itself is known exactly (i.e., that it has already been calibrated). If this were not the case, then the parameters characterizing the system would have to be identified. The area of system identification is a large area of research in itself, which is not addressed here.
Elements of a Classical Control System
Published in Thrishantha Nanayakkara, Ferat Sahin, Mo Jamshidi, Intelligent Control Systems with an Introduction to System of Systems Engineering, 2018
Thrishantha Nanayakkara, Ferat Sahin, Mo Jamshidi
The generalized forces or torques applied on a rigid body, or the generalized momentums in a generalized coordinate system, are given by the Lagrange equation: () Bi=ddt(dLdθ˙i)−dLdθi
Kinetics of Human Body Models
Published in Ronald L. Huston, Principles of Biomechanics, 2008
Generalized forces provide the desired efficiency by automatically eliminating the so-called nonworking forces such as interactive forces at joints, which do not ultimately contribute to the governing dynamical equations. This elimination is accomplished by projecting the forces along the partial velocity vectors (see Section 11.10). Partial velocity vectors, which are velocity vector coefficients of the generalized speeds, may be interpreted as base vectors in the n-dimensional space corresponding to the degrees of freedom of the system. The projection of forces along these base vectors may be interpreted as a generalized work.
Enhanced model including moment-rotation dependency for stability of thin-walled structures
Published in International Journal for Computational Methods in Engineering Science and Mechanics, 2020
Atef S. Gendy, Samir S. Marzouk
The generalized forces acting on a mechanical system may be classified into two categories: conservative and non-conservative forces. The conservative force can be defined as any generalized force associated with stationary single-value potential function dependent only on the generalized displacement. Its work over compatible actual displacement depends on the initial and final configuration of the system (i.e., path independent); and its virtual work over any admissible virtual displacement can be written as a first variation of the displacement-dependent potential function. Dead loads (displacement-independent) and centrifugal forces (displacement-dependent) are examples of conservative forces. On the other hand, the non-conservative force can be defined as any force processing a velocity- or time-dependent potential. It may be depending explicitly on time which is denoted as instationary force. Furthermore, a non-conservative time independent force (i.e., stationary non-conservative force) may be classified either as velocity-dependent, or as velocity-independent; i.e., purely displacement-dependent (more precisely rotation-dependent). The force in this latter case is denoted as circulatory force which is very common in the engineering practical applications. This force does not possess a potential; therefore, its virtual work for any admissible virtual displacement of the body cannot be written as variational of displacement dependent functional. The present work is limited to the large displacement analysis of systems subjected to conservative or non-conservative force of the circulatory type.
Parallel manipulator dynamics embedded in singularity free domains of functionality
Published in Mechanics Based Design of Structures and Machines, 2021
Equations of motion for the parallel manipulator are first written in terms of mechanism generalized coordinates q, applied forces, and actuator forces that are to control motion of the manipulator, using the d’Alembert variational formulation (Pars 1965; Haug 2020b), which holds for all that satisfy and associated and that satisfy linearized forms of Eqs. (2) and (3). The first term in Eq. (4) accounts for kinetics of the mechanism, where is the mass matrix of the mechanism and contains velocity coupling terms, sometimes called Coriolis forces. The generalized force accounts for external forces and torques that act on the mechanism, including gravity, friction, and any compliant components of the mechanism. The generalized force accounts for forces and torques that resist motion of the output component, or end effector, of the manipulator. The input generalized force is comprised of actuator forces and torques associated with input coordinates that are exerted to control motion of the manipulator. To obtain ODE of motion for the manipulator that are equivalent to Eq. (4), manipulator kinematic relations are presented in Section 2.