Indeterminate system

Abstract: Prediction of passive forces in a frictional workpiece-fixture system is an important problem, since the contact forces have a strong influence on clamp design and on workpiece accuracy during machining. This paper presents a general method for the computation of the contact forces. First, based on the rigid-body kinematics, an indeterminate system of static equilibrium is defined, in which the passive, frictional contact forces cannot be determined arbitrarily as in an actively controlled robotic multi-finger grasp. Then, we define a locally elastic contact model to describe the nonlinear coupling between the contact forces and elastic deformations at the contact point. This model captures the essence of the passive contact. Further, a set of “compatibility” equations are given so that the elastic deformations among all passive contacts in the workpiece-fixture system result in a consistent set of rigid-body displacement of the workpiece in its global system. Finally, combining the locally elastic contact model and the “compatibility” conditions, we transform the force computation problem into a determinate system of nonlinear equations governing all of the elastic deformations at all of the passive contacts. By solving the resulting nonlinear equations with frictional constraints, we can accurately predict all contact forces in the frictional workpiece-fixtures system. This method is illustrated with example cases. The method presented here may also have an application to other passive, indeterminate problems such as power grasps in robotics.Copyright © 2003 by ASME

Abstract: The invention provides a coupling enhancing non-linear PD-type sliding mode controller for a bridge crane system, and a method The designed controller is composed of a PD control part and an SMC control part The SMC control part is used for constructing a frame of the controller Quite high robustness is achieved aiming at an indeterminate model, different and indeterminate system parameters andexternal disturbance of a system The PD control part is used for stably controlling the system In addition, a generalized function is introduced, the coupling relation among trolley movement, lifting hook swinging and load swinging is enhanced, and thus the transient control property of the system is improved By utilizing the Lyapunov theorem and Schur complement, it is proved that the asymptotic stability and convergence of the system can still be ensured through the provided control method even if the model and the system parameters are indeterminate and external disturbance exists Thesimulation result shows the correctness of the provided control method and the excellent control property

Abstract: Start-up dynamics plays an essential role in ensuring the comfort and running safety and structural integrity of trains. Based on the discontinuous dynamics framework, in the present work, an efficient innovative model is proposed. The model is derived from previous train braking studies and in order to highlight the possibility of a non-smooth approach to train start longitudinal dynamics. Set-valued friction of Coulomb’s law type is accounted for and motion equations are formulated as a differential inclusion. Static friction forces which arise in buffers are computed in a very intuitive and efficient manner, using involving generalised inverses of matrices. The corresponding algorithm is described. Numerical integration is done by an event-driven algorithm. Indeterminate system configurations can be appropriately handled. The number of train vehicles may be easily adjusted, and any wagon connection model can be embedded. Specific phenomena like stick–slip or persistent longitudinal forces can b...