Showing papers on "Virtual work published in 1997"

Adaptive control of the Hexaglide, a 6 dof parallel manipulator

Abstract: This paper presents the dynamic equation, nonlinear control and dynamic parameters identification of the Hexaglide, a new 6-DOF parallel manipulator intended to be used as a high speed milling machine. Using a method based on the virtual work principle, the dynamic equation is found in a compact linear form and then used in a nonlinear adaptive control algorithm based on the minimization of the tracking error. The dynamic parameters are learned during motion and introduced in an inverse dynamic model used as a feedforward compensator. Specific trajectories, exciting the parameters separately, enable a fast stepwise learning of the 12 parameters. A simulation demonstrates the validity of the approach.

A body-oriented method for finding a linear form of the dynamic equation of fully parallel robots

Abstract: In order to identify the dynamic parameters in nonlinear adaptive control the robot's dynamic equation has to be written in a linear form. Many methods have been proposed for serial robots, but for parallel robots, the few solutions proposed so far lead to complicated equations that are not readily usable for real-time implementation. In this paper we propose a new method based on the virtual work principle to find a linear form of the dynamic equation of robots. Compared to other methods, it has the advantage that it does not need to open the closed loop structure into a tree-structure robot. It considers rather each body separately using its Jacobian matrix to project the forces into the joint space of the robot. Thus, simplification can be made at the very beginning of the modeling. This is very efficient when used to model fully parallel robots. As an illustration, the proposed method is applied to the 3dof DELTA parallel robot.

Geometrically Nonlinear Theory of Multilayered Plates with Interlayer Slips

Abstract: The formulation of a geometrically nonlinear theory of anisotropic multilayered plates of general layups featuring interlayer slips is discussed. The theory rests on a displacement field, which accounts for an arbitrary distribution of the tangential displacements through the laminate thickness, fulfills a priori the static continuity conditions of tangential stresses at the layer interfaces, and allows for jumps in the tangential displacements so as to provide the possibility of incorporating effects of interfacial imperfection. For the interlayer displacement jump, a linear shear slip law is postulated. No a priori assumption is made on the type and order of the expansion in the thicknesswise direction of the tangential displacements. The pertinent equations of motion and consistent boundary conditions are derived by means of the dynamic version of the principle of virtual work. These are given in terms of force and moment stress resultants and in terms of generalized displacements. The generalization achieved by the proposed approach is shown by deriving, as particular cases, the recently proposed first-order and third-order models for laminated plates featuring interlayer slips

Mechanical systems with nonholonomic constraints

Abstract: A geometric setting for the theory of first-order mechanical systems subject to general nonholonomic constraints is presented. Mechanical systems under consideration are not supposed to be Lagrangian systems, and the constraints are not supposed to be of a special form in the velocities (as, e.g., affine or linear). A mechanical system is characterized by a certain equivalence class of 2-forms on the first jet prolongation of a fibered manifold. The nonholonomic constraints are defined to be a submanifold of the first jet prolongation. It is shown that this submanifold is canonically endowed with a distribution—this distribution (resp., its vertical subdistribution) has the meaning of generalized possible (resp., virtual) displacements. The concept of a constraint force is defined, and a geometric version of the principle of virtual work is proposed. From the principle of virtual work a formula for a workless constraint force is obtained. A mechanical system subject nonholonomic constraints is modeled as a deformation of the original (unconstrained) system. A direct characterization of a constrained system by means of a class of 2-forms along the canonical distribution is given, and “constrained equations of motion” in an intrinsic form are found. A geometric definition of regularity for systems under nonholonomic constraints is provided. In particular, the case of Lagrangian systems is discussed. Also systems subject to holonomic constraints and nonholonomic constraints affine in the velocities are investigated within the range of the general scheme.

A superconvergent stress recovery technique with equilibrium constraint

Abstract: A stress recovery technique is developed to extract more accurate nodal stress values from the raw stress values obtained directly from the finite element analysis. In the present method a stress field is assumed over a patch of elements, and a least-squares functional is formed using the discrete stress errors at the superconvergent stress points and the residual of the equilibrium equation expressed in the virtual work form. The results of numerical tests conducted on one-dimensional and two-dimensional example problems demonstrate the validity and effectiveness of the present method. The introduction of an equilibrium constraint allows a patch stress field of higher order than is possible without the equilibrium constraint and this leads to a recovered stress field of higher accuracy. Because the residual of equilibrium is expressed in the virtual work form, the proposed method can easily be applied to arbitrarily curved shell structures. © 1997 by John Wiley & Sons, Ltd.

Modern Formulation for Preelastic Theories on Masonry Arches

Abstract: The masonry arch as a system of rigid voussoirs subject to unilateral constraints has been investigated applying the principle of virtual work in order to define a general criterion providing the necessary and sufficient conditions for the equilibrium of the system Since the assumptions of the formulation coincide with those of the preelastic theories, the main historical approaches have been revisited, showing that their criteria are encompassed in the present formulation A parametric analysis has been carried out with reference to geometry and friction for a semicircular arch of constant thickness and subject to its own weight The ranges of values for the thrust at the crown required for the equilibrium to exist have been thus determined and a geometric safety factor has been defined A comparison of these results for the arch of minimum thickness with those obtained from the historical theories and more recent formulations has also been made

Simulating the Mechanical Properties of a Yarn Based on the Properties and Arrangement of its Fibers Part I: The Finite Element Model:

Abstract: A theoretical model is established to predict stress-strain and torque-tensile strain curves of a yarn. The yarn is described by its properties and the arrangement of its fibers, which have a finite length. The yarn is transformed into finite elements. Equilibrium is expressed by virtual work, and is calculated iteratively using the dynamic relaxation technique. The principles of the model, its potential, limitations, and possible improvements are discussed.

Electromechanical Interactions in Multibody Systems Containing Electromechanical Drives

Abstract: Electromechanical systems are characterized by interaction of electromagnetic fields with inertial bodies. Electromechanical interactions can be described by so-called constitutive equations.Constitutive equations describing the coupling of multibody dynamics with Kirchhoff‘s theory of electrical networks as a quasi stationaryapproximation of Maxwell‘s theory define discrete electromechanicalsystems, i.e. systems with a finite degree of freedom.Then, based on the principle of virtual work, motion equations can be obtained as Lagrange‘s equations in explicit form due to a unified approach. The motion equations can be generated automatically. Hence, all electromechanical interactions are correctly taken into account.Examples for a MAGLEV and a planar motor are given.

Space Interface Device for Artificial Reality – SPIDAR –

Abstract: To realize the human interface which efficiently models a three-dimensional shape on a computer, it is necessary to provide an environment in which the shape model can be manipulated directly as the actual three-dimensional object. Such an environment is called the virtual work space. In the human manipulation of an object by hand, such sensations as visual, tactile (touch), and force are utilized unconsciously. To compose the virtual work space, it is important that the human be given such sensory information in an integrated way. Such information must totally be generated artificially by computer processing. Based on such an idea, this paper proposes anew a space interface device called SPIDAR, as the I/O device needed in composing the virtual work space. The device functions to derive the information concerning the finger position and to provide the force sense information to the finger tip. The virtual work space for generation and manipulation of the three-dimensional shape is composed using SPIDAR. An experiment is conducted to examine the effect of the force sense on the direct manipulation of the three-dimensional shape in the virtual work space, and the usefulness of the method is verified.

Using Energy Methods to Derive Beam Finite Elements Incorporating Piezoelectric Materials

Abstract: We apply the principle of virtual work to derive the equations of motion for arbitrarily shaped linear piezoelectric materials which are either embedded in or perfectly bonded to the surface of an ...

Optimal design of nonlinear structures and mechanical systems

Abstract: This paper presents an optimal structural design system based on a variational theory of design sensitivity analysis for linear and nonlinear structures and mechanical systems. So called flexible systems and structures, as well as design and control variables, are treated within a unified frame. The concept of an auxiliary system, the principle of virtual work, and a Lagrangean-Eulerian description of the deformations and design variations, are used to develop the unified viewpoint. Finite element and finite difference methods are used for spatial and time discretization of the sensitivity equations. The isoparametric concept of the finite element formulation is related to the concept of control volume. The concept of a design element is used for the design modeling of the structure and to generate the analysis model from the design model. Structural analysis and optimization codes are combined to create an optimal design capability. Optimalily criteria methods and nonlinear programming are applied as opt...

Lumped impulses, discrete displacements and a moving load analysis

Abstract: Finite element models are usually presented as relations between lumped forces and discrete displacements. Mostly finite element models are found by the elaboration of the method of the virtual work - which is a special case of the Galerkin's variational principle -. By application of Galerkin's variational principle to time dependent problems, considering elements bordered by ge()metry and time b()undaries, we obtain relations between lumped impulses and discrete displacements. The analogy with respect to static models which formulates relati()ns between lumped forces and discrete displacements is striking. Models are formulated using linear and quadratic displacement fields with respect to time. Free model parameters are used to manipulate numerical stability, accuracy and numerical damping. These numerical tools are used for the numerical simulation ()f a m()ving vehicle at a rail track structure. The analysis sh()ws the natural way ()f m()delling a moving structure (the train) with respect to a fixed supporting structure (the rail track).

Deviation of Equation of Motion of Closed Loop Mechanisms

Abstract: Derivation of an equation of motion of closed loop mechanisms by the motor algebra is presented in this paper. The equation can be given by first determining the velocities and accelerations of the links, next deriving the equilibrium equations of the forces and moments on links, and then appling conditions of the virtual work of joint motions to the equilibrium equations. Simple description of the derivation method are shown by using the motor algebra. In order to reduce the computational cost for the dynamic analysis, it is essential to utilizing the geometrical specialities in a mechanism to the derivation of an equation of motion. It is shown, by two examples of the derivation for a translational table mechanism and a parallel mechanism, that the expression of derivation by the motor algebra makes their utilization easier.

SRM torque computation from 3D finite element field solutions

Abstract: Force and torque computation from finite element field solutions is a key step in the design of some electromechanical devices, and a successful simulation of such devices demands an accurate and reliable method of force or torque calculation. There are four established ways of predicting EM forces or torques: (1) the Lorentz or the JxB method; (2) the Maxwell stress tensor (MST) method; (3) the classical virtual work method; and (4) the Coulomb virtual work (CVW) method. The first three methods have limitations when used in the finite element context. The CVW method, however, provides a more general algorithm which is easier to implement especially in 3D finite element electromagnetic field analysis. The theory of the CVW method is now well known but no results have been published which illustrate its application to practical problems which require 3D finite element analysis. This paper corrects this deficiency and shows that the CVW method can be superior in accuracy and implementation to the MST method. To highlight this superiority, a switched reluctance motor is considered and investigated using both 2D and 3D finite element analyses. The motor, which has six poles on the stator and four poles on the rotor, has been extensively and carefully tested. The torque-angle characteristics are obtained by the application of the CVW method in both 2D and 3D for various excitations at different positions of the rotor. Comparison between the 2D, 3D and the experimental data shows that the torque computed from the 3D analysis is in much better agreement with the experimental data than that obtained from 2D.

Semiconductor shape prediction simulation and system thereof

Abstract: PROBLEM TO BE SOLVED: To obtain a semiconductor shape prediction simulation method, which can predict the shape of a semiconductor, which is close to the shape of the real semiconductor, and reduces the labor of users, and the system of the method SOLUTION: Three-dimensional meshes 8 are set on an analytic plane, which is the object of a simulation The meshes 8 are made to expand and nodes 7 are made to displace on the basis of the principle of a virtual work The shape of a semiconductor is predicted by the positions of the nodes 7 A constraint in the principle of the virtual work makes it a condition that some out of the nodes 7 are displaced only on the analytic plane, some of the nodes 7 are displaced outside of the analytic plane and a stress from the outside of the analytic plane acts on some of the nodes 7 By imposing this constraint, the nodes 7 can be brought close to an actualer restraint and in the prediction for the shape of the semiconductor, the shape of the semiconductor, which is remarkably close to the shape of the real semiconductor, can be predicted

Statics, engineering mechanics

Abstract: Part 1 Statistics: introduction vectors forces systems of forces and moments objects in equilibrium structures in equilibrium centroids and centres of mass moments of inertia distributed forces friction virtual work and potential energy appendices. Part 2 Dynamics: introduction motion of a point force, mass and acceleration energy methods momentum methods motion of rigid bodies two dimensional dynamics of rigid bodies energy and momentum in rigid body dynamics three-dimensional dynamics of rigid bodies vibrations.

Dynamic Analysis of Flexible Manipulator Arms With Distributed Viscoelastic Damping

Abstract: The main objective of this work is to predict the effect of distributed viscoelastic damping on the dynamic response of multilink flexible robot manipulators. A general approach, based on the principle of virtual work, is presented for the modeling of flexible robot arms with distributed viscoelastic damping. The finite element equations are developed, and a recurrence formulation for numerical integration of these equations is obtained. It is demonstrated, by a numerical example, that the viscoelastic damping treatments have a significant effect on the dynamic response of flexible robot manipulators.

A degenerate solid element formulation for large deformations of thin shell structures

Abstract: A geometrically nonlinear finite element formulation for an 18-node degenerated solid element was developed for analyzing large deformations of thin shell structures. The element, degenerated from a 27node solid element from the Lagrange family, contains only translational degrees-of-freedom and thus it can be used to analyze not only thin shell structures but also beam and non-thin-wall structures. Reduced integration is employed to relax locking which is a deficiency in finite elements based upon the ReissnerMindlin theory. A stabilization procedure using an assumed strain field was developed to alleviate spurious energy modes resulting from the use of reduced integration. Compared with the stabilization procedure formulated based upon the HellingerReissner principle1, the proposed stabilization procedure in conjunction with the principle of virtual work yielded a more efficient finite element formulation.

On the variational equations of thermoelasticity for inhomogeneous anisotropic shells

Abstract: On the basis of the complete system of equations that describes the thermoelastic behavior of an inhomogeneous anisotropic shell under the action of force and thermal loads we derive variational equations that are analogs of the principle of virtual work, the principle of complementary energy, and the Biot equation in three-dimensional thermoelasticity.

Dynamic Stability of an Elastic Rotating System:Shell-Disc-Shaft

Abstract: This paper presents a methodology and some results on the dynamic stability of an elastic rotating system consisting of one- and twodimensional members. These parts may contain different kinds of unsymmetries: either from mass- or stiffness imperfections or from anisotropic especially hydrodynamic bearings. The equations of motion are formulated using virtual work and an Finite Element approach. Special attention is paid to a kinematically consistent coupling of the elastic shell and disc. The eigenvalue extraction is based upon the method of Lanczos including a modal reduction and a correction process in order to ensure true diagonal system matrices. Some typical results for a shaft-disc-shell system with different bearings and imperfections are presented in detail.

Implementation of Free-Formulation-Based Flat Shell Elements into NASA Comet Code and Development of Nonlinear Shallow Shell Element

Abstract: This study presents a transient nonlinear finite element analysis within the realm of a multi-body dynamics formulation for determining the dynamic response of a moderately thick laminated shell undergoing a rapid and large rotational motion and nonlinear elastic deformations. Nonlinear strain measure and rotation, as well as 'the transverse shear deformation, are explicitly included in the formulation in order to capture the proper motion-induced stiffness of the laminate. The equations of motion are derived from the virtual work principle. The analysis utilizes a shear deformable shallow shell element along with the co-rotational form of the updated Lagrangian formulation. The shallow shell element formulation is based on the Reissner-Mindlin and Marguerre theory.

Dynamics and Control of Discrete Electromechanical Systems

Abstract: Dynamics and control of complex mechatronic systems can be investigated efficiently by using a suitable mathematical standard model. Based on such a mathematical standard model, well-known approaches to dynamics and control can be used in different application fields. Some of the most important mechatronic systems are electromechanical systems which can be regarded as physical structures characterized by interaction of electromagnetic fields with inertial bodies. The equations governing discrete electromechanical systems are obtained by combining Kirchhoff’s theory with the appropriate constitutive equations. The motion of an electromechanical system will be understood as the motion of its representing point in its configuration space. Based on the principle of virtual work, the equations of motion are Lagrange’s equations of the second kind (Maiser and Steigenberger, 1979). The analytical mechanics and its application to multibody dynamics can be regarded as a suitable starting point (Maiser, 1991). Lagrange’s equations of mixed type for constrained mechanical systems constitute a mathematical standard model which is often used in dynamics as well as in force and position control of robot manipulators (Arimoto et al. 1993). Often the so called disturbed equations of motion obtained by linearization of Lagrange’s equations near a nominal trajectory q(t) are used to design optimal controllers in mechatronics