Determination of Bearing Reactions of Spatial Linkages and Manipulators

1990 ◽  
Vol 112 (2) ◽  
pp. 168-174 ◽  
Author(s):  
F. L. Litvin ◽  
J. Tan
Keyword(s):  
Virtual Work ◽  
Parallel Manipulators ◽  
System Of Equations ◽  
Principle Of Virtual Work ◽  
Simultaneous Solution ◽  
Combined Application ◽  
Spatial Linkages ◽  
Virtual Velocity ◽  
D'alembert's Principle

Application of D’Alembert’s principle for determination of dynamic bearing reactions in joints of spatial linkages and parallel manipulators needs the simultaneous solution of a large system of equations. The authors of this paper propose an approach that is a combined application of principle of virtual work and D’Alembert’s principle. The main advantages of the proposed approach are: (1) reduction of the number of equations that have to be solved simultaneously, and (2) simplification of the expressions for the relative virtual velocity. The proposed approach is illustrated with the example of a 7-bar linkage and its application is explained with the crank-slider linkage.

Static analysis of spatial parallel manipulators by means of the principle of virtual work

2012 ◽  
Vol 28 (3) ◽  
pp. 385-401 ◽  
Author(s):  
J. Jesús Cervantes-Sánchez ◽  
José M. Rico-Martínez ◽  
Salvador Pacheco-Gutiérrez ◽  
Gustavo Cerda-Villafaña
Keyword(s):  
Static Analysis ◽  
Virtual Work ◽  
Parallel Manipulators ◽  
Principle Of Virtual Work

Dynamic Analysis of Spatial Four-Degree-of-Freedom Parallel Manipulators

1997 ◽  
Author(s):  
Jiegao Wang ◽  
Clément M. Gosselin
Keyword(s):  
Dynamic Analysis ◽  
Virtual Work ◽  
Parallel Manipulators ◽  
Degree Of Freedom ◽  
Principle Of Virtual Work ◽  
Numerical Examples ◽  
Euler Approach

Abstract The dynamic analysis of spatial four-degree-of-freedom parallel manipulators is presented in this article. First, expressions for the position, velocity and acceleration of each link constituting the manipulators are obtained. Then, the principle of virtual work is used to derive the generalized input forces of the manipulators. The corresponding algorithm is implemented and numerical examples are given in order to illustrate the results. The results obtained are verified using the classical Newton-Euler approach.

Solving active wrench of limited-degree of freedom parallel manipulators based on translational/rotational Jacobian matrices

2009 ◽  
Vol 223 (3) ◽  
pp. 221-229 ◽  
Author(s):  
Y Lu ◽  
B Hu ◽  
J Yu
Keyword(s):  
Virtual Work ◽  
Parallel Manipulators ◽  
Degree Of Freedom ◽  
Geometric Constraints ◽  
Principle Of Virtual Work ◽  
Jacobian Matrices ◽  
Limited Degree

A methodology is proposed for unified solving active wrench of the limited-degree of freedom (DOF) parallel manipulators (PMs). First, the geometric constraints and the inverse displacement kinematics are analysed. Second, the formulae for unified solving the inverse/forward velocity and the translational/rotational Jacobian matrices and inverse/forward Jacobian matrices are derived. Third, the analytic formulae for unified solving the active wrench of limited-DOF PMs are derived based on the principle of virtual work. Finally, a 3-DOF PM with linear/rotational active legs is presented to illustrate the use of the methodology.

Determining Critical States of Equilibrium of Plates and Shells Under Initial Stress

1942 ◽  
Vol 9 (1) ◽  
pp. A27-A30
Author(s):  
H. Hencky
Keyword(s):  
Cylindrical Shell ◽  
Energy Method ◽  
Virtual Work ◽  
The Body ◽  
Principle Of Virtual Work ◽  
Practical Applications ◽  
Fundamental Knowledge ◽  
Plates And Shells ◽  
The Stability

Abstract The purpose of this paper is to show that Rayleigh’s energy method, used by Timoshenko for the determination of critical loads in plates and shells, is capable of an important generalization. The work involved is a direct continuation of the energy method of Timoshenko and is based on the principle of virtual work. According to this principle the variation of the work of the outer forces together with the variation of the kinetic energy is equal to the variation of the elastic energy stored up in the body. The author develops a series of formulas, by means of which the stability of a cylindrical shell under various conditions of stress may be determined. The practical applications of these formulas, requiring only a fundamental knowledge of the mathematics of engineering, are illustrated by suitable examples.

Kinematic Analysis and Design of Planar Parallel Mechanisms Actuated With Cables

2000 ◽  
Author(s):  
Guillaume Barrette ◽  
Clément M. Gosselin
Keyword(s):  
Virtual Work ◽  
Parametric Representation ◽  
Dynamic State ◽  
Parallel Mechanisms ◽  
Principle Of Virtual Work ◽  
Systematic Analysis ◽  
End Effector ◽  
Analysis And Design ◽  
Spring Mechanism

Abstract In this paper, we present a general and systematic analysis of planar parallel mechanisms actuated with cables. The equations for the velocities are derived, and the forces in the cables are obtained by the principle of virtual work. Then, a detailed analysis of the workspace is performed and an analytical method for the determination of the boundaries of an x-y two-dimensional subset is proposed. The new notion of dynamic workspace is denned, as its shape depends on the accelerations of the end-effector. We demonstrate that any subset of the workspace can be considered as a combination of three-cable sub-workspaces, with boundaries being of two kinds: two-cable equilibrium loci and three-cable singularity loci. By using a parametric representation, we see that for the x-y workspace of a simple no-spring mechanism, the two-cable equilibrium loci represent a hyperbolic section, degenerating, in some particular cases, to one or two linear segments. Examples of such loci are presented. We use quadratic programming to choose which sections of the curves constitute the boundaries of the workspace for any particular dynamic state. A detailed example of workspace determination is included for a six-cable mechanism.

Determination of the Dynamic Workspace of Cable-Driven Planar Parallel Mechanisms

2005 ◽  
Vol 127 (2) ◽  
pp. 242-248 ◽  
Author(s):  
Guillaume Barrette ◽  
Cle´ment M. Gosselin
Keyword(s):  
Virtual Work ◽  
Parametric Representation ◽  
Dynamic State ◽  
Two Dimensional ◽  
Parallel Mechanisms ◽  
Principle Of Virtual Work ◽  
Systematic Analysis ◽  
End Effector ◽  
Spring Mechanism

In this paper, we present a general and systematic analysis of cable-driven planar parallel mechanisms. The equations for the velocities are derived, and the forces in the cables are obtained by the principle of virtual work. Then, a detailed analysis of the workspace is performed and an analytical method for the determination of the boundaries of an x-y two-dimensional subset is proposed. The new notion of dynamic workspace is defined, as its shape depends on the accelerations of the end-effector. We demonstrate that any subset of the workspace can be considered as a combination of three-cable subworkspaces, with boundaries being of two kinds: two-cable equilibrium loci and three-cable singularity loci. By using a parametric representation, we see that for the x-y workspace of a simple no-spring mechanism, the two-cable equilibrium loci represent a hyperbolic section, degenerating, in some particular cases, to one or two linear segments. Examples of such loci are presented. We use quadratic programming to choose which sections of the curves constitute the boundaries of the workspace for any particular dynamic state. A detailed example of workspace determination is included for a six-cable mechanism.

Theoretical and FEM Research on Inelastic Displacement of Assembled Truss Bridge with Cable Reinforcement

2012 ◽  
Vol 178-181 ◽  
pp. 2038-2042
Author(s):  
Yin Zhi Zhou ◽  
Ke Bin Jiang ◽  
Yong Ding ◽  
Jian Kui Yang
Keyword(s):  
Finite Element ◽  
Virtual Work ◽  
The Self ◽  
Principle Of Virtual Work ◽  
Element Analysis ◽  
Inelastic Displacement ◽  
Prestressing Force ◽  
Truss Bridge ◽  
Theoretical Results

This paper presents theoretical and finite element investigations on inelastic displacement of assembled truss bridge with cable reinforcement (hereinafter referred to as ATCR). A method based on the Principle of virtual work for the determination of the inelastic displacement of ATCR is proposed. Finite element analysis was conducted on the specimen models using the ANSYS program, in order to obtain the inelastic displacement of ATCR and to compare with theoretical results. This study focuses on Bailey bridge under the self-weight load and prestressing force on cable. This paper analyzes various specimens to obtain inelastic displacement in different cases. The approximations of a relation between the inelastic displacement and prestressing force on cable are found. It can be seen that the method in this paper can both calculate the inelastic displacement of traditional truss and prestressed truss (ATCR). Based on both the theoretical and the finite element results, it can be concluded that the relation curve between inelastic displacement and prestressing force is stepwise.

D’Alembert’s Principle

2017 ◽  
Author(s):  
Jennifer Coopersmith
Keyword(s):  
Quantum Mechanics ◽  
Virtual Work ◽  
Inertial Force ◽  
Black Box ◽  
Principle Of Virtual Work ◽  
Conservation Of Energy ◽  
Fundamental Nature ◽  
Worked Example ◽  
The Law ◽  
D'alembert's Principle

It is explained how the mysterious Principle of Virtual Work in statics is extended to the even more mysterious Principle of d’Alembert’s in dynamics. This is achieved by d’Alembert’s far-sighted stratagem: considering a reversed massy acceleration as an inertial force. A worked example is given (the half-Atwood machine or “black box”). Some counter-intuitive aspects are made intuitive by more examples: the Pluto-Charon system of orbiting planets; Newton’s and then Mach’s explanation of Newton’s bucket. Also, it is demonstrated that the law of the conservation of energy actually follows from d’Alembert’s Principle. The reader is alerted to the astoundingly fundamental nature of d’Alembert’s Principle. It is the cornerstone of classical, relativistic, and quantum mechanics. As Lanczos writes: “All the different principles of mechanics are merely mathematically different formulations of d’Alembert’s Principle”.

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