Kinematic, Stiffness, and Dynamic Analyses of a Compliant Tensegrity Mechanism

2014 ◽  
Vol 6 (4) ◽  
Author(s):  
Bahman Nouri Rahmat Abadi ◽  
S. M. Mehdi Shekarforoush ◽  
Mojtaba Mahzoon ◽  
Mehrdad Farid
Keyword(s):  
Dynamic Characteristics ◽  
Stiffness Matrix ◽  
Analytical Procedure ◽  
Inverse Dynamics ◽  
Virtual Work ◽  
Equations Of Motion ◽  
Degree Of Freedom ◽  
Principle Of Virtual Work ◽  
Numerical Examples ◽  
Dynamic Analyses

The objective of this study is to present an analytical procedure for analysis of a compliant tensegrity mechanism focusing on its stiffness and dynamic characteristics. The screw calculus is used to derive the static equations and stiffness matrix of a full degree-of-freedom tensegrity mechanism, and the equations of motion are derived based on the principle of virtual work. Finally, some numerical examples are solved for the inverse dynamics of the mechanism.

Dynamics of a Two-DOF Parallel Pointing Mechanism

2005 ◽  
Author(s):  
Alessandro Cammarata ◽  
Rosario Sinatra
Keyword(s):  
Numerical Simulation ◽  
Parallel Mechanism ◽  
Inverse Dynamics ◽  
Kinematic Model ◽  
Degree Of Freedom ◽  
Numerical Examples ◽  
Proposed Model ◽  
Dynamic Analyses ◽  
Moving Platform ◽  
Two Degree Of Freedom

This paper presents kinematic and dynamic analyses of a two-degree-of-freedom pointing parallel mechanism. The mechanism consists of a moving platform, connected to a fixed platform by two legs of type PUS (prismatic-universal-spherical). At first a simplified kinematic model of the pointing mechanism is introduced. Based on this proposed model, the dynamics equations of the system using the Natural Orthogonal Complement method are developed. Numerical examples of the inverse dynamics results are presented by numerical simulation.

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.

Inverse dynamics of the 6-dof out-parallel manipulator by means of the principle of virtual work

Robotica ◽  
2009 ◽  
Vol 27 (2) ◽  
pp. 259-268 ◽  
Author(s):  
Yongjie Zhao ◽  
Feng Gao
Keyword(s):  
Parallel Manipulator ◽  
Inverse Dynamics ◽  
Virtual Work ◽  
Equations Of Motion ◽  
Principle Of Virtual Work ◽  
Constraint Forces ◽  
Dynamical Equations ◽  
Robot System ◽  
Lead Screw ◽  
Moving Platform

SUMMARYIn this paper, the inverse dynamics of the 6-dof out-parallel manipulator is formulated by means of the principle of virtual work and the concept of link Jacobian matrices. The dynamical equations of motion include the rotation inertia of motor–coupler–screw and the term caused by the external force and moment exerted at the moving platform. The approach described here leads to efficient algorithms since the constraint forces and moments of the robot system have been eliminated from the equations of motion and there is no differential equation for the whole procedure. Numerical simulation for the inverse dynamics of a 6-dof out-parallel manipulator is illustrated. The whole actuating torques and the torques caused by gravity, velocity, acceleration, moving platform, strut, carriage, and the rotation inertia of the lead screw, motor rotor and coupler have been computed.

Solving the Inverse Dynamics of a Stewart-Gough Manipulator by the Principle of Virtual Work

1999 ◽  
Vol 122 (1) ◽  
pp. 3-9 ◽  
Author(s):  
Lung-Wen Tsai
Keyword(s):  
Computational Algorithm ◽  
Inverse Dynamics ◽  
Virtual Work ◽  
Equations Of Motion ◽  
Linear Equations ◽  
Principle Of Virtual Work ◽  
Dynamical Equations ◽  
Jacobian Matrices ◽  
Systematic Methodology ◽  
Moving Platform

This paper presents a systematic methodology for solving the inverse dynamics of a Stewart-Gough manipulator. Based on the principle of virtual work and the concept of link Jacobian matrices, a methodology for deriving the dynamical equations of motion is developed. It is shown that the dynamics of the manipulator can be reduced to solving a system of six linear equations in six unknowns. A computational algorithm for solving the inverse dynamics of the manipulator is developed and several trajectories of the moving platform are simulated. [S1050-0472(00)00401-3]

Solving the Inverse Dynamics of Parallel Manipulators by the Principle of Virtual Work

1998 ◽  
Author(s):  
Lung-Wen Tsai
Keyword(s):  
Parallel Manipulator ◽  
Inverse Dynamics ◽  
Virtual Work ◽  
Equations Of Motion ◽  
Linear Equations ◽  
Parallel Manipulators ◽  
Principle Of Virtual Work ◽  
Dynamical Equations ◽  
Systematic Methodology ◽  
Stewart Gough Platform

Abstract This paper presents a systematic methodology for solving the inverse dynamics of parallel manipulators. Based on the principle of virtual work and the concept of link Jacobian matrices, a methodology for deriving the dynamical equations of motion is developed. It is shown that the dynamics of a parallel manipulator can be reduced to solving a system of six linear equations. To demonstrate the methodology, the dynamical equations of a Stewart-Gough platform are derived. A computer algorithm is developed and several different trajectories of the moving platform are simulated.

Analytical Modelling of the Dynamics of the Four-Bar Mechanism: A Comparison of Some Methods

2018 ◽  
Author(s):  
J. P. Meijaard ◽  
V. van der Wijk
Keyword(s):  
Virtual Work ◽  
Equations Of Motion ◽  
Differential Algebraic Equations ◽  
Force Balance ◽  
Dynamic Force ◽  
Algebraic Equations ◽  
Principle Of Virtual Work ◽  
Principal Vector ◽  
Reaction Forces ◽  
Principal Points

Some thoughts about different ways of formulating the equations of motion of a four-bar mechanism are communicated. Four analytic methods to derive the equations of motion are compared. In the first method, Lagrange’s equations in the traditional form are used, and in a second method, the principle of virtual work is used, which leads to equivalent equations. In the third method, the loop is opened, principal points and a principal vector linkage are introduced, and the equations are formulated in terms of these principal vectors, which leads, with the introduced reaction forces, to a system of differential-algebraic equations. In the fourth method, equivalent masses are introduced, which leads to a simpler system of principal points and principal vectors. By considering the links as pseudorigid bodies that can have a uniform planar dilatation, a compact form of the equations of motion is obtained. The conditions for dynamic force balance become almost trivial. Also the equations for the resulting reaction moment are considered for all four methods.

Effect of the Gravity Force on the Propagation of a Rotating Flexible Rod After Impact

1997 ◽  
Author(s):  
Wei-Hsin Gau
Keyword(s):  
Elastic Waves ◽  
Virtual Work ◽  
Impact Load ◽  
Equations Of Motion ◽  
Fourier Method ◽  
Gravity Force ◽  
Principle Of Virtual Work ◽  
Shape Functions ◽  
Concentrated Force ◽  
The Impact

Abstract The aim of this paper is to analyze the effect of the gravity force on the impact-induced elastic waves which propagate on a radially rotating rod. The equations of motion of the system are developed using the principle of virtual work in dynamics. The impact load is included by the use of the generalized impulse momentum equations, involving the coefficient of restitution. The system is solved using the Fourier method. The deformation of the rod is supposed to be at any instant a linear combination of a set of shape functions. These shape functions are, in this investigation, the modes of a cantilever beam. The weight of the rod is modeled as a concentrated force applied at any instant at the center of the rod.

Exact Solutions of Dynamic Characteristics for Curved Beams with Pinned-Pinned Ends

2013 ◽  
Vol 405-408 ◽  
pp. 702-705
Author(s):  
Xiao Fei Li ◽  
Wei Ming Yan ◽  
Hao Xiang He
Keyword(s):  
Exact Solutions ◽  
Dynamic Characteristics ◽  
Analytical Solutions ◽  
Stiffness Matrix ◽  
Virtual Work ◽  
Analytic Method ◽  
Curved Beam ◽  
Curved Beams ◽  
Curved Bridges ◽  
Scientific Base

Based on the theory of virtual work and principle of thermal elasticity, exact solutions for in-plane displacements of curved beams with pinned-pinned ends are derived explicitly. In the case of infinite limit of radius, these equations coincide with that of the straight beams. Compared with the results of FEM, the analytical solutions by the proposed formulae are accurate. Basing on the stiffness matrix of statically indeterminate curved beams at three freedom direction, the dynamic characteristics are derived explicitly. The analytic method of dynamic characteristics for curved beam performed in this paper would provide a scientific base for further study and design of the curved bridges.

Modal Analysis for the Active Multi-Layer Beams by Using Spectrally Formulated Exact Eigenfunctions

1999 ◽  
Author(s):  
Usik Lee ◽  
Joohong Kim
Keyword(s):  
Modal Analysis ◽  
Closed Form ◽  
Dynamic Characteristics ◽  
Equations Of Motion ◽  
Hamilton’S Principle ◽  
Analysis Method ◽  
Hamilton's Principle ◽  
Numerical Examples ◽  
Coupled Equations ◽  
Fully Coupled

Abstract In this paper, a modal analysis method (MAM) is introduced for the active multi-layer laminate beams. Two types of active multi-layer laminate beams are considered: the elastic-viscoelastic-piezoelectric three-layer beams and the elastic-piezoelectric two-layer beams. The dynamics of the multi-layer laminate beams are represented by a set of fully coupled equations of motion, derived by using Hamilton’s principle. The exact eigenfunctions are spectrally formulated and the orthogonality of eigenfunctions is derived in a closed form. The present MAM is evaluated through some numerical examples. It is shown that the dynamic characteristics obtained by the present MAM certainly converge to the exact ones obtained by SEM as the number of eigenfunctions superposed in MAM is increased. The modal analysis results are also compared with the results obtained by FEM.

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