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.

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.

A Closed-Form Dynamics of a Novel Fully Wrist Driven by Revolute Motors

2016 ◽  
Vol 32 (4) ◽  
pp. 479-490
Author(s):  
J. Enferadi ◽  
A. Shahi
Keyword(s):  
Closed Form ◽  
Inverse Dynamics ◽  
Virtual Work ◽  
Angular Displacement ◽  
Equations Of Motion ◽  
Linear Equations ◽  
Spherical Robot ◽  
Dynamics Modeling ◽  
Dynamical Equations ◽  
Moving Platform

AbstractThis paper proposes a systematic methodology to obtain a closed-form formulation for dynamics analysis of a novel spherical robot that is called a 3(RPSP)-S parallel manipulator. The proposed manipulator provides high rotational displacement of the moving platform for low angular displacement of the motors. The advised robot is suitable for repetitive oscillatory applications (for example, wrist and ankle rehabilitation and table of autopilot and gyroscope life test, etc.). First, we describe the structure of the proposed manipulator and solve the inverse kinematics problem of the manipulator. Next, based on the principle of virtual work, a methodology for deriving the dynamical equations of motion is developed. The elaborated approach shows that the inverse dynamics of the manipulator can be reduced to solving a system of three linear equations in three unknowns. Finally, a computational algorithm to solve the inverse dynamics of the manipulator is advised and several trajectories of the moving platform are simulated and verified by a special dynamics modeling commercial software (MSC ADAMS).

RESEARCH ON RIGID BODY INVERSE DYNAMICS OF A NOVEL 6-PRRS PARALLEL ROBOT

2018 ◽  
Vol 18 (08) ◽  
pp. 1840037
Author(s):  
YUBIN LIU ◽  
GANGFENG LIU
Keyword(s):  
Dynamic Model ◽  
Inverse Dynamics ◽  
Virtual Work ◽  
Equations Of Motion ◽  
Parallel Robot ◽  
Simulation Software ◽  
Real Time Control ◽  
Dynamical Equations ◽  
Time Control ◽  
Systematic Methodology

A systematic methodology for solving the inverse dynamics of a 6-PRRS parallel robot is presented. Based on the principle of virtual work and the Lagrange approach, a methodology for deriving the dynamical equations of motion is developed. To resolve the inconsistency between complications of established dynamic model and real-time control, a simplifying strategy of the dynamic model is presented. The dynamic character of the 6-PRRS parallel robot is analyzed by example calculation, and a full and precise dynamic model using simulation software is established. Verification results show the validity of the presented algorithm, and the simplifying strategies are practical and efficient.

Introducing and Analyzing a Novel Three-Degree-of-Freedom Spatial Tensegrity Mechanism

2014 ◽  
Vol 9 (2) ◽  
Author(s):  
Bahman Nouri Rahmat Abadi ◽  
Mehrdad Farid ◽  
Mojtaba Mahzoon
Keyword(s):  
Virtual Work ◽  
Equations Of Motion ◽  
Translational Motion ◽  
Parallel Robot ◽  
Principle Of Virtual Work ◽  
Dynamical Equations ◽  
Spatial Mechanism ◽  
Gravitational Forces ◽  
Three Degree Of Freedom ◽  
Special Case

The objective of the present paper is to introduce and analyze a particular spatial mechanism as a modification of the Stewart robot. The three limbs of the Stewart parallel robot are replaced by springs. Three hydraulic actuators control translational motion of the mechanism. Kinematics of the mechanism is studied and its static equations are derived and for a special case where external and gravitational forces are neglected, an analytical solution is presented. Also, the principle of virtual work is employed to derive the equations of motion of the proposed mechanism. Based on the dynamical equations, the motion of the system is simulated.

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.

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.

scholarly journals Investigation on the Dynamics of an On-Board Rotor-Bearing System

2012 ◽  
Author(s):  
Mzaki Dakel ◽  
Sébastien Baguet ◽  
Régis Dufour
Keyword(s):  
Dynamic Behavior ◽  
Fourier Transforms ◽  
Virtual Work ◽  
Equations Of Motion ◽  
Linear Equations ◽  
Beam Theory ◽  
Rigid Base ◽  
The Finite Element Method ◽  
Mass Unbalance ◽  
Motion Display

In ship and aircraft turbine rotors, the rotating mass unbalance and the different movements of the rotor base are among the main causes of vibrations in bending. The goal of this paper is to investigate the dynamic behavior of an on-board rotor under rigid base excitations. The modeling takes into consideration six types of base deterministic motions (rotations and translations) when the kinetic and strain energies in addition to the virtual work of the rotating flexible rotor components are computed. The finite element method is used in the rotor modeling by employing the Timoshenko beam theory. The proposed on-board rotor model takes into account the rotary inertia, the gyroscopic inertia, the shear deformation of shaft as well as the geometric asymmetry of shaft and/or rigid disk. The Lagrange’s equations are applied to establish the differential equations of the rotor in bending with respect to the rigid base which represents a noninertial reference frame. The linear equations of motion display periodic parametric coefficients due to the asymmetry of the rotor and time-varying parametric coefficients due to the base rotational motions. In the proposed applications, the rotor mounted on rigid/elastic bearings is excited by a rotating mass unbalance associated with sinusoidal vibrations of the rigid base. The dynamic behavior of the rotor is analyzed by means of orbits of the rotor as well as fast Fourier transforms (FFTs).

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