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.

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]

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.

Inverse dynamics modeling of a (3-UPU)+(3-UPS+S) serial-parallel manipulator

Robotica ◽  
2014 ◽  
Vol 34 (3) ◽  
pp. 687-702 ◽  
Author(s):  
Bo Hu ◽  
Jingjing Yu ◽  
Yi Lu
Keyword(s):  
Parallel Manipulator ◽  
Inverse Dynamics ◽  
Virtual Work ◽  
Principle Of Virtual Work ◽  
Dynamics Modeling ◽  
Dynamics Model ◽  
Velocity Mapping

SUMMARYThe inverse dynamics model of a novel (3-UPU)+(3-UPS+S) serial–parallel manipulator (S-PM) formed by a 3-UPU PM and a 3-UPS+S PM connected in serial is studied in this paper. First, the inverse position, velocity, and acceleration of this S-PM are studied systematically. Second, the velocity mapping relations between each component and the terminal platform of (3-UPU)+(3-UPS+S) S-PM are derived. Third, the dynamics model of the whole (3-UPU)+(3-UPS+S) S-PM is established by means of the principle of virtual work. The process for establishing the dynamics model of this S-PM is fit for other S-PMs.

Inverse Dynamics Formulation and Analysis of a Parallel Manipulator with 3DOFs Based on the Virtual Work Principle

2013 ◽  
Vol 455 ◽  
pp. 360-365
Author(s):  
Yong Gang Li ◽  
Li Xin Xu ◽  
Hui Wang
Keyword(s):  
Dynamic Optimization ◽  
Parallel Manipulator ◽  
Inverse Dynamics ◽  
Virtual Work ◽  
Hessian Matrix ◽  
Parameters Estimation ◽  
Principle Of Virtual Work ◽  
Virtual Work Principle ◽  
Optimization Control ◽  
Strategy Design

Dynamics formulation is a primary task for dynamic optimization, control strategy design and servomotor parameters estimation of the parallel manipulator (PM). In this paper, by using the simple operation form of reciprocal screw and Lie Algebra, the compact expressions of complete Jacobian and Hessian matrix are derived. Then the inverse dynamics of 3PRS parallel manipulator is formulated based on the efficient principle of virtual work. In this model, the generalized forces of both actuation and constraint can be solved. Finally, a numerical simulation example is given to demonstrate this simple yet effective approach.

Analyses of the stiffness and elastic deformation of a 2(3-SPR) serial—parallel manipulator

2009 ◽  
Vol 223 (3) ◽  
pp. 189-198 ◽  
Author(s):  
Y Lu ◽  
B Hu ◽  
J Yu
Keyword(s):  
Elastic Deformation ◽  
Machine Tools ◽  
Parallel Manipulator ◽  
Virtual Work ◽  
Parallel Manipulators ◽  
Robot Arm ◽  
Principle Of Virtual Work ◽  
Compliance Matrix ◽  
End Effector ◽  
Machining Speed

Stiffness is one of the important indices for evaluating the performances of serial—parallel manipulators (S—PMs), particularly when the S—PMs are used as machine tools and the robot arm/leg, and higher stiffness allows higher machining speed with higher accuracy of the end-effector. In this article, the stiffness and the elastic deformation of a 2(3-SPR) S—PM are studied systematically. First, a 2(3-SPR) S—PM, including an upper 3-SPR parallel manipulator (PM) and a lower 3-SPR PM, is constructed, and its characteristics are analysed. Second, some formulae for solving the elastic deformation and the compliance matrix of the active legs are derived from the available kinematics/statics of this S—PM. Third, based on the principle of virtual work and the compliance matrix of the active legs, the elastic deformation and the total stiffness matrix of this S—PM are solved and analysed.

Design of a Boat Simulator Using Two Parallel Manipulators

2014 ◽  
Author(s):  
Juan David López ◽  
Carlos Francisco Rodríguez
Keyword(s):  
Degrees Of Freedom ◽  
Inverse Dynamics ◽  
Virtual Work ◽  
Equations Of Motion ◽  
Parallel Manipulators ◽  
Dimensional Synthesis ◽  
Detail Design ◽  
Inverse Dynamics Analysis ◽  
Future Work ◽  
High Payload

In this paper a boat simulator is designed using parallel manipulators. The simulator allows the training of five or seven people in a river environment. Due to the high payload and high inertial forces, it was proposed to divide the simulator into various synchronized platforms. Additionally different configurations of mechanisms were evaluated as well as linear or rotational actuation. The dimensional synthesis was performed by introducing a power index based on the Virtual Work equations of motion, and applying Genetic Algorithms for optimization. This design process results in using two coordinated manipulators with rotational actuators. The first one has two degrees of freedom (pitch and roll); it will simulate the motion of the boat’s stern. The second one has three degrees of freedom: pitch, roll and heave; and simulates the motion of the boat’s bow. The detail design was concluded and the manipulators were built. A real time controller is under design nowdays and the integration of the fluid and the boat dynamics into the inverse dynamics analysis of the manipulators is proposed as future work.

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.

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