Inverse Dynamics of a 3-P[2(US)] Translational Parallel Robot

Robotica ◽  
2018 ◽  
Vol 37 (4) ◽  
pp. 708-728 ◽  
Author(s):  
Mahmood Mazare ◽  
Mostafa Taghizadeh ◽  
M. Rasool Najafi
Keyword(s):  
Degrees Of Freedom ◽  
Dynamic Models ◽  
Inverse Dynamics ◽  
Virtual Work ◽  
Equations Of Motion ◽  
Parallel Robot ◽  
Qualitative Behavior ◽  
Work Model ◽  
Forward Kinematic ◽  
Good Agreement

SummaryIn this paper, a type of parallel robot with three translational degrees of freedom is studied. Inverse and forward kinematic equations are extracted for position and velocity analyses. The dynamic model is derived by Lagrange’s approach and the principle of virtual work and related computational algorithms implementing inverse and forward dynamics are presented. Furthermore, some numerical simulations are performed using the kinematic and dynamic models in which the results show good agreement with expected qualitative behavior of the mechanism. Comparisons with the results of work-energy and impulse-momentum methods quantitatively verify the validity of the derived equations of motion. Also, a relative computational effectiveness is observed in implementation of virtual work model via the simulations.

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.

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.

Trajectory Tracking of Underactuated Multibody Systems

2011 ◽  
Author(s):  
Stefan Reichl ◽  
Wolfgang Steiner
Keyword(s):  
Trajectory Tracking ◽  
Multibody Systems ◽  
Degrees Of Freedom ◽  
Inverse Dynamics ◽  
Feedforward Control ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Differential Algebraic Equations ◽  
State Variables ◽  
Algebraic Equations

This work presents three different approaches in inverse dynamics for the solution of trajectory tracking problems in underactuated multibody systems. Such systems are characterized by less control inputs than degrees of freedom. The first approach uses an extension of the equations of motion by geometric and control constraints. This results in index-five differential-algebraic equations. A projection method is used to reduce the systems index and the resulting equations are solved numerically. The second method is a flatness-based feedforward control design. Input and state variables can be parameterized by the flat outputs and their time derivatives up to a certain order. The third approach uses an optimal control algorithm which is based on the minimization of a cost functional including system outputs and desired trajectory. It has to be distinguished between direct and indirect methods. These specific methods are applied to an underactuated planar crane and a three-dimensional rotary crane.

Toward a Minimal Dynamic Model of a 6-DOF Parallel Robot

1997 ◽  
Author(s):  
L. Beji ◽  
M. Pascal ◽  
P. Joli
Keyword(s):  
Dynamic Model ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Computational Cost ◽  
Closed Form Solution ◽  
Parallel Robot ◽  
Form Solution ◽  
Lagrangian Formalism ◽  
Inverse Kinematic Problem ◽  
Geometrical Properties

Abstract In this paper, an architecture of a six degrees of freedom (dof) parallel robot and three limbs is described. The robot is called Space Manipulator (SM). In a first step, the inverse kinematic problem for the robot is solved in closed form solution. Further, we need to inverse only a 3 × 3 passive jacobian matrix to solve the direct kinematic problem. In a second step, the dynamic equations are derived by using the Lagrangian formalism where the coordinates are the passive and active joint coordinates. Based on geometrical properties of the robot, the equations of motion are derived in terms of only 9 coordinates related by 3 kinematic constraints. The computational cost of the obtained dynamic model is reduced by using a minimum set of base inertial parameters.

Modeling of Multibody Flexible Articulated Structures With Mutually Coupled Motions: Part II — Application and Results

1992 ◽  
Author(s):  
Jiechi Xu ◽  
Joseph R. Baumgarten
Keyword(s):  
Experimental Data ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Open Loop ◽  
Body Motion ◽  
Universal Joint ◽  
Open Loop System ◽  
Numerical Examples ◽  
Kinematic Properties ◽  
Good Agreement

Abstract The application of the systematic procedures in the derivation of the equations of motion proposed in Part I of this work is demonstrated and implemented in detail. The equations of motion for each subsystem are derived individually and are assembled under the concept of compatibility between the local kinematic properties of the elastic degrees of freedom of those connected elastic members. The specific structure under consideration is characterized as an open loop system with spherical unconstrained chains being capable of rotating about a Hooke’s or universal joint. The rigid body motion, due to two unknown rotations, and the elastic degrees of freedom are mutually coupled and influence each other. The traditional motion superposition approach is no longer applicable herein. Numerical examples for several cases are presented. These simulations are compared with the experimental data and good agreement is indicated.

DELTA: a simple and efficient parallel robot

Robotica ◽  
1990 ◽  
Vol 8 (2) ◽  
pp. 105-109 ◽  
Author(s):  
F. Pierrot ◽  
C. Reynaud ◽  
A. Fournier
Keyword(s):  
Inverse Kinematics ◽  
Research Team ◽  
Dynamic Models ◽  
Inverse Dynamics ◽  
Parallel Robot ◽  
Parallel Robots ◽  
Kinematic Parameters ◽  
Mechanical Structure ◽  
Serial Robots ◽  
École Polytechnique

SummaryThe DELTA parallel robot, designed by an EPFL (Ecole Polytechnique Fédérale de Lausanne) research team, is a mechanical structure which has the advantage of parallel robots and ease of serial robots modeling. This paper presents solutions for a complete modeling of the DELTA parallel robot (direct and inverse kinematics, inverse statics, inverse dynamics), with few arithmetic and trigonometric operations. Our method is based on a satisfactory choice of kinematic parameters and on a few restricting hypotheses for the static and dynamic models. We give some details of each model, we present some computation results and we put the emphasis on some particular points, showing the capabilities of this mechanical structure.

Methods of Using a Vibratory System to Measure Small Rates of Turn

1969 ◽  
Vol 11 (5) ◽  
pp. 526-533 ◽  
Author(s):  
J. A. Linnett
Keyword(s):  
Angular Velocity ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Exciting Force ◽  
Velocity Curve ◽  
Alternative Methods ◽  
Vibratory System ◽  
Mass System ◽  
The One ◽  
Good Agreement

The equations of motion for a vibratory two-degrees-of-freedom spring mass system subjected to rotation about an axis perpendicular to its plane of vibration are considered, taking into account the various couplings that may be present. The rate of turn can be measured by three alternative methods, two of which involve an exciting force in the sensing direction in addition to the one vibrating the system. The shape of the phase angle against angular velocity curve is shown to be independent of damping, enabling the transient performance to be improved without affecting the sensitivity of the device. Experimental work shows good agreement with the developed theory.

Dynamics of Serial Multibody Systems Using the Decoupled Natural Orthogonal Complement Matrices

1999 ◽  
Vol 66 (4) ◽  
pp. 986-996 ◽  
Author(s):  
S. K. Saha
Keyword(s):  
Multibody Systems ◽  
Degrees Of Freedom ◽  
Inverse Dynamics ◽  
Equations Of Motion ◽  
Kinematic Chain ◽  
Rigid Bodies ◽  
Dynamic Equations ◽  
Orthogonal Complement ◽  
Forward Dynamics ◽  
Velocity Constraints

Constrained dynamic equations of motion of serial multibody systems consisting of rigid bodies in a serial kinematic chain are derived in this paper. First, the Newton-Euler equations of motion of the decoupled rigid bodies of the system at hand are written. Then, with the aid of the decoupled natural orthogonal complement (DeNOC) matrices associated with the velocity constraints of the connecting bodies, the Euler-Lagrange independent equations of motion are derived. The De NOC is essentially the decoupled form of the natural orthogonal complement (NOC) matrix, introduced elsewhere. Whereas the use of the latter provides recursive order n—n being the degrees-of-freedom of the system at hand—inverse dynamics and order n3 forward dynamics algorithms, respectively, the former leads to recursive order n algorithms for both the cases. The order n algorithms are desirable not only for their computational efficiency but also for their numerical stability, particularly, in forward dynamics and simulation, where the system’s accelerations are solved from the dynamic equations of motion and subsequently integrated numerically. The algorithms are illustrated with a three-link three-degrees-of-freedom planar manipulator and a six-degrees-of-freedom Stanford arm.

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.

Modeling and Adaptive Control for Tracking Wing Trajectories

2013 ◽  
Author(s):  
Ian P. Murphy ◽  
Shirin Dadashi ◽  
Jessica Gregory ◽  
Yu Lei ◽  
Javid Bayandor ◽  
...  
Keyword(s):  
Dynamic Models ◽  
Virtual Work ◽  
Equations Of Motion ◽  
Micro Air Vehicles ◽  
Adaptive Controller ◽  
Flapping Wing ◽  
Lyapunov Analysis ◽  
Unknown Parameters ◽  
Open Problems ◽  
Nonlinear Equations Of Motion

Studies of Micro Air Vehicles (MAVs) have gained increased attention over the past decade, while a significant range of open problems in this emerging field remain unaddressed. This paper highlights the investigations entailing flapping wing vehicles, designed based on inspiration from observations of avian flight. The nonlinear equations of motion of a ground fixed flapping wing robot are derived that incorporates a quasi-steady model of aerodynamics. The equations of motion are developed using Lagrange’s equations and the aerodynamic contributions are formulated using virtual work principles. The aerodynamics are constructed with a quasi-steady state formulation where the functions representing lift and drag coefficients as a function of angle of attack are treated as unknowns. An adaptive controller is introduced that seeks to learn the aerodynamic effects. A Lyapunov analysis of the controller guarantees boundedness of all error terms and asymptotic stability in both the joint position and derivative error. The controllers are simulated using two dynamic models based on flapping wing prototypes designed at Virginia Tech. The numerical experiments validate the Lyapunov analysis and verify that unknown parameters are learned if persistently excited.

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