Dynamic modelling of planar flexible manipulators: Computational and algorithmic efficiency

1997 ◽  
Vol 211 (2) ◽  
pp. 119-133 ◽  
Author(s):  
Y-J Shyu ◽  
K F Gill
Keyword(s):  
Linear Equations ◽  
Dynamic Modelling ◽  
Approximate Solutions ◽  
Experimental Information ◽  
Open Loop ◽  
Flexible Manipulator ◽  
Time Step ◽  
End Effector ◽  
And Control ◽  
Non Linear Equations

Traditionally, many robot arms are very rigid in construction; this was believed to be necessary for accurate placement and repeatability but led to higher material costs and increased energy consumption. Higher operational speeds and the use of lightweight materials cause elastic deformations to occur during the operation of the manipulator. These deformations degrade the path-tracking performance of the end-effector. The dynamic behaviour of a flexible manipulator is described mathematically by non-linear equations which are difficult to solve analytically. Unfortunately, there is currently no experimental information available with which to compare this design of flexible structure. For design and control purposes, it is suggested in this paper that it is more appropriate to employ approximate solutions with the emphasis on the development of a fast computational algorithm. An analytical study was undertaken to investigate the relevant uncertainties that are either inappropriately described or unavailable in the literature. The purpose of the paper is essentially to include the initial deflections in the simulation, to select the size of the time step, to select the models for emulating the end-effector, payload and joint actuator and, finally, to suppress the uncontrollable off-plane vibrations when encountered. When this knowledge has been obtained, the design and development of the simulation process can begin. In order to demonstrate the practicability of the open-loop simulation proposed and test the software, two representative models were investigated.

scholarly journals Fuzzy Version of Secant Method to Solve Fuzzy Non-Linear Equations

2016 ◽  
Vol 35 ◽  
pp. 127-134
Author(s):  
Goutam Kumar Saha ◽  
Shapla Shirin
Keyword(s):  
Linear Equation ◽  
Linear Equations ◽  
Approximate Solutions ◽  
Secant Method ◽  
Graphical Representations ◽  
Non Linear Equation ◽  
Non Linear ◽  
Optimum Solution ◽  
Non Linear Equations

In this paper fuzzy version of secant method has been introduced to obtain approximate solutions of a fuzzy non-linear equation. Graphical representations of the approximate solutions have also been shown. The idea of converging to the root to the desired degree of accuracy, which is the optimum solution, of a fuzzy non-linear equation has been focused.GANIT J. Bangladesh Math. Soc.Vol. 35 (2015) 127-134

scholarly journals Time-step limits for stable solutions of the ice-sheet equation

1996 ◽  
Vol 23 ◽  
pp. 74-85 ◽  
Author(s):  
Richard C. A. Hindmarsh ◽  
Antony J. Payne
Keyword(s):  
Linear Equations ◽  
Computational Cost ◽  
Ice Sheet ◽  
Two Dimensions ◽  
Picard Iteration ◽  
Time Step ◽  
Iterated Maps ◽  
A New Technique ◽  
The Stability ◽  
Non Linear Equations

Various spatial discretizations for the ice sheet are compared for accuracy against analytical solutions in one and two dimensions. The computational efficiency of various iterated and non-iterated marching schemes is compared.The stability properties of different marching schemes, with and without iterations on the non-linear equations, are compared. Newton–Raphson techniques permit the largest time steps. A new technique, which is based on the fact that the dynamics of unstable iterated maps contain information about where the unstable root lies, is shown to improve substantially the performance of Picard iteration at a negligible computational cost.

scholarly journals Time-step limits for stable solutions of the ice-sheet equation

1996 ◽  
Vol 23 ◽  
pp. 74-85 ◽  
Author(s):  
Richard C. A. Hindmarsh ◽  
Antony J. Payne
Keyword(s):  
Linear Equations ◽  
Computational Cost ◽  
Ice Sheet ◽  
Two Dimensions ◽  
Picard Iteration ◽  
Time Step ◽  
Iterated Maps ◽  
A New Technique ◽  
The Stability ◽  
Non Linear Equations

Various spatial discretizations for the ice sheet are compared for accuracy against analytical solutions in one and two dimensions. The computational efficiency of various iterated and non-iterated marching schemes is compared. The stability properties of different marching schemes, with and without iterations on the non-linear equations, are compared. Newton–Raphson techniques permit the largest time steps. A new technique, which is based on the fact that the dynamics of unstable iterated maps contain information about where the unstable root lies, is shown to improve substantially the performance of Picard iteration at a negligible computational cost.

scholarly journals Dynamic Modelling of Flexible Manipulator System Using Genetic Algorithm

2012 ◽  
Vol 60 (2) ◽  
pp. 239-245
Author(s):  
M. S. Alam
Keyword(s):  
Genetic Algorithm ◽  
Dynamic Modelling ◽  
Robotic Manipulators ◽  
Comparative Assessment ◽  
Flexible Manipulator ◽  
Structural Optimisation ◽  
Fitness Sharing ◽  
System A ◽  
New Variant ◽  
And Control

Flexible robotic manipulators pose various challenges in modelling, design, structural optimisation and control. This paper presents investigations into practical dynamic modelling of a flexible manipulator system using genetic algorithm (GA). Conventional genetic algorithms (GAs) often converge prematurely to a suboptimal region and fail to provide effective solutions due to lack of diversity in the population set as the algorithm proceeds. In order to improve and maintain diversity in the population set, a relatively new variant of GA, namely, fitness sharing based replacement genetic algorithm (FSR-GA1) is employed where some individuals are replaced periodically based on a fitness sharing method. The algorithm is utilised to extract dynamic model of 1-DOF (degree of freedom) motion of a flexible manipulator system. A comparative assessment between FSR-GA and conventional GA is presented in the same application to highlight the novelty of the used GA. Results show that the FSR-GA significantly improves the searching capability of the optimisation process compared to conventional GA. Time domain and frequency domain results clearly reveal the potential of the proposed method in modelling flexible manipulator systems.DOI: http://dx.doi.org/10.3329/dujs.v60i2.11526 Dhaka Univ. J. Sci. 60(2): 239-245, 2012 (July) 

Analytic Approximate Solutions and Numerical Results for Stagnation Point Flow of Jeffrey Fluid Towards an Off-Centered Rotating Disk

2014 ◽  
Vol 31 (2) ◽  
pp. 201-215 ◽  
Author(s):  
N. A. Khan ◽  
S. Khan ◽  
F. Riaz
Keyword(s):  
Linear Equations ◽  
Three Dimensional ◽  
Rotating Disk ◽  
Approximate Solutions ◽  
Jeffrey Fluid ◽  
Analysis Method ◽  
Convergence Region ◽  
Homotopy Analysis ◽  
Special Case ◽  
Non Linear Equations

AbstractThe present paper studies the three-dimensional, off centered stagnation flow of a Jeffrey fluid over a rotating disk. The governing non-linear equations and their associated boundary conditions are transformed into coupled ordinary differential equations by utilizing an appropriate similarity transformation. Homotopy analysis method is utilized to evaluate the analytical solution in the form of infinite series. Also, the convergence region of the obtained solution is determined and plotted. The effects of pertaining parameters on radial, azimuthal and induced velocities of the fluid flow are presented graphically and discussed. Moreover comparisons have also been made with the previous results as a special case.

Dynamic Modelling of an Elephant Trunk Like Flexible Bionic Manipulator

2019 ◽  
Author(s):  
Mrunal Kanti Mishra ◽  
Arun Kumar Samantaray ◽  
Goutam Chakraborty ◽  
Aditya Jain ◽  
Pushparaj Mani Pathak ◽  
...  
Keyword(s):  
Spatial Dynamics ◽  
Dynamic Modelling ◽  
Bending Moment ◽  
Flexible Manipulator ◽  
Lumped Mass ◽  
Elephant Trunk ◽  
End Effector ◽  
Body Dynamics ◽  
Section Model ◽  
Multi Body

Abstract In this paper, an attempt is made to model and study the planar and spatial dynamics of flexible elephant trunk-like manipulator by using multi-body dynamics software MSC-ADAMS. The flexible manipulator is modelled for bending with variable curvature. The entire manipulator length is divided into two sub-sections with associated lumped mass, damping and stiffness for the dynamic analysis. In this model, each section has three pressure actuated bellow tubes, which are modelled as simple spring-damper with the net mass distributed at the ends. Besides, a torsional spring-damper system is also incorporated in each section model to resist the bending about the transverse axes when the pressures in the bellow tubes are unequal. The manipulator is so designed that due to different actuation forces (corresponding to different bellows), the resultant action is finally a bending moment at the tip of each section. The effect of the gravitational force is also included. The change in behaviour of the end-effector position and orientation with respect to time is studied along with the elongation of bellow tubes. The nature of the velocity profile of the end-effector is also determined to study the behaviour of the manipulator.

Pedal Actuator of Driver Robot Based on Flexible Manipulator

2017 ◽  
Author(s):  
Liangyao Yu ◽  
Sheng Zheng ◽  
Jinghu Chang ◽  
Xiaoxue Liu
Keyword(s):  
Three Dimensional ◽  
Flexible Manipulator ◽  
Ball Screw ◽  
Testing Time ◽  
Three Dimensional Model ◽  
End Effector ◽  
Human Driver ◽  
Working Principle ◽  
Testing Accuracy ◽  
And Control

In most testing scenarios, driver robot can improve the testing accuracy and reduce the testing time when it replaces human driver. In this paper, an innovative pedal actuator of driver robot based on flexible manipulator is designed. This pedal actuator of driver robot can save the driver cabin space by changing the shape of manipulator according to different vehicle models, so that the human driver can sit in the cabin, together with the driver robot, monitor the testing process and take over the driver robot when necessary. The proposed pedal actuator of driver robot is composed of a flexible manipulator and end effector. The end effector which is respected to generate 500N pressure in maximum is based on ball screw pairs actuated by DC motor. The flexible manipulator is designed referring to 2-DOF universal joints. The designed prism shells around joint can improve rigidity of flexible manipulator under the condition of small size. Modular link design is used and every module has 2 degrees of freedoms. Its reaching range can be adjusted by increasing or decreasing the amount of modules. A three dimensional model has been constructed and the working principle of flexible manipulator is demonstrated in this paper. Simplified kinematics model of flexible manipulator is established, and the homogeneous coordinate transformation matrix and Denavit-Hartenberg convention are used to derive the kinematics equations. And the rotation angle of prism shell which is directly related to the servo motor angle is used to express the bending angle of the universal joint in the kinematics equations, so that it becomes straightforward and simple to solve the forward kinematics problem and control the manipulator.

scholarly journals Model of an electro-rheological shock absorber and coupled problem for partial and ordinary differential equations with variable unknown domain

2007 ◽  
Vol 18 (4) ◽  
pp. 513-536 ◽  
Author(s):  
W. G. LITVINOV ◽  
T. RAHMAN ◽  
R. H. W. HOPPE
Keyword(s):  
Numerical Simulation ◽  
Exact Solution ◽  
Shock Absorber ◽  
Linear Equations ◽  
Approximate Solutions ◽  
Electrorheological Fluid ◽  
Coupled Problem ◽  
Uniqueness Of The Solution ◽  
Convergence Of Approximate Solutions ◽  
Non Linear Equations

Amortization of a shock in an electro-rheological shock absorber is carried out in the motion of a piston in an electrorheological fluid. The drag force acting on the piston is regulated by varying the voltage applied to electrodes. A model of an electrorheological shock absorber is constructed. A problem on shock absorber reduces to the solution of a coupled problem for motion equation of the piston and non-linear equations of fluid flow in an unknown domain that varies with the time. A method of semi-discretization for approximate solution of the coupled problem is considered. Results on the existence and on the uniqueness of the solution of the coupled problem are obtained. Convergence of approximate solutions to the exact solution is proved. Numerical simulation of the operation of the shock absorber is performed.

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