On the Properties of a Dynamic Model of Flexible Robot Manipulators

1998 ◽  
Vol 120 (1) ◽  
pp. 8-14 ◽  
Author(s):  
Marco A. Arteaga
Keyword(s):  
Dynamic Model ◽  
Structural Properties ◽  
Robot Manipulators ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Control Design ◽  
Flexible Manipulator ◽  
Robot Dynamics ◽  
Flexible Link ◽  
Flexible Robot

Control design of flexible robot manipulators can take advantage of the structural properties of the model used to describe the robot dynamics. Many of these properties are physical characteristics of mechanical systems whereas others arise from the method employed to model the flexible manipulator. In this paper, the modeling of flexible-link robot manipulators on the basis of the Lagrange’s equations of motion combined with the assumed modes method is briefly discussed. Several notable properties of the dynamic model are presented and their impact on control design is underlined.

A Constrained Lagrange Formulation of Multilink Planar Flexible Manipulator

2008 ◽  
Vol 130 (3) ◽  
Author(s):  
M. Vakil ◽  
R. Fotouhi ◽  
P. N. Nikiforuk ◽  
H. Salmasi
Keyword(s):  
Closed Form ◽  
Dynamic Model ◽  
Vibration Suppression ◽  
Equations Of Motion ◽  
Flexible Manipulator ◽  
Dynamic Equations ◽  
Flexible Link ◽  
Element Analysis ◽  
Constraint Matrix ◽  
Generalized Coordinates

In this article, the closed-form dynamic equations of planar flexible link manipulators (FLMs), with revolute joints and constant cross sections, are derived combining Lagrange’s equations and the assumed mode shape method. To overcome the lengthy and complicated derivative calculation of the Lagrangian function of a FLM, these computations are done only once for a single flexible link manipulator with a moving base (SFLMB). Employing the Lagrange multipliers and the dynamic equations of the SFLMB, the equations of motion of the FLM are derived in terms of the dependent generalized coordinates. To obtain the closed-form dynamic equations of the FLM in terms of the independent generalized coordinates, the natural orthogonal complement of the Jacobian constraint matrix, which is associated with the velocity constraints in the linear homogeneous form, is used. To verify the proposed closed-form dynamic model, the simulation results obtained from the model were compared with the results of the full nonlinear finite element analysis. These comparisons showed sound agreement. One of the main advantages of this approach is that the derived dynamic model can be used for the model based end-effector control and the vibration suppression of planar FLMs.

scholarly journals The Study of Dynamic Modeling and Multivariable Feedback Control for Flexible Manipulators with Friction Effect and Terminal Load

Sensors ◽  
2021 ◽  
Vol 21 (4) ◽  
pp. 1522
Author(s):  
Fuli Zhang ◽  
Zhaohui Yuan
Keyword(s):  
Dynamic Model ◽  
Vibration Suppression ◽  
Control Method ◽  
Coupling Effect ◽  
Flexible Manipulator ◽  
Flexible Beam ◽  
Robot Dynamics ◽  
Joint Friction ◽  
Balance Principle ◽  
Multivariable Feedback

The flexible manipulato is widely used in the aerospace industry and various other special fields. Control accuracy is affected by the flexibility, joint friction, and terminal load. Therefore, this paper establishes a robot dynamics model under the coupling effect of flexibility, friction, and terminal load, and analyzes and studies its control. First of all, taking the structure of the central rigid body, the flexible beam, and load as the research object, the dynamic model of a flexible manipulator with terminal load is established by using the hypothesis mode and the Lagrange method. Based on the balance principle of the force and moment, the friction under the influence of flexibility and load is recalculated, and the dynamic model of the manipulator is further improved. Secondly, the coupled dynamic system is decomposed and the controller is designed by the multivariable feedback controller. Finally, using MATLAB as the simulation platform, the feasibility of dynamic simulation is verified through simulation comparison. The results show that the vibration amplitude can be reduced with the increase of friction coefficient. As the load increases, the vibration can increase further. The trajectory tracking and vibration suppression of the manipulator are effective under the control method of multi-feedback moment calculation. The research is of great significance to the control of flexible robots under the influence of multiple factors.

Dynamic Analysis of Flexible Manipulator Arms With Distributed Viscoelastic Damping

1997 ◽  
Vol 119 (4) ◽  
pp. 831-833 ◽  
Author(s):  
Fan Zijie ◽  
Lu Bingheng ◽  
C. H. Ku
Keyword(s):  
Finite Element ◽  
Dynamic Response ◽  
Dynamic Analysis ◽  
Virtual Work ◽  
Robot Manipulators ◽  
Flexible Manipulator ◽  
Viscoelastic Damping ◽  
Principle Of Virtual Work ◽  
Flexible Robot ◽  
Damping Treatments

The main objective of this work is to predict the effect of distributed viscoelastic damping on the dynamic response of multilink flexible robot manipulators. A general approach, based on the principle of virtual work, is presented for the modeling of flexible robot arms with distributed viscoelastic damping. The finite element equations are developed, and a recurrence formulation for numerical integration of these equations is obtained. It is demonstrated, by a numerical example, that the viscoelastic damping treatments have a significant effect on the dynamic response of flexible robot manipulators.

Dynamic Analysis of Mechanical Systems With Time-Varying Topologies: Part 1 — Dynamic Model and Stability Analysis

1990 ◽  
Author(s):  
Yu Wang
Keyword(s):  
Stability Analysis ◽  
Dynamic Model ◽  
Local Stability ◽  
Global Analysis ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Time Varying ◽  
Discrete Equations ◽  
Local Stability Analysis ◽  
Multiple Collisions

Abstract A model is developed for analyzing mechanical systems with a pair of bodies with topological changes in their kinematic constraints. It is built upon the concept of Poincaré map rather than following the traditional methods of differential equations. The model provides a set of well-defined and naturally-discrete equations of motion and is capable of giving physical insights of dynamic characteristics of deadbeat convergence of multiple collisions and periodic or chaotic responses. The development of dynamic model and a local stability analysis are presented in Part 1, and the global analysis and numerical simulation are discussed in Part 2.

About the Use of the Floating Frame in the Optimal Control of the Flexible Robot Arm

1992 ◽  
Vol 4 (4) ◽  
pp. 330-338 ◽  
Author(s):  
M. Bisiacco ◽  
◽  
R. Caracciolo ◽  
M. Giovagnoni ◽  
◽  
...  
Keyword(s):  
Optimal Control ◽  
Linear Model ◽  
Equations Of Motion ◽  
Flexible Manipulator ◽  
Robot Arm ◽  
Flexible Robot ◽  
Coupled Equations ◽  
Weakly Coupled ◽  
Tip Position ◽  
The Mathematical Model

The mathematical model of a single-link flexible manipulator is obtained by measuring transverse deflections in a rotating reference frame which is floating with respect to the link. The use of this particular frame, the rigidbody mode frame, enables one to obtain weakly coupled equations of motion. The size of the inertia coupling terms can be easily evaluated: these terms can be shown to be negligible thus leading to an essentially linear model. An example of optimal control of manipulator's tip position is numerically reproduced. The same controller is first applied to the mechanical model of the arm accounting for non-linear coupling and then to the linear model: the two responses are found to be very close to each other.

A Finite Element Approach for Single-Link Flexible Manipulator

2013 ◽  
Vol 347-350 ◽  
pp. 453-456
Author(s):  
Jing Yuan Shi ◽  
Kai Jun Ji ◽  
Yan Kun Tang ◽  
Kun Yang
Keyword(s):  
Finite Element ◽  
Equations Of Motion ◽  
Energy Approach ◽  
Flexible Manipulator ◽  
Flexible Link ◽  
Finite Element Approach ◽  
Single Link ◽  
Element Approach

Many researchers have studied the dynamics of the single-link flexible manipulator. A finite element approach is used in this study to describe the dynamics of the flexible link. The displacement of any point on the link is described in terms of modal displacements. Energy approach is used to formulate the equations of motion.

Dynamics and Motion Control of Flexible Manipulators With Multi-Degree of Kinematic Redundancy

2005 ◽  
Author(s):  
Yue-Qing Yu ◽  
Ji-Yun Yang
Keyword(s):  
Motion Control ◽  
Robot Manipulator ◽  
Robot Manipulators ◽  
Flexible Manipulator ◽  
Flexible Manipulators ◽  
Kinematic Redundancy ◽  
Flexible Robot ◽  
Flexible Robots ◽  
Dynamic Performances ◽  
Self Motion

The dynamics and motion control of flexible robot manipulators is an advanced topic in the study of robotics. The precise tracking of the end-effector trajectory of flexible robots can be improved by the self-motion of redundant manipulators. The flexible manipulator with single-degree of kinematic redundancy has been considered only at present. This study addresses on the dynamics and motion control of flexible robots with multi-degree of kinematic redundancy. Compared with the robot with one-degree of redundancy, the optimal motion programming of a flexible robot manipulator with two-degree of redundancy has been obtained successfully based on pseudo-inverse solution. The numerical results of planar three-link and four-link flexible manipulators show the advantage of multi-degree of redundancy in improving the kinematic and dynamic performances of flexible robot manipulators.

scholarly journals Dynamic Modeling of Planar Multi-Link Flexible Manipulators

Robotics ◽  
2021 ◽  
Vol 10 (2) ◽  
pp. 70
Author(s):  
Dipendra Subedi ◽  
Ilya Tyapin ◽  
Geir Hovland
Keyword(s):  
Dynamic Model ◽  
Equations Of Motion ◽  
Frequency Domain Analysis ◽  
Flexible Manipulator ◽  
Time Domain Simulation ◽  
Theoretical Derivation ◽  
Modes Of Vibration ◽  
Robot Configuration ◽  
The Time Domain ◽  
Explicit Equations Of Motion

A closed-form dynamic model of the planar multi-link flexible manipulator is presented. The assumed modes method is used with the Lagrangian formulation to obtain the dynamic equations of motion. Explicit equations of motion are derived for a three-link case assuming two modes of vibration for each link. The eigenvalue problem associated with the mass boundary conditions, which changes with the robot configuration and payload, is discussed. The time-domain simulation results and frequency-domain analysis of the dynamic model are presented to show the validity of the theoretical derivation.

Vibration Control of a Space Flexible Robot Manipulator Using PZT Actuators

2011 ◽  
Vol 66-68 ◽  
pp. 1142-1148 ◽  
Author(s):  
Jun Qiang Lou ◽  
Yan Ding Wei
Keyword(s):  
Control Strategy ◽  
Vibration Suppression ◽  
Robot Manipulator ◽  
Equations Of Motion ◽  
System Stability ◽  
Flexible Manipulator ◽  
Flexible Robot ◽  
Simulation Results ◽  
And Control ◽  
And Robotics

The dynamic analysis and control of flexible robot manipulators have been the main concerns of many recent studies in aeronautics and robotics. Moreover, the complexity of this problem increases when a flexible manipulator carries a payload. In this paper, we proposed a space two-link flexible manipulator with tip payload featuring surface-bonded piezoelectric torsional actuator and shear actuator. The equations of motion for the system are obtained using Hamilton’s principle. A Lyapunov-based controller is proposed to suppress the vibration of the system. Stability of the system is also investigated. The simulation results demonstrate the proposed control strategy is well suited for active control of vibration suppression on flexible manipulators.

scholarly journals Experimental Validation of Hybrid Polymer Composite Material Robotic Single Link Flexible Manipulator

2020 ◽  
Vol 9 (3) ◽  
pp. 488-494
Keyword(s):  
Composite Material ◽  
Hybrid Composite ◽  
Experimental Validation ◽  
Equations Of Motion ◽  
Polymer Composite Material ◽  
Flexible Manipulator ◽  
Control Analysis ◽  
Flexible Link ◽  
Amplitude Control ◽  
Hybrid Composite Material

The prime aim of this research is to conduct an experimental validation for the assessment of behaviour of a hybrid composite material. The hybrid lightweight composite material is used as a robotic link for replacement of rigid and giant manipulators. The combination of fibre material methodically processed and technically merged with epoxy, resulting in hybrid composite material which is used as robotic link movement application and experimentally validated with respect to its functional behavior and cost-effectiveness. In this experimental investigation, composite material is taken as a flexible link for vibration amplitude control analysis and flexible deflection determination using modern control system with various joint stiffness coefficient. The numerical evaluations are conducted for lightweight composite material as an alternate of rigid and solid link. The modelling of composite flexible link is carried out for precision and accuracy on the basis of Lagrange’s equations of motion. The vibration investigation of the system is carried out and reduction of vibration is evaluated using model-based controller in the experiment.

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