Resonance Analysis of Manipulators with Flexible Link and Flexible Joint

2011 ◽  
Vol 383-390 ◽  
pp. 2868-2874
Author(s):  
Zhi Hui Gao ◽  
Yu Shu Bian
Keyword(s):  
Motion Planning ◽  
Structure Design ◽  
Flexible Manipulator ◽  
Dynamic Equations ◽  
Flexible Link ◽  
Flexible Joint ◽  
Joint Flexibility ◽  
Resonance Analysis ◽  
Link Flexibility ◽  
Main Factors

Worse than common vibration, resonance is a form of severe vibration. It is very important and useful to know what factors and conditions can result in resonance of flexible manipulators, when both link flexibility and joint flexibility are taken into account. In this paper, resonance analysis of the flexible manipulator with both link flexibility and joint flexibility is studied. Based on the flexible dynamic equations, main factors resulting in resonance of the flexible manipulator are analyzed. Furthermore, several conditions exciting resonance are derived and verified with numerical simulations. These conclusions are helpful to predict resonance and useful to the structure design and motion planning for a flexible manipulator to evade resonance

A Lagrangian Formulation of the Dynamic Model for Flexible Manipulator Systems

1988 ◽  
Vol 110 (2) ◽  
pp. 175-181 ◽  
Author(s):  
K. H. Low ◽  
M. Vidyasagar
Keyword(s):  
Differential Equations ◽  
Boundary Value Problems ◽  
Natural Extension ◽  
Flexible Manipulator ◽  
Dynamic Equations ◽  
Continuous Systems ◽  
Flexible Link ◽  
Flexible Links ◽  
Generalized Coordinates ◽  
Kinetic And Potential Energies

This paper presents a procedure for deriving dynamic equations for manipulators containing both rigid and flexible links. The equations are derived using Hamilton’s principle, and are nonlinear integro-differential equations. The formulation is based on expressing the kinetic and potential energies of the manipulator system in terms of generalized coordinates. In the case of flexible links, the mass distribution and flexibility are taken into account. The approach is a natural extension of the well-known Lagrangian method for rigid manipulators. Properties of the dynamic matrices, which lead to a less computation, are shown. Boundary-value problems of continuous systems are briefly described. A two-link manipulator with one rigid link and one flexible link is analyzed to illustrate the procedure.

A Model-Based Control of Flexible-Joint Flexible-Link Robots Based on a V-Shape Lyapunov Function

2000 ◽  
Author(s):  
Ho-Hoon Lee
Keyword(s):  
Computer Simulation ◽  
Lyapunov Function ◽  
Control Problems ◽  
Velocity Control ◽  
Flexible Link ◽  
Flexible Joint ◽  
Model Based Control ◽  
Model Based ◽  
Link Flexibility ◽  
Flexible Link Robots

Abstract This paper proposes a model-based control of flexible-joint flexible-link robots based on a V-shape Lyapunov function. The proposed control solves the control problems of the joint and link flexibility simultaneously and is not restricted by the degree of the flexibility. The proposed control guarantees the global asymptotic stability for the position and velocity control of the links and joints with all internal signals bounded. The effectiveness of the proposed control has been shown by computer simulation.

Dynamic Stability Analysis of a Two-Link Force-Controlled Flexible Manipulator

1990 ◽  
Vol 112 (4) ◽  
pp. 661-666 ◽  
Author(s):  
B. C. Chiou ◽  
M. Shahinpoor
Keyword(s):  
Dynamic Stability ◽  
Closed Loop ◽  
Position Control ◽  
Dynamic Instability ◽  
Force Sensor ◽  
System Stability ◽  
Flexible Manipulator ◽  
Dynamic Equations ◽  
Equilibrium Configurations ◽  
Link Flexibility

This study investigates the effect of link flexibility on the dynamic stability of a two-link force-controlled robot manipulator. The nonlinear open-loop equations for the compliant motion are derived first. By employing the hybrid force/position control law, the closed-loop dynamic equations are then explicitly derived. The nonlinear closed-loop equations are linearized about some equilibrium configurations. Stability analyses are carried out by computing the eigenvalues of the linearized system equations. Results are verified by the numerical simulations using the complete nonlinear dynamic equations. The effect of the wrist force sensor stiffness on the dynamic stability is also investigated. Results show that the link flexibility is indeed an important source of dynamic instability in the motion of force-controlled manipulators. Moreover, the system stability is dominated by the effect of the distributed flexibility of the first link.

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.

Coupling Effects in a Manipulator With Both a Flexible Link and Joint

1994 ◽  
Vol 116 (4) ◽  
pp. 826-831 ◽  
Author(s):  
F. Xi ◽  
R. G. Fenton ◽  
B. Tabarrok
Keyword(s):  
Natural Frequencies ◽  
Coupling Effect ◽  
Joint Stiffness ◽  
The Other ◽  
Dynamic Equations ◽  
Mode Shapes ◽  
Flexible Link ◽  
Flexible Joint ◽  
Special Cases ◽  
The Moment

The manipulator considered in this paper consists of a flexible link and a flexible joint. The coupling effect between link and joint deflections is investigated. The dynamic equations for the of manipulator are derived and analytical solutions are obtained. It is shown that the natural frequencies and mode shapes of a manipulator with both a flexible link and joint may be parametrized in terms of two ratios. One is the ratio of the moment of inertia of the link to that of the rotor and the other is the ratio of the link stiffness to the joint stiffness. Two special cases are discussed: (1) a manipulator with a relatively flexible link and a relatively rigid joint; and (2) a manipulator with a relatively flexible joint and a relatively rigid link.

Incorporation of Joint Flexibility With Link Flexibility: Dynamic Modeling and Analysis

1995 ◽  
Author(s):  
Degao Li ◽  
Jean W. Zu ◽  
Andrew A. Goldenberg
Keyword(s):  
Dynamic Modeling ◽  
Mode Analysis ◽  
Mode Shapes ◽  
Flexible Robot ◽  
Flexible Robots ◽  
Flexible Joint ◽  
Joint Flexibility ◽  
Modeling And Analysis ◽  
Assumed Mode Method ◽  
Link Flexibility

Abstract Flexible robots with both link flexibility and joint flexibility have received increasing attention recently. In modeling the flexible robots with the assumed mode method, the model accuracy is highly dependent on the mode shapes of the link deflection. For flexible-link, flexible-joint robots, conventionally used clamped-free or pinned-free modes may cause large errors. To address this problem, this paper presents a systematic approach to dynamic modeling and mode analysis of a single-link flexible robot, which has a flexible joint and a hub at the base end and a payload at the free end. Accurate modes of the system are obtained. The following important conclusions are obtained: (1) Even a small joint flexibility can significantly affect the system frequencies; (2) The fundamental frequency is sensitive to the change in the payload and is not sensitive to the change in the hub inertia.

Vibration Control of a Flexible Link Manipulator Using an Array of Fiber-Optic Curvature Sensors and Piezoelectric Actuators

2007 ◽  
Author(s):  
Kerem Gurses ◽  
Bradley J. Buckman ◽  
Edward J. Park
Keyword(s):  
Motion Control ◽  
Sensor Array ◽  
Fiber Optic ◽  
Element Model ◽  
Flexible Manipulator ◽  
Flexible Link ◽  
Velocity Feedback ◽  
Lyapunov Approach ◽  
Single Link ◽  
Actuator Control

This paper presents a novel feedback sensing approach for actively suppressing vibrations of a single-link flexible manipulator. Slewing of the flexible link by a rotating hub induces vibrations in the link that persist long after the hub stops rotating. These vibrations are suppressed through a combined scheme of PD-based hub motion control and proposed piezoelectric (PZT) actuator control, which is a composite linear and velocity feedback controller. Lyapunov approach was used to synthesize the controller based on a finite element model of the system. Its realization was possible due to the availability of both linear and angular velocity feedback provided by a unique, commercially-available fiber optic curvature sensor array, called ShapeTape™. It is comprised of an array of fiber optic curvature sensors, laminated on a long, thin ribbon tape, geometrically arranged in such a way that, when it is embedded into the flexible link, the bend and twist of the link’s centerline can be measured. Experimental results show the effectiveness of the proposed approach.

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.

An Approach for the Dynamics of Robotic Manipulators With Structural Flexibility of Links and Joints

1997 ◽  
Author(s):  
J. Kövecses ◽  
R. G. Fenton ◽  
W. L. Cleghorn
Keyword(s):  
Equations Of Motion ◽  
Robotic Manipulators ◽  
Structural Flexibility ◽  
Flexible Link ◽  
Dynamic Effects ◽  
Flexible Joint ◽  
Modeling And Analysis ◽  
Discrete Parameter ◽  
Rigid Link ◽  
Different Types

Abstract In this paper, an approach is presented for the dynamic modeling and analysis of robotic manipulators having structural flexibility in the links and joints. The formulation allows the user to include different types of flexibilities, as required. This approach includes the dynamic effects of joint driving systems by considering the mass and moments of inertia of their elements, the rotor-link interactions, and the gear reduction ratios; all of which can have significant influences on the behavior of the manipulator. Both distributed-discrete and discretized-discrete parameter models of a robot can be analysed. In the discretized-discrete case, dynamic equations of motion are developed for four model types: rigid link - rigid joint, rigid link - flexible joint, flexible link - rigid joint, and flexible link - flexible joint. An example of a two-link manipulator is considered. Simulation results are presented for different models (flexible joint - rigid link, rigid joint - flexible link, flexible joint - flexible link) of the manipulator. The computations show the influence of joint and link flexibilities on the manipulator performance.

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