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.

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 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 New Method for Dynamic Modeling of Flexible-Link Flexible-Joint Manipulators

2011 ◽  
Vol 134 (1) ◽  
Author(s):  
M. Vakil ◽  
R. Fotouhi ◽  
P. N. Nikiforuk
Keyword(s):  
Closed Form ◽  
Dynamic Model ◽  
Lagrange Multipliers ◽  
New Method ◽  
Flexible Link ◽  
Flexible Joint ◽  
Generalized Coordinates ◽  
Lagrange’S Equations ◽  
Mass Moment ◽  
Lagrange's Equations

In this article, by combining the assumed mode shape method and the Lagrange’s equations, a new and efficient method is introduced to obtain a closed-form finite dimensional dynamic model for planar Flexible-link Flexible-joint Manipulators (FFs). To derive the dynamic model, this new method separates (disassembles) a FF into two subsystems. The first subsystem is the counterpart of the FF but without joints’ flexibilities and rotors’ mass moment of inertias; this subsystem is referred to as a Flexible-link Rigid-joint manipulator (FR). The second subsystem has the joints’ flexibilities and rotors’ mass moment of inertias, which are excluded from the FR; this subsystem is called Flexible-Inertia entities (FI). While the method proposed here employs the Lagrange’s equations, it neither requires the derivation of the lengthy Lagrangian function nor its complex derivative calculations. This new method only requires the Lagrangain function evaluation and its derivative calculations for a Single Flexible link manipulator on a Moving base (SFM). By using the dynamic model of a SFM and the Lagrange multipliers, the dynamic model of the FR is first obtained in terms of the dependent generalized coordinates. This dynamic model is then projected into the tangent space of the constraint manifold by the use of the natural orthogonal complement of the Jacobian constraint matrix. Therefore, the dynamic model of the FR is obtained in terms of the independent generalized coordinates and without the Lagrange multipliers. Finally, the joints’ flexibilities and rotors’ mass moment of inertias, which are included in the FI, are added to the dynamic model of the FR and a closed-form dynamic model for the FF is derived. To verify this new method, the results of simulation examples, which are obtained from the proposed method, are compared with those of a full-nonlinear finite element analysis, where the comparisons indicate sound agreement

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.

Simplification of manipulator dynamic formulations utilizing a dimensionless method

Robotica ◽  
1993 ◽  
Vol 11 (2) ◽  
pp. 139-147 ◽  
Author(s):  
Yueh-Jaw Lin ◽  
Hai-Yan Zhang
Keyword(s):  
Dynamic Model ◽  
Inverse Dynamics ◽  
Equations Of Motion ◽  
Dynamics Simulation ◽  
Dynamic Equations ◽  
New Approach ◽  
Magnitude Comparison ◽  
Dynamic Formulation ◽  
Order Of Magnitude ◽  
Physical Quantities

SUMMARYThis paper presents a new approach for simplifying dynamic equations of motion of robot manipulators by using a nondimensionalization scheme. With this approach the dynamic analysis is done in a nondimensional space. That is, it is required to establish a dimensionless coordinate system in which the dynamic equations of motion of manipulators are formulated. The characteristic parameters of the manipulators are then defined by choosing proper physical quantities as basic units for nondimensionalization. Within the nondimensional space the Lagrange method is applied to the manipulator to obtain a set of general dimensionless equations of motion. This dimensionless dynamic formulation of manipulators leads to an easier way to simplify the dynamic formulation by neglecting insignificant terms using the order of magnitude comparison. The dimensionless dynamic model and its simplified version of PUMA 560 robot are implemented using the proposed approach. It is found that the simplified dynamic model greatly reduces the computation burden of the inverse dynamics. Simulation results also show that the simplified model is extremely accurate. This implies that the proposed nondimensional simplification emethod is reliable.

Dynamic Modeling and Vibration Control of a Space Flexible Manipulator Using Piezoelectric Actuators and Sensors

2011 ◽  
Vol 345 ◽  
pp. 46-52 ◽  
Author(s):  
Jun Qiang Lou ◽  
Yan Ding Wei
Keyword(s):  
Vibration Control ◽  
Dynamic Modeling ◽  
Vibration Suppression ◽  
Equations Of Motion ◽  
Linear Quadratic Regulator ◽  
Flexible Manipulator ◽  
Coupled Vibration ◽  
Linear Quadratic ◽  
Space Manipulator ◽  
Tip Mass

This paper concerns the dynamic modeling and vibration control of a space two-link flexible manipulator. Two types of PZT actuators, PZT shear actuator and torsional actuator, are used to suppress the bending-torsional-coupled vibration of the space manipulator. Using extended Hamilton’s principle and the finite element method, equations of motion of the space flexible manipulator with PZT actuators and tip mass are obtained. Based on modal analyze theory, the state space model of the system is then used to design the control system. A linear quadratic regulator (LQR) controller is designed to achieve vibration suppression of the space manipulator system. From the numerical results, we can get that the proposed controller has a suitable and efficient performance suppressing the bending-torsional-coupled vibration of the space two-link flexible manipulator.

scholarly journals Nonlinear Dynamic Analysis and Optimization of Closed-Form Planetary Gear System

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Qilin Huang ◽  
Yong Wang ◽  
Zhipu Huo ◽  
Yudong Xie
Keyword(s):  
Differential Equations ◽  
Closed Form ◽  
Dynamic Model ◽  
Total Mass ◽  
Nonlinear Differential Equations ◽  
Equations Of Motion ◽  
Planetary Gear ◽  
Transmission System ◽  
Gear Transmission ◽  
Gear Transmission System

A nonlinear purely rotational dynamic model of a multistage closed-form planetary gear set formed by two simple planetary stages is proposed in this study. The model includes time-varying mesh stiffness, excitation fluctuation and gear backlash nonlinearities. The nonlinear differential equations of motion are solved numerically using variable step-size Runge-Kutta. In order to obtain function expression of optimization objective, the nonlinear differential equations of motion are solved analytically using harmonic balance method (HBM). Based on the analytical solution of dynamic equations, the optimization mathematical model which aims at minimizing the vibration displacement of the low-speed carrier and the total mass of the gear transmission system is established. The optimization toolbox in MATLAB program is adopted to obtain the optimal solution. A case is studied to demonstrate the effectiveness of the dynamic model and the optimization method. The results show that the dynamic properties of the closed-form planetary gear transmission system have been improved and the total mass of the gear set has been decreased significantly.

Vibration control of coupled Duffing oscillators in flexible single-link manipulators

2020 ◽  
pp. 107754632095259
Author(s):  
Jie Huang ◽  
Jinchen Ji
Keyword(s):  
High Speed ◽  
Vibration Suppression ◽  
Control Method ◽  
Negative Impact ◽  
Nonlinear Modeling ◽  
Flexible Manipulator ◽  
Flexible Link ◽  
Structural Nonlinearity ◽  
Single Link ◽  
Coupled Duffing Oscillators

Motion-induced oscillations of the flexible single link and its payload at the tip have negative impact on the anticipated performance of the flexible manipulators and thus should be suppressed to achieve tip positioning accuracy and high-speed operation. Because of the structural flexibility, the dynamics of the flexible manipulator can be described by coupled Duffing oscillators when considering the inherent structural nonlinearity of the flexible link into the dynamic modeling. However, little research has been focused on addressing the dynamic coupling issue in the nonlinear modeling of flexible-link manipulators using coupled Duffing oscillators. This article presents coupled Duffing oscillators for the nonlinear modeling of flexible single-link manipulators and then proposes a control method for suppressing the nonlinear vibrations of the coupled Duffing oscillators. Simulated and experimental results obtained from a flexible single-link manipulator test bench are in good agreement with the proposed nonlinear modeling and also demonstrate the effectiveness of the proposed control techniques for vibration suppression of the flexible manipulator.

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.

Dynamic Characterization of a Partially Treated MR Based Sandwich Plate: Finite Element Modeling and Experimental Study

2014 ◽  
Author(s):  
Mehdi Eshaghi ◽  
Ramin Sedaghati ◽  
Subhash Rakheja
Keyword(s):  
Magnetic Field ◽  
Finite Element ◽  
Sandwich Plate ◽  
Vibration Suppression ◽  
Equations Of Motion ◽  
Excitation Frequency ◽  
Core Layer ◽  
Fe Model ◽  
Element Analysis ◽  
Mr Fluid

The dynamic characteristics of a partially treated MR sandwich plate are investigated through finite element analysis and laboratory experiments. A finite element (FE) model is developed to formulate the governing equations of motion of the multi-layer plate with a partial MR fluid core layer, while considering the slippage between the constraining top and bottom aluminum layers. A phenomenological model is further proposed to describe the complex shear modulus of the MR fluid in the pre-yield region as a function of both the applied magnetic field and the excitation frequency. The validity of the FE model is demonstrated through measurements in the laboratory under different intensities of the magnetic field. The results show important effect of the shear deformations in vibration suppression capability of the MR sandwich plate.

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