scholarly journals Dynamic Modeling and Development of Symbolic Calculation Software for N-DOF Flexible-Link Manipulators Incorporating Lumped Mass

2019 ◽  
Vol 2019 ◽  
pp. 1-16 ◽  
Author(s):  
Feng Yu ◽  
Xinyuan Chen
Keyword(s):  
Dynamic Modeling ◽  
Lagrange Equation ◽  
Modeling Method ◽  
Flexible Manipulator ◽  
Flexible Manipulators ◽  
Lumped Mass ◽  
Symbolic Expression ◽  
Symbolic Calculation ◽  
Assumed Mode Method ◽  
Calculation Software

Considering the complex dynamic modeling of multi-DOF planar flexible manipulators, a general-purpose method for the rigid-flexible coupling dynamic modeling of N-DOF flexible manipulators is proposed in this paper, and symbolic calculation software is developed. The modeling method is based on the Lagrange equation and assumed mode method (AMM). First, the N-DOF flexible manipulator is divided into two parts, which are assumed to be rigid and flexible. On this basis, the rigid part and the flexible part are coupled, and the calculation process of the model is further simplified. Then, the simplest general symbolic expression of the dynamic model of the N-DOF flexible manipulator is obtained with the induction method. According to the modeling method, “symbolic expression computation software for dynamic equations of N-DOF flexible manipulators” is developed using the symbolic calculation software Mathematica. Finally, the dynamic modeling method and the symbolic calculation software are verified by a trajectory tracking experiment with a PD control applied to a 2-DOF flexible manipulator. Compared with the traditional modeling method, the calculation time can be reduced by more than 90% using the modeling method proposed in this paper, which significantly reduces the complexity of the modeling process.

Influence of backlash in gear reducer on dynamic of single-link manipulator arm

Robotica ◽  
2014 ◽  
Vol 33 (08) ◽  
pp. 1671-1685 ◽  
Author(s):  
Jian-Wei Lu ◽  
Xiao-Ming Sun ◽  
Alexander F. Vakakis ◽  
Lawrence A. Bergman
Keyword(s):  
Dynamic Response ◽  
Dynamic Modeling ◽  
Excitation Frequency ◽  
Planetary Gear ◽  
Flexible Manipulator ◽  
Lumped Mass ◽  
Modeling And Control ◽  
Single Link ◽  
Manipulator Arm ◽  
And Control

SUMMARYThe dynamic modeling of a flexible single-link manipulator arm with consideration of backlash in the planetary gear reducer at the joint is presented, and the influence of backlash on the dynamic response of the system is evaluated. A 2K-H planetary gear reducer with backlash was employed as an example to discuss the dynamic modeling of the sub-model of the planetary gear reducer, and the sub-model of the planetary gear reducer was established based on the lumped mass method. The flexible manipulator was regarded as an Euler--Bernoulli beam, and the dynamic model of the flexible manipulator arm with backlash in the planetary gear reducer was determined from Lagrange's equations. Based on the this model, the influence of the backlash in the planetary gear reducer and excitation frequency on the dynamic response of the system were evaluated through simulation, and the results showed that the dynamic response of the system is sensitive to the backlash and the excitation frequency simultaneously, which provides a theoretical foundation for improvement of dynamic modeling and control of the flexible manipulator arm.

scholarly journals Control Method of Flexible Manipulator Servo System Based on a Combination of RBF Neural Network and Pole Placement Strategy

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 896
Author(s):  
Dongyang Shang ◽  
Xiaopeng Li ◽  
Meng Yin ◽  
Fanjie Li
Keyword(s):  
Neural Network ◽  
Rotation Angle ◽  
Control Method ◽  
Rbf Neural Network ◽  
Servo System ◽  
Flexible Manipulator ◽  
Pole Placement ◽  
Flexible Manipulators ◽  
Angle Error ◽  
Assumed Mode Method

Gravity and flexibility will cause fluctuations of the rotation angle in the servo system for flexible manipulators. The fluctuation will seriously affect the motion accuracy of end-effectors. Therefore, this paper adopts a control method combining the RBF (Radial Basis Function) neural network and pole placement strategy to suppress the rotation angle fluctuations. The RBF neural network is used to identify uncertain items caused by the manipulator’s flexibility and the time-varying characteristics of dynamic parameters. Besides, the pole placement strategy is used to optimize the PD (Proportional Differential) controller’s parameters to improve the response speed and stability. Firstly, a dynamic model of flexible manipulators considering gravity is established based on the assumed mode method and Lagrange’s principle. Then, the system’s control characteristics are analyzed, and the pole placement strategy optimizes the parameters of the PD controllers. Next, the control method based on the RBF neural network is proposed, and the Lyapunov stability theory demonstrates stability. Finally, numerical analysis and control experiments prove the effectiveness of the control method proposed in this paper. The means and standard deviations of rotation angle error are reduced by the control method. The results show that the control method can effectively reduce the rotation angle error and improve motion accuracy.

Model Reduction of Rigid-Flexible Manipulators with Experimental Validation

2013 ◽  
Vol 655-657 ◽  
pp. 1101-1107 ◽  
Author(s):  
Lin Chen ◽  
Hua Deng
Keyword(s):  
Model Simulation ◽  
Lagrange Equation ◽  
Flexible Manipulator ◽  
Flexible Manipulators ◽  
Spectral Approximation ◽  
Nonlinear Dynamic Equation ◽  
Simulation Results ◽  
Experimental Validations ◽  
Set Up ◽  
Platform System

An investigation into the dynamic modeling of rigid-flexible manipulator systems based on spectral approximation methods was presented. The nonlinear dynamic equation of the rigid-flexible manipulator was established on the theory of Lagrange equation and the model was approximated with the spectral approximation method. Furthermore, an experimental platform system was set up to validate the effectiveness of the model. Simulation results of the response of the rigid-flexible manipulators were presented. Moreover, experimental validations were carried out to assess the effectiveness of the modeling approach by comparing with the simulation results. The results verified that the method is effective and feasible.

scholarly journals Dynamic Modeling and Experiment Research on Twin Ball Screw Feed System Considering the Joint Stiffness

Symmetry ◽  
2018 ◽  
Vol 10 (12) ◽  
pp. 686 ◽  
Author(s):  
Meng Duan ◽  
Hong Lu ◽  
Xinbao Zhang ◽  
Yongquan Zhang ◽  
Zhangjie Li ◽  
...  
Keyword(s):  
Dynamic Modeling ◽  
Dynamic Characteristics ◽  
Friction Model ◽  
Numerical Control ◽  
Ball Screw ◽  
Cnc Machine Tools ◽  
Axial Stiffness ◽  
Cnc Machine ◽  
Feed System ◽  
Lumped Mass

It is of great significance to study the dynamic characteristics of twin ball screw (TBS) feed system to improve the precision of gantry-type dual-driven computer numerical control (CNC) machine tools. In this paper, an equivalent dynamic model of the TBS feed system is established utilizing lumped mass method considering the stiffness of joints. Equivalent axial stiffness of screw-nut joints and bearing joints are both calculated by Hertz contact theory. Furthermore, a friction model is proposed because the friction force of the screw nut affects the stiffness of the joints. Then, the friction parameters are obtained by using the nonlinear system identification method. Meanwhile, a finite element model (FEM) is developed to assess the dynamic characteristics of TBS feed system under the stiffness of joints. Finally, validation experiments are conducted, and the results show that the positions of the nut and the velocities of worktable greatly affect the dynamic characteristics of the TBS feed system. Compared with the theoretical calculation, FEM and experiments indicate that the dynamic modeling proposed in this article can reach a higher accuracy.

Analysis of Elastic Motion Stability of Flexible Manipulator Arm Based on Lyapunov Stability Theory

2014 ◽  
Vol 620 ◽  
pp. 321-329
Author(s):  
Guang Rui Liu ◽  
Wen Bo Zhou ◽  
Rong Fu Liu
Keyword(s):  
Lyapunov Stability ◽  
Stability Theory ◽  
Lagrange Equation ◽  
Lyapunov Stability Theory ◽  
The State ◽  
Flexible Manipulator ◽  
Rotational Inertia ◽  
Control Input ◽  
Motion Stability ◽  
Manipulator Arm

In order to study the elastic motion stability of flexible manipulator arm , to compute the maximum dynamic allowable payload , the partial differential equation of elastic motion of the flexible manipulator arm is solved using the method of Laplace transformation , the dynamic model of flexible manipulator arm carried addition mass on its end position is established ,simplified and truncated using Lagrange equation . the state space expression is established with the state variable and control input and output variable designated , the elastic motion stability rule is built upon and simplified using Lyapunov stability theory . The influence of the end position addition mass and articulation rotational inertia of flexible manipulator arm on its elastic motion stability is analyzed using the stability rule , and the dynamic maximum allowable payload of flexible manipulator arm on its end position is computed in order to guarantee its elastic motion stability . this study is important to the design of robot mechanical manipulator and corresponding drive control system .

The Method of Tree Dynamic Modeling under Rainfall Field

2013 ◽  
Vol 475-476 ◽  
pp. 1551-1554
Author(s):  
Tie Nan Li ◽  
Shun Yu ◽  
Feng Yang
Keyword(s):  
Dynamic Modeling ◽  
Young Modulus ◽  
Modeling Method ◽  
Tree Modeling ◽  
Almost All

Almost all the fields use tree modeling in society, so it analyses the tree modeling in the academic circles. But it is difficult to find an efficient tree modeling method because its own complexity and wind, rain acting on tree. The object suffers rain power that the force calculated by momentum theorem. And then compare the value of rupture limit to Young modulus. It is determined object to fracture or sway. Then it constructs tree dynamic modeling in the nature.

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