Oblique Impact of Multi-Flexible-Link Systems

2016 ◽  
Vol 24 (5) ◽  
pp. 904-923 ◽  
Author(s):  
AM Shafei ◽  
HR Shafei
Keyword(s):  
Beam Theory ◽  
Oblique Impact ◽  
Algebraic Equations ◽  
Flexible Link ◽  
Governing Equations ◽  
Assumed Mode Method ◽  
Virtual Links ◽  
Mode Method ◽  
Impact Phase ◽  
Curved Walls

The main goal of this paper is to present an automatic approach for the dynamic modeling of the oblique impact of a multi-flexible-link robotic manipulator. The behavior of a multi-flexible-link system confined inside a closed environment with curved walls can be completely expressed by two distinct mathematical models. A set of differential equations is employed to model the system when it has no contact with the curved walls (Flight phase); and a set of algebraic equations is used whenever it collides with the confining surfaces (Impact phase). In this article, in addition to the Assumed Mode Method (AMM), the Euler-Bernoulli Beam Theory (EBBT), and the Newton’s kinematic impact law, the Gibbs-Appell (G-A) formulation has been employed to derive the governing equations in both phases. Also, instead of using 3 × 3 rotational matrices, which involves lengthy kinematic and dynamic formulations for deriving the governing equations, 4 × 4 transformation matrices have been used. Moreover, for the systematic modeling of flexible multiple links through the space, two virtual links have been added to the n real links of a manipulator. Finally, two case studies have been simulated to demonstrate the validity of the proposed approach.

Dynamic Behavior of Flexible Multiple Links Captured Inside a Closed Space

2016 ◽  
Vol 11 (5) ◽  
Author(s):  
A. M. Shafei ◽  
H. R. Shafei
Keyword(s):  
Differential Equations ◽  
Beam Theory ◽  
Kinematic Chain ◽  
Algebraic Equations ◽  
Assumed Mode Method ◽  
Transformation Matrices ◽  
3D Space ◽  
Mode Method ◽  
Spatial Rotations ◽  
Euler Bernoulli Beam

This work presents a systematic method for the dynamic modeling of flexible multiple links that are confined within a closed environment. The behavior of such a system can be completely formulated by two different mathematical models. Highly coupled differential equations are employed to model the confined multilink system when it has no impact with the surrounding walls; and algebraic equations are exploited whenever this open kinematic chain system collides with the confining surfaces. Here, to avoid using the 4 × 4 transformation matrices, which suffers from high computational complexities for deriving the governing equations of flexible multiple links, 3 × 3 rotational matrices based on the recursive Gibbs-Appell formulation has been utilized. In fact, the main aspect of this paper is the automatic approach, which is used to switch from the differential equations to the algebraic equations when this multilink chain collides with the surrounding walls. In this study, the flexible links are modeled according to the Euler–Bernoulli beam theory (EBBT) and the assumed mode method. Moreover, in deriving the motion equations, the manipulators are not limited to have only planar motions. In fact, for systematic modeling of the motion of a multiflexible-link system in 3D space, two imaginary links are added to the n real links of a manipulator in order to model the spatial rotations of the system. Finally, two case studies are simulated to demonstrate the correctness of the proposed approach.

scholarly journals Vibrations of a Beam Moving Over Supports with Clearance

1994 ◽  
Vol 1 (6) ◽  
pp. 549-557
Author(s):  
H.P. Lee
Keyword(s):  
Piecewise Linear ◽  
Equations Of Motion ◽  
Beam Theory ◽  
Euler Beam ◽  
Assumed Mode Method ◽  
Mode Method ◽  
Euler Beam Theory ◽  
The Stability ◽  
Effect Of Support ◽  
Piecewise Linear Stiffness

The transverse vibration of a beam moving over two supports with clearance is analyzed using Euler beam theory. The equations of motion are formulated based on a Lagrangian approach and the assumed mode method. The supports with clearance are modeled as frictionless supports with piecewise-linear stiffness. A feature of the present formulation is that its complexity does not increase with increased number of supports. Results of numerical simulations are presented for various prescribed motions of the beam. The effect of support clearance on the stability of the beam is investigated.

Effects of surface energy on vibration characteristics of double-walled piezo-viscoelastic cylindrical nanoshell

2019 ◽  
Vol 233 (15) ◽  
pp. 5264-5279 ◽  
Author(s):  
Sayyid H Hashemi Kachapi ◽  
Morteza Dardel ◽  
Hamidreza Mohamadi Daniali ◽  
Alireza Fathi
Keyword(s):  
Surface Energy ◽  
Governing Equations ◽  
Assumed Mode Method ◽  
Remarkable Effect ◽  
Nanoscale System ◽  
Interface Theory ◽  
Piezoelectric Layers ◽  
Mode Method ◽  
Pasternak Model ◽  
Assumed Mode

In this paper, vibration analysis of double-walled piezo-viscoelastic cylindrical nanoshell integrated with piezoelectric layers is investigated using Gurtin–Murdoch surface/interface theory and Donnell's theory. Three parameters namely, shear modulus, damp coefficient, and Winkler modulus are used for simulation of visco-Pasternak model. Hamilton's principle is used for deriving the governing equations and boundary conditions and also the assumed mode method is used for changing the partial differential equations into ordinary differential equation. The effects of the surface energy, length and thickness of nanoshell and piezoelectric layer, boundary condition, van der Waals force, and visco-Pasternak effects on the undamped and damped natural frequencies of piezo-viscoelastic cylindrical nanoshell is studied. Also, the results show that on considering surface effects in the nanoscale system without considering the surface density, the maximum frequency will be obtained and this case will be considered as the critical state of the system. As a result, controlling the frequency of the system in this case is essential and it is quite clear that considering the effects of the surface energy will have a remarkable effect on the natural frequency of the piezo-viscoelastic nanoshell.

Longitudinal Vibration Modeling and Control of a Flexible Transporter System with Arbitrarily Varying Cable Lengths

2005 ◽  
Vol 11 (3) ◽  
pp. 431-456 ◽  
Author(s):  
Yuhong Zhang ◽  
Sunil K. Agrawal ◽  
Peter Hagedorn
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Longitudinal Vibration ◽  
Equations Of Motion ◽  
Nonlinear Partial Differential Equations ◽  
Governing Equations ◽  
Partial Differential ◽  
Modeling And Control ◽  
Assumed Mode Method ◽  
Mode Method

We present a systematic procedure for deriving the model of a cable transporter system with arbitrarily varying cable lengths. The Hamilton principle is applied to derive the governing equations of motion. The derived governing equations are nonlinear partial differential equations. The results are verified using the Newton law. The assumed mode method is used to obtain an approximate numerical solution of the governing equations by transforming the infinite-dimensional partial differential equations into a finite-dimensional discretized system. We propose a Lyapunov controller, based directly on the governing partial differential equations, which can both dissipate the vibratory energy during the motion of the transporter and guarantee the attainment of the desired goal point. The validity of the proposed controller is verified by numerical simulation.

scholarly journals Passive Walking Biped Robot Model with Flexible Viscoelastic Legs

2021 ◽  
Author(s):  
Masoumeh Safartoobi ◽  
HamidReza Mohammadi Daniali ◽  
Morteza Dardel
Keyword(s):  
Stable Condition ◽  
Numerical Procedure ◽  
Beam Theory ◽  
Biped Robot ◽  
Step Function ◽  
Assumed Mode Method ◽  
Passive Walking ◽  
Walking Motion ◽  
Mode Method ◽  
Definition Of

Abstract To simulate the complex human walking motion accurately, a suitable biped model has to be proposed that can significantly translate the compliance of biological structures. In this way, the simplest passive walking model is often used as a standard benchmark for making the bipedal locomotion so natural and energy-efficient. This work is devoted to a presentation of the application of internal damping mechanism to the mathematical description of the simplest passive walking model with flexible legs. This feature can be taken into account by using the viscoelastic legs, which are constituted by the Kelvin–Voigt rheological model. Then, the update of the impulsive hybrid nonlinear dynamics of the simplest passive walker is obtained based on the Euler–Bernoulli’s beam theory and using a combination of Lagrange mechanics and the assumed mode method, along with the precise boundary conditions. The main goal of this study is to develop a numerical procedure based on the new definition of the step function for enforcing the biped start walking from stable condition and walking continuously. The study of the influence of various system parameters is carried out through bifurcation diagrams, highlighting the region of stable period-one gait cycles. Numerical simulations clearly prove that the overall effect of viscoelastic leg on the passive walking is efficient enough from the viewpoint of stability and energy dissipation.

Impedance Control of a Two Degree-of-Freedom Flexible Link Manipulator Using Singular Perturbation and Sliding Mode Control Theory

Volume 1 ◽  
2004 ◽  
Author(s):  
A. Karimzadeh ◽  
G. R. Vossoughi
Keyword(s):  
Singular Perturbation ◽  
Sliding Mode Control ◽  
Sliding Mode ◽  
Impedance Control ◽  
Flexible Link ◽  
Singular Perturbation Method ◽  
Flexible Links ◽  
Assumed Mode Method ◽  
Mode Control ◽  
Mode Method

In this article, impedance control of a two link flexible link manipulators is addressed. The concept of impedance control of flexible link robots is rather new and is being addressed for the first time. Impedance Control provides a universal approach to the control of flexible robots — in both constrained and unconstrained maneuvers. The initial part of the paper concerns the use Hamilton’s principle to derive the mathematical equations governing the dynamics of joint angles, vibration of the flexible links and the constraining forces. The approximate elastic deformations are then derived by means of the Assumed-Mode-Method (AMM). Using the singular perturbation method, the dynamic of the manipulator is decomposed to the fast and the slow subsystems. The slow dynamic corresponds to the rigid manipulator and fast dynamic is due to vibrations of flexible links. The sliding mode control (SMC) theory has been used as the means to achieve the 2nd order target impedance for the slow dynamics. A controller based on state feedback is also designed to stabilize the fast dynamics. The composite controller is constructed by using the slow and fast controllers. Simulation results for a 2 DOF robot in which only the 2nd link is flexible confirm that the controller performs remarkably well under various simulation conditions.

Impedance control of a two degree-of-freedom planar flexible link manipulator using singular perturbation theory

Robotica ◽  
2005 ◽  
Vol 24 (2) ◽  
pp. 221-228 ◽  
Author(s):  
G. R. Vossoughi ◽  
A. Karimzadeh
Keyword(s):  
Singular Perturbation ◽  
Sliding Mode ◽  
Impedance Control ◽  
Singular Perturbation Theory ◽  
Flexible Link ◽  
Singular Perturbation Method ◽  
Flexible Links ◽  
Assumed Mode Method ◽  
Mode Method ◽  
Flexible Link Robots

In this article, impedance control of a two link flexible link manipulators is addressed. The concept of impedance control of flexible link robots is rather new and is being addressed for the first time by the authors. Impedance Control provides a universal approach to the control of flexible robots, in both constrained and unconstrained maneuvers. The initial part of the paper concerns the use of Hamilton's principle to derive the mathematical equations governing the dynamics of joint angles, vibration of the flexible links and the constraining forces. The approximate elastic deformations are then derived by means of the Assumed-Mode-Method (AMM). Using the singular perturbation method, the dynamic of the manipulator is decomposed into fast and slow subsystems. The slow dynamic corresponds to the rigid manipulator and the fast dynamic is due to vibrations of flexible links. The sliding mode control (SMC) theory has been used as the means to achieve the 2nd order target impedance for the slow dynamics. A controller based on state feedback is also designed to stabilize the fast dynamics. The composite controller is constructed by using the slow and fast controllers. Simulation results for a 2-DOF robot in which only the 2nd link is flexible confirm that the controller performs remarkably well under various simulation conditions.

scholarly journals Composite Material Robot Manipulator with Joint Flexibility- Mode and Mode Shape Simulation

2019 ◽  
Vol 8 (4) ◽  
pp. 902-909
Keyword(s):  
Composite Material ◽  
Mode Shape ◽  
Robot Manipulator ◽  
Joint Stiffness ◽  
Flexible Link ◽  
Transient Vibration ◽  
Joint Flexibility ◽  
Assumed Mode Method ◽  
Work Volume ◽  
Mode Method

Simulation of composite material robot manipulator with joint flexibility is initiated. The lightweight three types of composite material manipulator links with different joint stiffness are considered for vibration mode and mode shape simulation. The model and its motion equations are obtained by using assumed mode method incorporating and joint flexibility. The structural flexibility of a composite material also included in the analyses. The purpose of simulation to predict the behavior of composite material links, which is inevitable for replacement of bulky manipulators. To reach a set point of flexible link manipulator in a work volume with vibration accuracy is analyzed. The thin flexible link for precise positioning will face transient vibration problems. The flexible deflection and residual vibration are affect the positioning of end point. The source of vibration of a manipulator is due to light structural weight when it is rotated by the actuator. The lightweight link will move faster, but the unwanted vibration in the link is raised. To reduce this vibration issue, without compromising the light weight material, the simulation is carried out

A Method to Improve the Modal Convergence for Structures With External Forcing

1987 ◽  
Vol 54 (4) ◽  
pp. 904-909 ◽  
Author(s):  
Keqin Gu ◽  
Benson H. Tongue
Keyword(s):  
Spatial Distribution ◽  
Free Vibration ◽  
Convergence Rate ◽  
Traditional Approach ◽  
Vibration Modes ◽  
External Forcing ◽  
Slow Convergence ◽  
Assumed Mode Method ◽  
Mode Method ◽  
Assumed Mode

The traditional approach of using free vibration modes in the assumed mode method often leads to an extremely slow convergence rate, especially when discete interactive forces are involved. By introducing a number of forced modes, significant improvements can be achieved. These forced modes are intrinsic to the structure and the spatial distribution of forces. The motion of the structure can be described exactly by these forced modes and a few free vibration modes provided that certain conditions are satisfied. The forced modes can be viewed as an extension of static modes. The development of a forced mode formulation is outlined and a numerical example is presented.

scholarly journals Vibration and Instability of Rotating Composite Thin-Walled Shafts with Internal Damping

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Ren Yongsheng ◽  
Zhang Xingqi ◽  
Liu Yanghang ◽  
Chen Xiulong
Keyword(s):  
Virtual Work ◽  
Numerical Study ◽  
Equations Of Motion ◽  
Beam Theory ◽  
Dynamical Analysis ◽  
Design Parameters ◽  
Internal Damping ◽  
Analysis Method ◽  
Governing Equations ◽  
Thin Walled

The dynamical analysis of a rotating thin-walled composite shaft with internal damping is carried out analytically. The equations of motion are derived using the thin-walled composite beam theory and the principle of virtual work. The internal damping of shafts is introduced by adopting the multiscale damping analysis method. Galerkin’s method is used to discretize and solve the governing equations. Numerical study shows the effect of design parameters on the natural frequencies, critical rotating speeds, and instability thresholds of shafts.

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