Position analysis and nonlinear phenomena of flexible manipulator with generic payload mounted on a moving base
28 Jan 2020-Vol. 234, Iss: 2, pp 408-423
TL;DR: In this article, the authors investigated the end-point trajectory and nonlinear oscillation of elastic manipulator with offset payload mounted on moving base by demonstrating the modal parametrization.
Abstract: The investigation of the end-point trajectory and the nonlinear oscillation of elastic manipulator with offset payload mounted on moving base has been carried out by demonstrating the modal paramet...
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TL;DR: This critical review is advantageous and indispensable for researchers who are interested in the area to gain fruitful knowledge on the mathematical modelling methods and guides researchers to select the suitable method for modelling.
Abstract: Mathematical modelling plays an important role for robotic manipulators in order to design their particular controllers. Also, it is hard challenge to obtain an accurate mathematical model or obtain a suitable modelling method in such vast field. Thus, this critical review is advantageous and indispensable for researchers who are interested in the area to gain fruitful knowledge on the mathematical modelling methods. This paper is classified based on the type of robotic manipulators such as flexible link manipulators (FLMs), rigid link manipulators (RLMs) and hybrid manipulators which involves rigid links and flexible links. The used modelling methods for FLMs are the assumed mode method, the finite element method, and the lumped parameter method as approximation techniques which are well explained and reviewed. The Lagrangian method has inclusive explanation and review which is widely participated for obtaining the dynamic equations of FLMs, and it is appropriate and commonly employed for modelling RLMs. The Newtonian method, the forward kinematic, and the inverse kinematic are also well discussed and reviewed which are suitable and commonly employed for modelling RLMs. The critical discussion of 170 articles reported in this paper guides researchers to select the suitable method for modelling. This paper reviews the published articles in the period of 2010–2020 except for few older articles for the need of providing essential theoretical knowledge. The advantages and disadvantages of each method are well summarized at the end of the paper. The intelligent identification methods are briefly discussed due to the lack of publications especially on the period of 2010–2020.
6 citations
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TL;DR: In this paper, motion-induced oscillations of the flexible single link and its payload at the tip have negative impact on the anticipated performance of flexible manipulators and thus should be suppressed to suppress them.
Abstract: 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 ...
4 citations
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TL;DR: In this paper , a nonlinear dynamic modeling, free vibration and nonlinear analysis of three-dimensional viscoelastic Euler-Bernoulli beam undergoing hub motion incorporating substantial tip mass is accomplished.
Abstract: In this paper, the nonlinear dynamic modelling, free vibration and nonlinear analysis of three-dimensional viscoelastic Euler-Bernoulli beam undergoing hub motion incorporating substantial tip mass is accomplished. The kinetic, and potential energy of the system are derived in terms of velocities of general point on the link and center of gravity of the tip mass expressed in multi-floating co-ordinate systems. Hamilton's principle is used to obtain the governing equations of motion and linearly coupled boundary conditions. The material of the beam is considered as viscoelastic constituted of Kelvin-Voigt rheological model. The mass attached at the terminal end of the beam is assumed to have eccentricity in axial, lateral, as well as transverse directions. Free vibration analysis is performed on the linearized system model to obtain the transcendental eigenfrequency equation. Further, the dynamic equations of motion of beam are discretized using the obtained mode shapes and the response of system under rotary motion of hub is investigated. The steady state solutions and frequency response curves exhibiting bi-stable and tri-stable regions are obtained using method of multiple scales. The bifurcation diagrams of the system are studied for resonance conditions when the frequency of the rotary motion becomes equal or nearly equal to the normalized beam frequencies. The saddle node and pitchfork bifurcations exhibiting multiple solutions and jump phenomena are observed and investigated to avoid catastrophic failure of the system. The numerical simulations of modal parameters of the system, nonlinear characteristics, and their parametric dependency is discussed thoroughly.
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TL;DR: In this article, the dynamic equations of a flexible-link manipulator with revolute-prismatic joints as a case of time-variant dynamic system are obtained by Hamilton's principle with the assumption of nonlinear strains.
Abstract: The analysis of motion equations of flexible-link manipulators indicates that nonlinear terms and behavioral instability exist in their outcomes. In this system, when the differential equations possess structural time-dependent parameters, there is a higher chance for system instability, especially chaos in comparison to time-invariant ones. It is a point for abnormal behavior that is unpredictable and always accompanied by damages. Therefore, the physical parameters and system inputs that cause chaotic responses should be detected and prevented as much as possible. To this aim, the dynamic equations of flexible link manipulator with revolute-prismatic joints as a case of time-variant dynamic system are obtained by Hamilton’s principle with the assumption of nonlinear strains. The discretized motion equations are solved and the results are presented in the forms of bifurcation diagrams (for variation of torque/force amplitude), Poincare maps, phase-plane portraits, and the largest Lyapunov exponent. Finally, the obtained results are validated with the aid of the experimental setup. The results indicate that although the system response in low torque/force amplitudes is subharmonic (amplitude of 0.01) and quasi-periodic (amplitudes of 0.02-0.03), it becomes quasi-periodic/chaotic with a mild slope with respect to time in high amplitude values. Moreover, since the behavior of modal generalized coordinate is different from the rigid ones, the quasi-periodic and chaotic vibrations do not hurt the joints.
References
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TL;DR: In this paper, the dynamic characteristics of a flexible hub-beam system with a tip mass are studied through numerical simulations under two cases: the large motion of the system is known and is unknown.
Abstract: For a dynamic system of a rigid hub and a flexible cantilever beam, the traditional hybrid coordinate model assumes the small deformation in structural dynamics where axial and transverse displacements at any point in the beam are uncoupled. This traditional hybrid coordinate model is referred as the zeroth-order approximation coupling model in this paper, which may result in divergence to the dynamic problem of some rigid–flexible coupling systems with high rotational speed. In this paper, characteristics of a flexible hub-beam system with a tip mass is studied. Based on the Hamilton theory and the finite element discretization method, and in consideration of the second-order coupling quantity of the axial displacement caused by the transverse displacement of the beam, the rigid–flexible coupling dynamic model (referred as the first-order approximation coupling (FOAC) model in this paper) and the corresponding model in non-inertial system for the flexible hub-beam system with a tip mass are presented firstly, then the dynamic characteristics of the system are studied through numerical simulations under twos cases: the large motion of the system is known and is unknown. Simulation and comparison studies using both the traditional zeroth-order model and the proposed first-order model show that even small tip mass may affect dynamic characteristics of the system significantly, which may result in the largening of vibrating amplitude and the descending of vibrating frequency of the beam, and may affect end position of the hub-beam system as well. The effect of the tip mass becomes large along with the increasing of rotating speed of large motion of the system. When the large motion of the system is at low speed, the traditional ZOAC model may lead to a large error, whereas the proposed FOAC model is valid. When the large motion is at high speed, the ZOAC model may result in divergence to the dynamic problem of the flexible hub-beam system, while the proposed second model can still accurately describe the dynamic hub-beam system.
81 citations
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TL;DR: In this paper, the non-linear vibration of a harmonically excited single link roller-supported flexible Cartesian manipulator with a payload was analyzed using generalized Galerkin's method.
Abstract: The present work deals with the non-linear vibration of a harmonically excited single link roller-supported flexible Cartesian manipulator with a payload. The governing equation of motion of this system is developed using extended Hamilton's principle, which is reduced to the second-order temporal differential equation of motion, by using generalized Galerkin's method. This equation of motion contains both cubic non-linearities of geometric and inertial type in addition to linear forced and non-linear parametric excitation terms. Method of multiple scales is used to solve this non-linear equation and study the stability and bifurcations of the system. Influence of amplitude of the base excitation and mass ratio on the steady state response of the system is investigated for both simple and subharmonic resonance conditions. Critical bifurcation points are determined from the fixed-point responses and periodic, quasi-periodic responses are also found for different system parameters. The results obtained using the perturbation analysis are compared with the previously published experimental work and are found to be in good agreement. This work will be useful for the designer of a flexible manipulator.
33 citations
"Position analysis and nonlinear phe..." refers background in this paper
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TL;DR: In this article, the nonlinear free vibration of an axially translating viscoelastic beam with an arbitrarily varying length and axial velocity is investigated, and the coupling effects between the axial motion and transverse vibration are assessed under various prescribed time-varying velocity fields.
Abstract: The nonlinear free vibration of an axially translating viscoelastic beam with an arbitrarily varying length and axial velocity is investigated. Based on the linear viscoelastic differential constitutive law, the extended Hamilton’s principle is utilized to derive the generalized third-order equations of motion for the axially translating viscoelastic Bernoulli–Euler beam. The coupling effects between the axial motion and transverse vibration are assessed under various prescribed time-varying velocity fields. The inertia force arising from the longitudinal acceleration emerges, rendering the coupling terms between the axial beam acceleration and the beam flexure. Semi-analytical solutions for the governing PDE are obtained through the separation of variables and the assumed modes method. The modified Galerkin’s method and the fourth-order Runge–Kutta method are employed to numerically analyze the resulting equations. Further, dynamic stabilization is examined from the system energy standpoint for beam extension and retraction. Extensive numerical simulations are presented to illustrate the influences of varying translating velocities and viscoelastic parameters on the underlying dynamic responses. The material viscosity always dissipates energy and helps stabilize the transverse vibration.
32 citations
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TL;DR: In this paper, a clamped-free flexible beam rotating in a horizontal plane and carrying a moving mass is modelled by the Euler-Bernoulli beam theory, and the equation of motion is a coupled non-linear partial differential equation where the coupling terms have to be evaluated at the position of the moving mass.
Abstract: A clamped–free flexible beam rotating in a horizontal plane and carrying a moving mass is modelled by the Euler–Bernoulli beam theory. The equation of motion is derived by Hamilton's principle including the effects of centrifugal stiffening arising from the rotation of the beam. The motion of the moving mass and the beam is coupled. The equation of motion is a coupled non-linear partial differential equation where the coupling terms have to be evaluated at the position of the moving mass. In order to obtain the mode shapes which account for the motion of the moving mass, the solution is discretized into space and time functions and the beam is divided into two separate regions with respect to the moving mass. This results in two non-homogeneous linear mode shape ordinary differential equations with four boundary, one discontinuity and three continuity conditions. The power series method is used to solve for the mode shape differential equations. A frequency equation is derived giving the relationship between the non-dimensional modal frequencies and the four non-dimensional parameters, i.e., the moving mass position, the moving mass, the beam angular velocity and the total moment of inertia about the hub. The numerical bisection method is used to solve for the vibration frequencies under different parameters. Results are presented for the first three modes of vibration.
20 citations
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TL;DR: In this article, the problem of controlling the vibration of a transversely excited cantilever beam with tip mass is analyzed within the framework of the Euler-Bernoulli beam theory.
Abstract: The problem of controlling the vibration of a transversely excited cantilever beam with tip mass is analyzed within the framework of the Euler–Bernoulli beam theory A sinusoidally varying transverse excitation is applied at the left end of the cantilever beam, while a payload is attached to the free end of the beam An active control of the transverse vibration based on cubic velocity is studied Here, cubic velocity feedback law is proposed as a devise to suppress the vibration of the system subjected to primary and subharmonic resonance conditions Method of multiple scales as one of the perturbation technique is used to reduce the second-order temporal equation into a set of two first-order differential equations that govern the time variation of the amplitude and phase of the response Then the stability and bifurcation of the system is investigated Frequency–response curves are obtained numerically for primary and subharmonic resonance conditions for different values of controller gain The numerical results portrayed that a significant amount of vibration reduction can be obtained actively by using a suitable value of controller gain The response obtained using method of multiple scales is compared with those obtained by numerically solving the temporal equation of motion and are found to be in good agreement Numerical simulation for amplitude is also obtained by integrating the equation of motion in the frequency range between 1 and 3 The developed results can be extensively used to suppress the vibration of a transversely excited cantilever beam with tip mass or similar systems actively
19 citations
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