Dynamic modeling and extended bifurcation analysis of flexible-link manipulator
02 Jan 2020-Mechanics Based Design of Structures and Machines (Taylor & Francis)-Vol. 48, Iss: 1, pp 87-110
TL;DR: The outcomes indicate that when there is no offset, the decrease in damping results in chaotic generalized modal coordinates, and as the excitation frequency decreases, a limiting amplitude is created at 0.35 before which the behavior of generalized rigid and modal coordinate is different, while this behavior has more similarity after this point.
Abstract: In this article, the nonlinear dynamic analysis of a flexible-link manipulator is presented. Especially, the possibility of chaos occurrence in the system dynamic model is investigated. Upon the oc...
Citations
More filters
TL;DR: This paper presents a new approach to the advanced dynamics of mechanical systems, following the differential principle in generalized form (a generalization of the Lagrange–D’Alembert principle), and establishing the equations of the dynamics of fast-moving systems include the acceleration energies of higher-order.
Abstract: This paper presents a new approach to the advanced dynamics of mechanical systems. It is known that in the movements corresponding to some mechanical systems (e.g., robots), accelerations of higher order are developed. Higher-order accelerations are an integral part of higher-order acceleration energies. Unlike other research papers devoted to these advanced notions, the main purpose of the paper is to present, in a matrix form, the defining expressions for the acceleration energies of a higher order. Following the differential principle in generalized form (a generalization of the Lagrange–D’Alembert principle), the equations of the dynamics of fast-moving systems include, instead of kinetic energies, the acceleration energies of higher-order. To establish the equations which characterize both the energies of accelerations and the advanced dynamics, the following input parameters are considered: matrix exponentials and higher-order differential matrices. An application of a 5 d.o.f robot structure is presented in the final part of the paper. This is used to illustrate the validity of the presented mathematical formulations.
20 citations
TL;DR: The paper presents an alternative method of calculation theses using the Gibbs–Appell (GA) formulation, which requires a smaller number of calculations and, as a result, is easier to apply in practice.
Abstract: When analyzing the dynamic behavior of multi-body elastic systems, a commonly used method is the finite element method conjunctively with Lagrange’s equations. The central problem when approaching such a system is determining the equations of motion for a single finite element. The paper presents an alternative method of calculation theses using the Gibbs–Appell (GA) formulation, which requires a smaller number of calculations and, as a result, is easier to apply in practice. For this purpose, the energy of the accelerations for one single finite element is calculated, which will be used then in the GA equations. This method can have advantages in applying to the study of multi-body systems with elastic elements and in the case of robots and manipulators that have in their composition some elastic elements. The number of differentiation required when using the Gibbs–Appell method is smaller than if the Lagrange method is used which leads to a smaller number of operations to obtain the equations of motion.
18 citations
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.
16 citations
15 May 2020
TL;DR: In this article, the Lagrange's equation is used to determine the finite element motion equations in the case of elasto-dynamic analysis of a multibody system (MBS).
Abstract: The Lagrange’s equation remains the most used method by researchers to determine the finite element motion equations in the case of elasto-dynamic analysis of a multibody system (MBS). However, applying this method requires the calculation of the kinetic energy of an element and then a series of differentiations that involve a great computational effort. The last decade has shown an increased interest of researchers in the study of multibody systems (MBS) using alternative analytical methods, aiming to simplify the description of the model and the solution of the systems of obtained equations. The method of Kane’s equations is one possibility to do this and, in the paper, we applied this method in the study of a MBS applying finite element analysis (FEA). The number of operations involved is lower than in the case of Lagrange’s equations and Kane’s equations are little used previously in conjunction with the finite element method (FEM). Results are obtained regardless of the type of finite element used. The shape functions will determine the final form of the matrix coefficients in the equations. The results are applied in the case of a planar mechanism with two degrees of freedom.
14 citations
TL;DR: A technical design of a universal versatile robotic manipulator for handling with automotive products is presented and it is recommended an appropriate material for the manufacture of the device to reach its optimal accuracy of positioning of handled objects during a long-term operation.
Abstract: Automation is a process of handling and transport of products, which allows replacing man’s control by operation of manipulators and robots. It represents a highly complex process, which includes s...
13 citations
Cites background from "Dynamic modeling and extended bifur..."
...Such a deformation significantly influences the accuracy of the manipulator in the operation process.(20) Therefore, the strength analyses of the effector have been the other important step in the design of the manipulator....
[...]
References
More filters
01 Jan 1988
1,033 citations
"Dynamic modeling and extended bifur..." refers methods in this paper
...According to the Poincar e-Bendixon theorem, if the Melnikov function has a simple zero, the corresponding system is expected to exhibit chaotic behavior (Wiggins 1988)....
[...]
TL;DR: In this paper, the complex sub and supercritical global dynamics of a parametrically excited microbeam subject to a time-dependent axial load involving a constant value together with a harmonic time-variant component are investigated with special consideration to chaotic motion.
Abstract: The complex sub and supercritical global dynamics of a parametrically excited microbeam is investigated with special consideration to chaotic motion. More specifically, for a microbeam subject to a time-dependent axial load involving a constant value together with a harmonic time-variant component, the bifurcation diagrams of Poincare sections of the system near critical point are constructed when the amplitude of the longitudinal load variations is varied as the control parameter. In terms of modelling and simulations, the small-size-dependent potential energy of the system is constructed by means of the modified couple stress theory and constitutive relations. Continuous expressions for the kinetic energy and the energy dissipation mechanism are also constructed. A transformation to a high-dimensional reduced-order model is performed via use of an assumed-mode method as well as the Galerkin scheme. A direct time-integration method is employed to solve the reduced-order model. For different cases in the sub and supercritical regimes, but close to the critical mean axial force, the bifurcation diagrams of Poincare sections are constructed as the amplitude of the axial load variations is chosen as the bifurcation parameter. The complex dynamical behaviour of the system is analysed more precisely through plotting time traces, fast Fourier transforms (FFTs), Poincare sections and phase-plane diagrams.
157 citations
"Dynamic modeling and extended bifur..." refers background in this paper
...…and Pratiher 2019a, 2019b; Mao, Ding, and Chen 2017a, 2017b; Pratiher and Dwivedy 2011), while most others focused on numerical results (Farokhi and Ghayesh 2018; Ghayesh 2012a, 2018; Ghayesh and Amabili 2013; Ghayesh, Amabili, and Farokhi 2013; Ghayesh and Farokhi 2015; Rehlicki et al. 2018)....
[...]
TL;DR: In this paper, a coupled nonlinear longitudinal-transverse-rotational set of equations governing the motion of axially functionally graded (AFG) shear deformable tapered beams subjected to external harmonic excitations is derived.
Abstract: This paper aims at investigating the nonlinear vibration characteristics of axially functionally graded (AFG) shear deformable tapered beams subjected to external harmonic excitations. A coupled nonlinear longitudinal-transverse-rotational set of equations governing the motion of the AFG system is derived utilising the third-order shear deformation beam theory via Hamilton's energy principle. The beam under consideration is tapered; i.e. the width of the beam varies along the length. The tapered geometry along with the nonuniform material properties arising from the AFG nature of the beam increases the complexity in the modelling and numerical simulations. The expressions for the kinetic and potential energies of the AFG shear-deformable tapered beam together with the expressions for the work of damping and external excitation are derived and implemented in Hamilton's principle. The nonlinear partial differential equations are discretised making use of the Galerkin technique and solved with the aid of a continuation scheme. The effect of different parameters such as the gradient index and the tapered ratios on the force- and frequency-amplitude diagrams of the AFG system is examined.
145 citations
"Dynamic modeling and extended bifur..." refers background in this paper
...…and Pratiher 2019a, 2019b; Mao, Ding, and Chen 2017a, 2017b; Pratiher and Dwivedy 2011), while most others focused on numerical results (Farokhi and Ghayesh 2018; Ghayesh 2012a, 2018; Ghayesh and Amabili 2013; Ghayesh, Amabili, and Farokhi 2013; Ghayesh and Farokhi 2015; Rehlicki et al. 2018)....
[...]
TL;DR: In this article, the forced non-linear vibrations of an axially moving beam fitted with an intra-span spring-support are investigated numerically, and the resulting nonlinear ordinary differential equations are solved via either the pseudo-arclength continuation technique or direct time integration.
Abstract: The forced non-linear vibrations of an axially moving beam fitted with an intra-span spring-support are investigated numerically in this paper. The equation of motion is obtained via Hamilton’s principle and constitutive relations. This equation is then discretized via the Galerkin method using the eigenfunctions of a hinged-hinged beam as appropriate basis functions. The resultant non-linear ordinary differential equations are then solved via either the pseudo-arclength continuation technique or direct time integration. The sub-critical response is examined when the excitation frequency is set near the first natural frequency for both the systems with and without internal resonances. Bifurcation diagrams of Poincare maps obtained from direct time integration are presented as either the forcing amplitude or the axial speed is varied; as we shall see, a sequence of higher-order bifurcations ensues, involving periodic, quasi-periodic, periodic-doubling, and chaotic motions.
91 citations
TL;DR: The nonlinear supercritical parametric dynamics of a Timoshenko microbeam subject to an axial harmonic excitation force is examined theoretically and theoretically by means of different numerical techniques, and employing a high-dimensional analysis.
Abstract: The nonlinear supercritical parametric dynamics of a Timoshenko microbeam subject to an axial harmonic excitation force is examined theoretically, by means of different numerical techniques, and employing a high-dimensional analysis. The time-variant axial load is assumed to consist of a mean value along with harmonic fluctuations. In terms of modelling, a continuous expression for the elastic potential energy of the system is developed based on the modified couple stress theory, taking into account small-size effects; the kinetic energy of the system is also modelled as a continuous function of the displacement field. Hamilton's principle is employed to balance the energies and to obtain the continuous model of the system. Employing the Galerkin scheme along with an assumed-mode technique, the energy terms are reduced, yielding a second-order reduced-order model with finite number of degrees of freedom. A transformation is carried out to convert the second-order reduced-order model into a double-dimensional first order one. A bifurcation analysis is performed for the system in the absence of the axial load fluctuations. Moreover, a mean value for the axial load is selected in the supercritical range, and the principal parametric resonant response, due to the time-variant component of the axial load, is obtained – as opposed to transversely excited systems, for parametrically excited system (such as our problem here), the nonlinear resonance occurs in the vicinity of twice any natural frequency of the linear system; this is accomplished via use of the pseudo-arclength continuation technique, a direct time integration, an eigenvalue analysis, and the Floquet theory for stability. The natural frequencies of the system prior to and beyond buckling are also determined. Moreover, the effect of different system parameters on the nonlinear supercritical parametric dynamics of the system is analysed, with special consideration to the effect of the length-scale parameter.
88 citations
"Dynamic modeling and extended bifur..." refers background in this paper
...…2016; Kumar and Pratiher 2019a, 2019b; Mao, Ding, and Chen 2017a, 2017b; Pratiher and Dwivedy 2011), while most others focused on numerical results (Farokhi and Ghayesh 2018; Ghayesh 2012a, 2018; Ghayesh and Amabili 2013; Ghayesh, Amabili, and Farokhi 2013; Ghayesh and Farokhi 2015; Rehlicki et…...
[...]