A study of the free vibration of flexible-link flexible-joint manipulators

2011 ◽  
Vol 225 (6) ◽  
pp. 1361-1371 ◽  
Author(s):  
M Vakil ◽  
R Fotouhi ◽  
P N Nikiforuk ◽  
F Heidari
Keyword(s):  
Joint Stiffness ◽  
Sensitivity Study ◽  
Frequency Equation ◽  
Mode Shapes ◽  
Flexible Link ◽  
Flexible Joint ◽  
Mass Moment ◽  
Mass Moment Of Inertia ◽  
Payload Mass ◽  
Analytical Expressions

In this article, explicit expressions for the frequency equation, mode shapes, and orthogonality of the mode shapes of a Single Flexible-link Flexible-joint manipulator (SFF) are presented. These explicit expressions are derived in terms of non-dimensional parameters which make them suitable for a sensitivity study; sensitivity study addresses the degree of dependence of the system’s characteristics to each of the parameters. The SFF carries a payload which has both mass and mass moment of inertia. Hence, the closed-form expressions incorporate the effect of payload mass and its mass moment of inertia, that is, the payload mass and its size. To check the accuracy of the derived analytical expressions, the results from these analytical expressions were compared with those obtained from the finite element method. These comparisons showed excellent agreement. By using the closed-form frequency equation presented in this article, a study on the changes in the natural frequencies due to the changes in the joint stiffness is performed. An upper limit for the joint stiffness of a SFF is established such that for the joint stiffness above this limit, the natural frequencies of a SFF are very close to those of its flexible-link rigid-joint counterpart. Therefore, the value of this limit can be used to distinguish a SFF from its flexible-link rigid-joint manipulator counterpart. The findings presented in this article enhance the accuracy and time-efficiency of the dynamic modeling of flexible-link flexible-joint manipulators. These findings also improve the performance of model-based controllers, as the more accurate the dynamic model, the better the performance of the model-based controllers.

Coupling Effects in a Manipulator With Both a Flexible Link and Joint

1994 ◽  
Vol 116 (4) ◽  
pp. 826-831 ◽  
Author(s):  
F. Xi ◽  
R. G. Fenton ◽  
B. Tabarrok
Keyword(s):  
Natural Frequencies ◽  
Coupling Effect ◽  
Joint Stiffness ◽  
The Other ◽  
Dynamic Equations ◽  
Mode Shapes ◽  
Flexible Link ◽  
Flexible Joint ◽  
Special Cases ◽  
The Moment

The manipulator considered in this paper consists of a flexible link and a flexible joint. The coupling effect between link and joint deflections is investigated. The dynamic equations for the of manipulator are derived and analytical solutions are obtained. It is shown that the natural frequencies and mode shapes of a manipulator with both a flexible link and joint may be parametrized in terms of two ratios. One is the ratio of the moment of inertia of the link to that of the rotor and the other is the ratio of the link stiffness to the joint stiffness. Two special cases are discussed: (1) a manipulator with a relatively flexible link and a relatively rigid joint; and (2) a manipulator with a relatively flexible joint and a relatively rigid link.

Optimal Performance of the TLCD in Structural Pitching Vibration Control

2002 ◽  
Vol 8 (5) ◽  
pp. 619-642 ◽  
Author(s):  
S. D. Xue ◽  
J. M. Ko ◽  
Y. L. Xu
Keyword(s):  
Numerical Optimization ◽  
Sensitivity Study ◽  
Optimization Approach ◽  
Optimum Control ◽  
Head Loss Coefficient ◽  
Tuning Ratio ◽  
Mass Moment ◽  
Practical Design ◽  
Mass Moment Of Inertia ◽  
Structural Uncertainties

A detailed optimal parametric study is performed for a tuned liquid column damper (TLCD) in suppressing the pitching vibration of structures. Due to the difficulty of finding analytical solutions for the damped structure, a numerical optimization approach is proposed and applied to the system to find the optimum TLCD parameters. The variations of the optimum control parameter with system parameters are determined and discussed. Using various numerical searching data, a set of practical design formulas for the optimum tuning ratio and optimum head loss coefficient of the TLCD are then derived through regression analysis. The comparison between practical design formula and numerical optimization shows a very close agreement between the two results. The practical design formulas provide a convenient tool for designers. In order to account for the possible effects of structural uncertainties, a parametric sensitivity study on the de-tuning of optimum damper parameters is also carried out. It is found that the detuning effect is more severe for low damped structure with lower ratios of mass moment of inertia, especially for the detuning of tuning ratio.

Vibration Frequencies for a Uniform Beam With One End Elastically Supported and Carrying a Mass at the Other End

1975 ◽  
Vol 42 (4) ◽  
pp. 878-880 ◽  
Author(s):  
D. A. Grant
Keyword(s):  
Normal Modes ◽  
Frequency Equation ◽  
The Other ◽  
Concentrated Mass ◽  
Mass Moment ◽  
Wide Range ◽  
Modes Of Vibration ◽  
Mass Moment Of Inertia ◽  
Elastically Supported ◽  
Range Of Values

In this paper the author obtains the frequency equation for the normal modes of vibration of uniform beams with linear translational and rotational springs at one end and having a concentrated mass at the other free end. The eigenfrequencies for the fundamental mode are given for a wide range of values of mass ratio, mass moment of inertia ratios, and stiffness ratios.

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

Dynamic Modeling and Analysis of Space Manipulator Considering the Flexible of Joint and Link

2013 ◽  
Vol 823 ◽  
pp. 270-275 ◽  
Author(s):  
Pan Dong ◽  
Zhao Yang ◽  
Zhang Yue ◽  
Wei Cheng ◽  
E Wei
Keyword(s):  
Joint Stiffness ◽  
Low Frequency ◽  
Flexible Link ◽  
Large Space ◽  
Flexible Joint ◽  
Modeling And Analysis ◽  
Position Accuracy ◽  
Low Frequency Vibration ◽  
Space Manipulators ◽  
The Impact

The long length, light weight, low frequency, flexible joint and link of large space manipulators impact dynamic stability and position accuracy seriously. In this paper, dynamical model of space flexible manipulators system is build base on Lagrange method. With three DOF manipulators as the research object, the impact of flexible link, joint stiffness and clearance on the system frequency and end position accuracy of manipulator is simulated and analyzed. The results indicate that the flexible joint lead to low frequency vibration and flexible link lead to high frequency vibration. Low frequency vibration is the dominant impact of end position accuracy, Flexible joint have greater impact on the dynamic characteristics of system than that of flexible link.

Modeling and validation of crankshaft speed fluctuations of a single-cylinder four-stroke diesel engine

2021 ◽  
pp. 095440702110262
Author(s):  
Mustafa Babagiray ◽  
Hamit Solmaz ◽  
Duygu İpci ◽  
Fatih Aksoy
Keyword(s):  
Diesel Engine ◽  
Dynamic Model ◽  
Moment Of Inertia ◽  
Mass Motion ◽  
Cylinder Pressure ◽  
Motion Equations ◽  
Single Cylinder ◽  
Mass Moment ◽  
Mass Moment Of Inertia ◽  
Speed Fluctuations

In this study, a dynamic model of a single-cylinder four-stroke diesel engine has been created, and the crankshaft speed fluctuations have been simulated and validated. The dynamic model of the engine consists of the motion equations of the piston, conrod, and crankshaft. Conrod motion was modeled by two translational and one angular motion equations, by considering the kinetic energy resulted from the mass moment of inertia and conrod mass. Motion equations involve in-cylinder gas pressure forces, hydrodynamic and dry friction, mass inertia moments of moving parts, starter moment, and external load moment. The In-cylinder pressure profile used in the model was obtained experimentally to increase the accuracy of the model. Pressure profiles were expressed mathematically using the Fourier series. The motion equations were solved by using the Taylor series method. The solution of the mathematical model was performed by coding in the MATLAB interface. Cyclic speed fluctuations obtained from the model were compared with experimental results and found compitable. A validated model was used to analyze the effects of in-cylinder pressure, mass moment of inertia of crankshaft and connecting rod, friction, and piston mass. In experiments for 1500, 1800, 2400, and 2700 rpm engine speeds, crankshaft speed fluctuations were observed as 12.84%, 8.04%, 5.02%, and 4.44%, respectively. In simulations performed for the same speeds, crankshaft speed fluctuations were calculated as 10.45%, 7.56%, 4.49%, and 3.65%. Besides, it was observed that the speed fluctuations decreased as the average crankshaft speed value increased. In the simulation for 157.07, 188.49, 219.91, 251.32, and 282.74 rad/s crankshaft speeds, crankshaft speed fluctuations occurred at rates of 10.45%, 7.56%, 5.84%, 4.49%, and 3.65%, respectively. The effective engine power was achieved as 5.25 kW at an average crankshaft angular speed of 219.91 rad/s. The power of friction loss in the engine was determined as 0.68 kW.

Vibrations of Spinning Rings With Radial and Circumferential Displacement Constraints

1991 ◽  
Author(s):  
Shyh-Chin Huang ◽  
Chen-Kai Su
Keyword(s):  
Natural Frequencies ◽  
Point Contact ◽  
Frequency Equation ◽  
Mode Shapes ◽  
Complex Conjugate ◽  
Constrained System ◽  
Form Complex ◽  
Circumferential Displacement ◽  
On The Road ◽  
Displacement Constraints

Abstract The frequencies and mode shapes of rolling rings with radial and circumferential displacement constraints are investigated. The displacement constraints practically come from the point contact, e.g., rolling tire on the road, or other applications. The proposed approach to analysis is calculating the natural frequencies and modes of a non-contacted spinning ring, then employing the receptance method for displacement constraints. The frequency equation for the constrained system is hence obtained, and it can be solved numerically or graphically. The receptance matrix developed for the spinning ring is surprisingly found not symmetric as usual. Moreover, the cross receptances are discovered to form complex conjugate pairs. That is a feature that has never been described in literature. The results show that the natural frequencies for the spinning ring in contact, as expected, higher than those for the non-contacted ring. The variance of frequencies to rotational speeds are then illustrated. The analytic forms of mode shapes are also derived and sketched. The traveling modes are then shown for cases.

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