Dynamic analysis of flexible linkage mechanisms under uniform temperature change

Hou, Wei; Zhang, Xianmin

doi:10.1016/j.jsv.2008.05.014

Cited by 22 publications

(14 citation statements)

References 57 publications

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“…We can mention that the method of Lagrange's equations was, in these works, practically the only method to approach this type of problems. Although, theoretically, analytical mechanics offers many equivalent formulations, the familiarity of researchers and the ease of obtaining equations for systems with a large number of degrees of freedom have made Lagrange's method preferred in studies [1][2][3][4][5][6][7][8][9][10][11][12][13][14].…”

Section: Introductionmentioning

confidence: 99%

Maggi’s Equations Used in the Finite Element Analysis of the Multibody Systems with Elastic Elements

2020

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The main method used to determine the equations of motion of a multibody system (MBS) with elastic elements is the method of Lagrange’s multipliers. The assembly of equations for the whole system represents an important step in the elastodynamic analysis of such a system. This paper presents a new method of approaching this stage, by applying Maggi’s equations. In this way, the links that exist between the finite elements and the connections that exist between different bodies of the MBS system are conveniently taken into account, each body having a distinct velocity and acceleration field. Although Maggi’s equations have been used, sporadically, in some applications so far, we are not aware that they have been used in the study of elastic systems using the finite element method. Finally, an algorithm is presented that uses the Maggi formalism to obtain the equations of motion for an MBS system.

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Section: Introductionmentioning

confidence: 99%

Maggi’s Equations Used in the Finite Element Analysis of the Multibody Systems with Elastic Elements

2020

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“…The vibration control of the manipulator was combined with piezoelectric actuation to improve the performance of the manipulator under parameter uncertainty. The dynamic characteristics of planar 3-RRR parallel manipulator with flexible linkages under temperature change are studies in [24][25][26][27][28] to determine the change of stresses in the links. Chen et al [29,30] developed a curvature-based finite element method for discretization of the flexible links for the dynamic modelling approach.…”

Section: Introductionmentioning

confidence: 99%

Dynamic Analysis of Flexible-Link Planar Parallel Manipulator with Platform Rigidity Considerations

Varalakshmi¹

2017

AJMIE

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This paper presents dynamic analysis studies of planar parallel flexible 3-RRR manipulator with and without considering the flexibility of mobile platform. Initially, by treating all the members of the manipulator as flexible, the joint displacements, reaction forces and stresses are obtained during a specified trajectory tracking in Cartesian space. A comparative study is conducted with manipulator configuration having rigid mobile platform using coupled dynamics of limbs and kinematic constraints of mobile platform. Dynamic response of flexible manipulator is validated using ANSYS simulations for two different cases of trajectories. The results show a remarkable effect of flexibility of mobile platform on the overall dynamic response. After validation of the model, the inverse dynamic analysis data is used to create the system dynamics by employing generalized regression neural network (GRNN) model and the forward dynamic solutions of the flexible manipulator are predicted instantaneously. This study is useful for the real time implementation of motion control of flexible manipulators with complex dynamic model of manipulators.

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“…In this method, rigid-body motion is first determined, and then the unknown elastic displacements are solved. In the derivation of equations of motion an assumption is made that the shape function for rigid-body motion is the same as for elastic motion [2][3][4][5][6]. As a result, the system inertia matrix for elastic displacement vector appears also together with the rigid-body acceleration vector on the right-hand side of equations of motions.…”

Section: Introductionmentioning

confidence: 99%

“…The model of a shape function for the planar rigid-body motion proposed in [19,20] is used. In this way, in contrast to many other studies [2][3][4][5][6], the shape function for elastic motion is not used to describe an arbitrary large rigid-body translation. Moreover, as proven in the Appendix, the shape function for planar beam elements is only an approximation of displacement distribution along rigid finite elements and for exact description of rigid motion the shape function proposed in this paper should be used.…”

Section: Introductionmentioning

confidence: 99%

On Equations of Motion of Elastic Linkages by FEM

Hać

2013

Mathematical Problems in Engineering

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Discussion on equations of motion of planar flexible mechanisms is presented in this paper. The finite element method (FEM) is used for obtaining vibrational analysis of links. In derivation of dynamic equations it is commonly assumed that the shape function of elastic motion can represent rigid-body motion. In this paper, in contrast to this assumption, a model of the shape function specifically dedicated to the rigid-body motion is presented, and its influence on elastic motion is included in equations of motion; the inertia matrix related to the rigid-body acceleration vector depends on both shape functions of the elastic and rigid elements. The numerical calculations are conducted in order to determine the influence of the assumed shape function for rigid-body motion on the vibration of links in the case of closed-loop and open-loop mechanisms. The results of numerical simulation show that for transient analysis and for some specific conditions (e.g., starting range, open-loop mechanisms) the influence of assumed shape functions on vibration response can be quite significant.

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Dynamic analysis of flexible linkage mechanisms under uniform temperature change

Cited by 22 publications

References 57 publications

Maggi’s Equations Used in the Finite Element Analysis of the Multibody Systems with Elastic Elements

Maggi’s Equations Used in the Finite Element Analysis of the Multibody Systems with Elastic Elements

Dynamic Analysis of Flexible-Link Planar Parallel Manipulator with Platform Rigidity Considerations

On Equations of Motion of Elastic Linkages by FEM

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