Study on the Effect of Elastic Deformations on Rigid Body Motions of a 3-PRR Flexible Parallel Manipulator

2007 ◽  
Author(s):  
Xuping Zhang ◽  
James K. Mills ◽  
William L. Cleghorn
Keyword(s):  
Rigid Body ◽  
Parallel Manipulator ◽  
Elastic Deformations ◽  
Rigid Body Motions

MULTIBODY DYNAMIC MODELING AND FLUTTER ANALYSIS OF A FLEXIBLE SLENDER VEHICLE

2012 ◽  
Vol 12 (06) ◽  
pp. 1250049 ◽  
Author(s):  
A. RASTI ◽  
S. A. FAZELZADEH
Keyword(s):  
Differential Equations ◽  
Rigid Body ◽  
Dynamic Modeling ◽  
Equations Of Motion ◽  
The Body ◽  
Elastic Deformations ◽  
Strip Theory ◽  
Multibody Dynamic ◽  
Flutter Analysis ◽  
Rigid Body Motions

In this paper, multibody dynamic modeling and flutter analysis of a flexible slender vehicle are investigated. The method is a comprehensive procedure based on the hybrid equations of motion in terms of quasi-coordinates. The equations consist of ordinary differential equations for the rigid body motions of the vehicle and partial differential equations for the elastic deformations of the flexible components of the vehicle. These equations are naturally nonlinear, but to avoid high nonlinearity of equations the elastic displacements are assumed to be small so that the equations of motion can be linearized. For the aeroelastic analysis a perturbation approach is used, by which the problem is divided into a nonlinear flight dynamics problem for quasi-rigid flight vehicle and a linear extended aeroelasticity problem for the elastic deformations and perturbations in the rigid body motions. In this manner, the trim values that are obtained from the first problem are used as an input to the second problem. The body of the vehicle is modeled with a uniform free–free beam and the aeroelastic forces are derived from the strip theory. The effect of some crucial geometric and physical parameters and the acting forces on the flutter speed and frequency of the vehicle are investigated.

The Use of Vector Techniques in Variational Problems

1986 ◽  
Vol 108 (2) ◽  
pp. 141-145 ◽  
Author(s):  
L. J. Everett ◽  
M. McDermott
Keyword(s):  
Rigid Body ◽  
Equations Of Motion ◽  
Variational Problems ◽  
Double Pendulum ◽  
Coordinate Transformations ◽  
Elastic Deformations ◽  
Variational Techniques ◽  
Convenient Means ◽  
Moving Coordinate ◽  
Rigid Body Motions

A convenient means for applying vector mathematics to variational problems is presented. The total and relative variations of a vector are defined and results which follow from these definitions are developed and proved. These results are then used to express the variation of a functional using vector techniques rather than the classical scalar or matrix techniques. The simple problems of deriving equations of motion for a rigid body and for a rigid double pendulum are presented as examples of the technique. The key advantages of the method are that (1) it allows the investigator who is familiar and proficient with vector techniques to apply these skills to variational problems and (2) it greatly simplifies the application of variational techniques to problems which include both rigid body motions and elastic deformations. This is accomplished by providing the techniques necessary for computing the variation of a vector defined in a moving coordinate system without using coordinate transformations.

Nonlinear Effects in Dynamic Analysis of Flexible Multibody Systems

2001 ◽  
Author(s):  
Y. C. Mbono Samba ◽  
M. Pascal
Keyword(s):  
Rigid Body ◽  
Standard Method ◽  
Multibody Systems ◽  
Nonlinear Effects ◽  
Elastic Deformations ◽  
Dynamics Of Multibody Systems ◽  
Flexible Parts ◽  
Order Of Magnitude ◽  
Rigid Body Motions ◽  
Crank Mechanism

Abstract The work is concerned with the dynamics of multibody systems with flexible parts undergoing large rigid body motions and small elastic deformations. The standard method used in most cases leads to keep only linear terms with respect to the deformations. However, for large rates or large accelerations, this linearisation is sometimes too premature. In this work, a non dimensional analysis of the system is performed, with some estimate about the order of magnitude of the different parameters occuring in the dynamical model obtained by Kane’s method [1]. A flexible slider crank mechanism is used as a test example, together with AUTOLEV [2] software for numerical results.

Analytical models for the rigid body motions of skew bridges

1987 ◽  
Vol 15 (8) ◽  
pp. 923-944 ◽  
Author(s):  
Emmanuel A. Maragakis ◽  
Paul C. Jennings
Keyword(s):  
Rigid Body ◽  
Analytical Models ◽  
Skew Bridges ◽  
Rigid Body Motions

Hydrostatics and Rigid-Body Motions

2018 ◽  
pp. 57-124
Keyword(s):  
Rigid Body ◽  
Rigid Body Motions

Correction of strain errors induced by small rigid-body motions in electronic speckle pattern interferometry measurement

2013 ◽  
Vol 20 (1) ◽  
pp. 2-11 ◽  
Author(s):  
Helen H. Chen ◽  
Ray K.L. Su ◽  
Albert K.H. Kwan ◽  
Alex S.L. Fok
Keyword(s):  
Rigid Body ◽  
Speckle Pattern ◽  
Electronic Speckle Pattern Interferometry ◽  
Rigid Body Motions

Synthesizing Precompressed Beams As Bistable Compliant Mechanisms

2017 ◽  
Author(s):  
Mohammed Abdullah Maaz Siddiqui ◽  
Hong Zhou
Keyword(s):  
Rigid Body ◽  
Axial Compression ◽  
Stable Equilibrium ◽  
Compliant Mechanisms ◽  
Input Power ◽  
Elastic Deformations ◽  
Buckling Instability ◽  
Beam Thickness ◽  
Fixed End ◽  
Input Torque

Bistable mechanisms provide two stable positions. Input power is not needed to maintain any of the two stable positions. To switch from one stable position to another, input power is required. Bistable mechanisms have many applications including valves, closures, switches and various other devices. Unlike conventional rigid-body bistable mechanisms that rely on relative motions of kinematic joints, bistable compliant mechanisms take advantage of elastic deformations of flexible members to achieve two stable positions. There are two symmetric buckled shapes in a precompressed beam that has one fixed end and one pinned end. The two buckled shapes match the two stable equilibrium positions of bistable compliant mechanisms. The precompressed beam can be rotationally actuated at the pinned end to snap from one buckled shape to another. Synthesizing precompressed beams as bistable mechanisms is challenging because of buckling instability and integrated force and deflection characteristics. In this paper, the buckled shape is derived for a precompressed beam with fixed and pinned ends. The input torque at the pinned end is analyzed for a precompressed beam to snap between its two symmetric buckled shapes. Precompressed beams are synthesized as bistable compliant mechanisms through axial compression and beam thickness in this paper.

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