Dynamic Modeling of a Flexible Manipulator With Prismatic Links

1999 ◽  
Vol 121 (4) ◽  
pp. 691-696 ◽  
Author(s):  
B. J. Torby ◽  
I. Kimura
Keyword(s):  
Moving Boundary ◽  
Dimensional Space ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Flexible Manipulator ◽  
Assumed Mode Method ◽  
Mode Method ◽  
Finite Element Node ◽  
Assumed Mode ◽  
Three Dimensional Space

In this paper the equations of motion for a flexible multi-link manipulator are derived. Each link of the manipulator, including those with prismatic motion, is represented by two finite elements in three-dimensional space. The prismatic links are treated as beams with moving boundary conditions, and the position of finite-element node points are not changed relative to the link. The equations are generated using Maple V, and the paper discusses a general approach for eliminating small terms. A sample calculation is performed for a RRP (Stanford arm) manipulator, and the shift of natural frequencies with time are plotted. Results are compared to those obtained by the assumed-mode method.

Squeal Analysis of a Disc Brake Considering Damping between a Disc and a Pad Lining

2012 ◽  
Vol 157-158 ◽  
pp. 1000-1003
Author(s):  
Ke Wei Zhou ◽  
Cheol Kim ◽  
Min Ok Yun ◽  
Ju Young Kim
Keyword(s):  
Finite Element ◽  
Equations Of Motion ◽  
Element Model ◽  
Disc Brake ◽  
Vibration Modes ◽  
Assumed Mode Method ◽  
Frictional Damping ◽  
System Components ◽  
Mode Method ◽  
Assumed Mode

The improved equations of motion for a friction-engaged brake system have been newly derived on the basis of the assumed mode method and frictional damping. The equations of motion with a finite element model were constructed by a set of vibration modes found from FE modal analysis on all system components. Consequently, the modal information of system components are combined with equations of motion derived from the analytical model. Numerical analysis showed the mode which was unstable in an undamped case became stable in a damped case.

scholarly journals Boundary Control of A Flexible Rotatable Manipulator in Three-Dimensional Space With Input Constraints and Actuator Faults

2021 ◽  
Author(s):  
Jiacheng Wang ◽  
Jinkun Liu ◽  
Fangfei Cao
Keyword(s):  
Boundary Control ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Flexible Manipulator ◽  
Control Input ◽  
Input Constraints ◽  
Actuator Faults ◽  
Flexible System ◽  
Actuator Failures ◽  
Three Dimensional Space

Abstract In this paper, the boundary control problem of a flexible rotatable manipulator in Three-Dimensional space with input constraints and actuator faults is taken into account. The Hamilton principle is introduced to derive the dynamic model represented by partial differential equations (PDEs), which can accurately reflect the characteristics of the distributed parameters of the flexible system. The hyperbolic tangent function is adopted to ensure that the control input is within a bounded range, and the projection-based adaptive laws are designed to estimate the degree of unknown actuator failures. Satisfying the input constraints, the system can still remain stable when the actuator failures ensue. The flexible manipulator can track the required angle, and both the elastic deformation and the deformation rate are effectively suppressed simultaneously. The numerical simulation results further illustrate the effectiveness of the proposed controller.

Closed-Form Primitives for Generating Volume Preserving Deformations

1993 ◽  
Author(s):  
Gregory S. Chirikjian
Keyword(s):  
Closed Form ◽  
Dimensional Space ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Physical Systems ◽  
Mechanics Of Materials ◽  
Time Simulation ◽  
Infinite Variety ◽  
Volume Preserving ◽  
Three Dimensional Space

Abstract In this paper, methods for generating closed-form expressions for locally volume preserving deformations of general volumes in three dimensional space are introduced. These methods potentially have applications to computer aided geometric design, the mechanics of materials, and realistic real-time simulation and animation of physical processes. In mechanics, volume preserving deformations are intimately related to the conservation of mass. The importance of this fact manifests itself in design, and in the realistic simulation of many physical systems. Whereas volume preservation is generally written as a constraint on equations of motion in continuum mechanics, this paper develops a set of physically meaningful basic deformations which are intrinsically volume preserving. By repeated application of these primitives, an infinite variety of deformations can be written in closed form.

Numerical Analysis of the Iced Transmission Line Galloping

2014 ◽  
Vol 607 ◽  
pp. 894-900
Author(s):  
Li Qin ◽  
Tian Yuan Xu
Keyword(s):  
Wind Speed ◽  
Transmission Line ◽  
Lagrange Equation ◽  
Equations Of Motion ◽  
Lyapunov Stability Theory ◽  
Assumed Mode Method ◽  
Torsional Response ◽  
Critical Wind Speed ◽  
Mode Method ◽  
Assumed Mode

By used the assumed mode method to simulate the iced transmission line galloping,with three generalized coordinates to represent the iced transmission line galloping. In order to avoid the complicated calculation of vector,used the Lagrange equation to build the nonlinear equations of iced transmission line from the perspective of energy,used the Runge-Kutta numerical calculation to solve the equations of motion and get the iced transmission line’s across-wind,along-wind and the torsional response. Based on Lyapunov stability theory to deduce the critical wind speed of the iced transmission line galloping. And had used a test iced transmission line to verify the feasibility of the numerical solution and the critical wind speed.

Modal Analysis of a Rotating Shaft-Disk-Blades System With a Cracked Blade

1997 ◽  
Author(s):  
Ming-Chuan Wu ◽  
Shyh-Chin Huang
Keyword(s):  
Natural Frequencies ◽  
Equations Of Motion ◽  
Rotating Shaft ◽  
Coupled Modes ◽  
Energy Principle ◽  
Assumed Mode Method ◽  
Discrete Equations ◽  
Mode Method ◽  
Released Energy ◽  
Assumed Mode

Abstract The dynamic behavior of a rotating shaft-disk-blades system containing a cracked blade is investigated. With the crack released energy, the flexibility due to crack is evaluated. An energy principle in conjunction with the assumed-mode method is applied to yield the discrete equations of motion. Numerical examples are given for cases with between two and five symmetrically arrayed blades. The results show that there exist both torsion-bending coupled modes and blade-coupling modes, which occur at repeated frequencies. When there is a cracked blade, the frequencies of torsion-bending coupled modes decrease due to the crack, and blade-coupling modes have the phenomena of frequency bifurcation. Finally, the effects of shaft speed on the natural frequencies are illustrated.

scholarly journals DYNAMIC ANALYSES OF A FLEXIBLE VEHICLE MOVING ALONG A FLEXIBLE GUIDEWAY CONSIDERING THE TIP-OFF EFFECT

2013 ◽  
Vol 13 (01) ◽  
pp. 1350009 ◽  
Author(s):  
S. N. CHOU ◽  
F. P. CHENG ◽  
C. S. HUANG
Keyword(s):  
Nonlinear Differential Equations ◽  
Equations Of Motion ◽  
Flexible Beam ◽  
Differentiation Formula ◽  
Assumed Mode Method ◽  
Dynamic Analyses ◽  
Mode Method ◽  
Assumed Mode ◽  
Bdf Method ◽  
Free Beam

A semi-analytical solution for the tip-off response of a vehicle moving along a guideway is obtained, considering the dynamic interaction between the two subsystems. The guideway is modeled as an inclined simply-supported uniform flexible beam, and the vehicle as a flexible free-free beam under a pre-specified thrust force. The equations of motion for the vehicle and guideway are developed using the Lagrangian approach and the assumed mode method based on the Euler–Bernoulli hypothesis. In the form of nonlinear differential equations, they are solved by the Petzold-Gear backward differentiation formula (BDF) method. The solutions obtained are validated by comparing them with the published results for the models with a rigid vehicle running over a rigid guideway or a flexible guideway. Comparisons of the present solutions with the existing ones for the vehicle and guideway reveal the advantages of the approach proposed herein. Other effects on the tip-off responses of the vehicle that are investigated include the length of the guideway, distance between the shoes of the vehicle, and mass and rigidity ratios of the vehicle to the guideway. The results presented herein provide valuable information for the design of the vehicle launch system.

scholarly journals Nontrivial Isometric Embeddings for Flat Spaces

Universe ◽  
2021 ◽  
Vol 7 (12) ◽  
pp. 477
Author(s):  
Sergey Paston ◽  
Taisiia Zaitseva
Keyword(s):  
Minkowski Space ◽  
Dimensional Space ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Ambient Space ◽  
The Other ◽  
Field Limit ◽  
Isometric Embeddings ◽  
Weak Gravitational Field ◽  
Three Dimensional Space

Nontrivial isometric embeddings for flat metrics (i.e., those which are not just planes in the ambient space) can serve as useful tools in the description of gravity in the embedding gravity approach. Such embeddings can additionally be required to have the same symmetry as the metric. On the other hand, it is possible to require the embedding to be unfolded so that the surface in the ambient space would occupy the subspace of the maximum possible dimension. In the weak gravitational field limit, such a requirement together with a large enough dimension of the ambient space makes embedding gravity equivalent to general relativity, while at lower dimensions it guarantees the linearizability of the equations of motion. We discuss symmetric embeddings for the metrics of flat Euclidean three-dimensional space and Minkowski space. We propose the method of sequential surface deformations for the construction of unfolded embeddings. We use it to construct such embeddings of flat Euclidean three-dimensional space and Minkowski space, which can be used to analyze the equations of motion of embedding gravity.

Dynamics of a Flexible Rod in a Quick Return Mechanism

1994 ◽  
Vol 116 (1) ◽  
pp. 70-74 ◽  
Author(s):  
Heow-Pueh Lee
Keyword(s):  
Numerical Simulations ◽  
Equations Of Motion ◽  
Angular Speed ◽  
Matrix Form ◽  
Euler Beam ◽  
Assumed Mode Method ◽  
Point Support ◽  
Mode Method ◽  
Stiff Spring ◽  
Assumed Mode

The equations of motion in matrix form are formulated for a flexible rod in a quick return mechanism using Hamilton’s principle and the assumed mode method. The rod is considered as an Euler beam. The crank is assumed to be rigid and rotating at a constant angular speed. The translating-rotating joint connecting the crank to the flexible rod is assumed to be a frictionless moving point support for the flexible rod. This support is regarded as a very stiff spring acting on the rotating flexible rod. Results of numerical simulations are presented for various prescribed crank positions, crank lengths, and crank speeds.

The Assumed Mode Method in Structural Dynamics of Bladed-Disk-Shaft Systems

1990 ◽  
Author(s):  
Naim Khader ◽  
Sanier Masoud
Keyword(s):  
Equations Of Motion ◽  
Analytical Investigation ◽  
Assumed Mode Method ◽  
Bladed Disk ◽  
Wide Range ◽  
Out Of Plane ◽  
Mode Method ◽  
Inertia Parameters ◽  
Inertia Properties ◽  
Assumed Mode

Analytical investigation into the effect of transverse bending of continuous flexible shafts is presented. While the blades are allowed both in-plane and out-of-plane deformations, the considered disk is rigid, and the shaft is allowed to bend in two planes. The assumed mode method is used to express flexible blade and shaft deformations, and the Lagrangian approach is used to derive the governing equations of motion for the considered structure. Stiffness and inertia properties of an actual experimental rotor, typical of a fan stage, are used in the analysis. Calculations are performed for three different disk-shaft configurations, and results are presented for different shaft stiffness and inertia parameters, as well as for a wide range of rotational speed.

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