Dynamics and Control of a Translating Flexible Beam With a Prismatic Joint

1992 ◽  
Vol 114 (3) ◽  
pp. 422-427 ◽  
Author(s):  
Sivakumar S. K. Tadikonda ◽  
Haim Baruh
Keyword(s):  
Rigid Body ◽  
The Other ◽  
Body Motion ◽  
Rigid Base ◽  
Flexible Beam ◽  
Positioning Control ◽  
Dynamics And Control ◽  
And Control ◽  
Tip Mass ◽  
Free Beam

The complete dynamic model of a translating flexible beam, with a tip mass at one end and emerging from or retracting into a rigid base at the other, is presented. The model considers the effect of elastic and translational motions of the beam on each other. The properties of the eigenfunctions of a fixed-free beam are exploited to obtain closed-form expressions for several domain integrals that arise in the model. It is shown that neglecting the effect of elastic motion on the rigid body motion leads to inaccuracies in positioning control. Issues associated with the feedback control of such a beam are discussed.

scholarly journals On the Hamel Coefficients and the Boltzmann–Hamel Equations for the Rigid Body

2021 ◽  
Vol 31 (2) ◽  
Author(s):  
Andreas Müller
Keyword(s):  
Rigid Body ◽  
Nonholonomic Systems ◽  
Rigid Bodies ◽  
Body Motion ◽  
Floating Body ◽  
Lagrange Equations ◽  
Local Coordinates ◽  
Dynamics And Control ◽  
Boltzmann Hamel Equations ◽  
And Control

AbstractThe Boltzmann–Hamel (BH) equations are central in the dynamics and control of nonholonomic systems described in terms of quasi-velocities. The rigid body is a classical example of such systems, and it is well-known that the BH-equations are the Newton–Euler (NE) equations when described in terms of rigid body twists as quasi-velocities. It is further known that the NE-equations are the Euler–Poincaré, respectively, the reduced Euler–Lagrange equations on SE(3) when using body-fixed or spatial representation of rigid body twists. The connection between these equations are the Hamel coefficients, which are immediately identified as the structure constants of SE(3). However, an explicit coordinate-free derivation has not been presented in the literature. In this paper the Hamel coefficients for the rigid body are derived in a coordinate-free way without resorting to local coordinates describing the rigid body motion. The three most relevant choices of quasi-velocities (body-fixed, spatial, and hybrid representation of rigid body twists) are considered. The corresponding BH-equations are derived explicitly for the rotating and free floating body. Further, the Hamel equations for nonholonomically constrained rigid bodies are discussed, and demonstrated for the inhomogenous ball rolling on a plane.

Computation of Nonlinear Response of Hydraulically Actuated Structures

1997 ◽  
Author(s):  
T. D. Burton ◽  
C. P. Baker ◽  
J. Y. Lew
Keyword(s):  
Rigid Body ◽  
Flexible Structures ◽  
Rigid Body Motion ◽  
Body Motion ◽  
Flexible Beam ◽  
Test Bed ◽  
Ode Models ◽  
Hydraulically Actuated ◽  
Pressure Dynamics ◽  
Low Order

Abstract The maneuvering and motion control of large flexible structures are often performed hydraulically. The pressure dynamics of the hydraulic subsystem and the rigid body and vibrational dynamics of the structure are fully coupled. The hydraulic subsystem pressure dynamics are strongly nonlinear, with the servovalve opening x(t) providing a parametric excitation. The rigid body and/or flexible body motions may be nonlinear as well. In order to obtain accurate ODE models of the pressure dynamics, hydraulic fluid compressibility must generally be taken into account, and this results in system ODE models which can be very stiff (even if a low order Galerkin-vibration model is used). In addition, the dependence of the pressure derivatives on the square root of pressure results in a “faster than exponential” behavior as certain limiting pressure values are approached, and this may cause further problems in the numerics, including instability. The purpose of this paper is to present an efficient strategy for numerical simulation of the response of this type of system. The main results are the following: 1) If the system has no rigid body modes and is thus “self-centered,” that is, there exists an inherent stiffening effect which tends to push the motion to a stable static equilibrium, then linearized models of the pressure dynamics work well, even for relatively large pressure excursions. This result, enabling linear system theory to be used, appears of value for design and optimization work; 2) If the system possesses a rigid body mode and is thus “non-centered,” i.e., there is no stiffness element restraining rigid body motion, then typically linearization does not work. We have, however discovered an artifice which can be introduced into the ODE model to alleviate the stiffness/instability problems; 3) in some situations an incompressible model can be used effectively to simulate quasi-steady pressure fluctuations (with care!). In addition to the aforementioned simulation aspects, we will present comparisons of the theoretical behavior with experimental histories of pressures, rigid body motion, and vibrational motion measured for the Battelle dynamics/controls test bed system: a hydraulically actuated system consisting of a long flexible beam with end mass, mounted on a hub which is rotated hydraulically. The low order ODE models predict most aspects of behavior accurately.

Dynamics and control of capture of a floating rigid body by a spacecraft robotic arm

2014 ◽  
Vol 33 (3) ◽  
pp. 315-332 ◽  
Author(s):  
Xiao-Feng Liu ◽  
Hai-Quan Li ◽  
Yi-Jun Chen ◽  
Guo-Ping Cai ◽  
Xi Wang
Keyword(s):  
Rigid Body ◽  
Robotic Arm ◽  
Dynamics And Control ◽  
And Control

scholarly journals A unified approach to rigid body rotational dynamics and control

2011 ◽  
Vol 468 (2138) ◽  
pp. 395-414 ◽  
Author(s):  
Firdaus E. Udwadia ◽  
Aaron D. Schutte
Keyword(s):  
Rigid Body ◽  
Closed Form ◽  
Equations Of Motion ◽  
Fundamental Equation ◽  
Rotational Dynamics ◽  
Constrained Motion ◽  
Dynamics And Control ◽  
Common Framework ◽  
The Stability ◽  
And Control

This paper develops a unified methodology for obtaining both the general equations of motion describing the rotational dynamics of a rigid body using quaternions as well as its control. This is achieved in a simple systematic manner using the so-called fundamental equation of constrained motion that permits both the dynamics and the control to be placed within a common framework. It is shown that a first application of this equation yields, in closed form, the equations of rotational dynamics, whereas a second application of the self-same equation yields two new methods for explicitly determining, in closed form, the nonlinear control torque needed to change the orientation of a rigid body. The stability of the controllers developed is analysed, and numerical examples showing the ease and efficacy of the unified methodology are provided.

Comparison of Methods for Determining Screw Parameters of Finite Rigid Body Motion From Initial and Final Position Data

1989 ◽  
Author(s):  
R. G. Fenton ◽  
X. Shi
Keyword(s):  
Rigid Body ◽  
Rigid Body Motion ◽  
The Other ◽  
Body Motion ◽  
Final Position ◽  
Comparison Of Methods ◽  
Rodrigues Formula ◽  
Position Data ◽  
Data Error

Abstract Five methods for determining the screw parameters of finite rigid body motion using position data of three non-collinear points are compared on the basis of their efficiency, accuracy, and sensitivity to data error. It is found that the method based on Rodrigues’ Formula (Bottema & Roth’s method) is the most efficient. Angeles’ method and Laub & Shiflett’s method provide approximately the same level of accuracy, which is superior to that of the other methods. In terms of sensitivity, Bottema & Roth’s method is preferable On the basis of this study it is recommended that Bottema & Roth’s method to be used if uncertainty exists in the data since it can provide a solution efficiently, accurately, and it is the least sensitive to data error.

Comparison of Methods for Determining Screw Parameters of Finite Rigid Body Motion From Initial and Final Position Data

1990 ◽  
Vol 112 (4) ◽  
pp. 472-479 ◽  
Author(s):  
R. G. Fenton ◽  
Xiaolun Shi
Keyword(s):  
Rigid Body ◽  
Rigid Body Motion ◽  
The Other ◽  
Body Motion ◽  
Final Position ◽  
Comparison Of Methods ◽  
Rodrigues Formula ◽  
Position Data ◽  
Data Error

Five methods for determining screw parameters of finite rigid body motion, using position data of three noncollinear points, are compared on the basis of their efficiency, accuracy, and sensitivity to data error. It is found that the method based on Rodrigues’ Formula (Bottema and Roth’s method) is the most efficient. Angeles’ method and Laub and Shiflett’s method provide approximately the same level of accuracy, which is superior to that of the other methods. In terms of sensitivity, Bottema and Roth’s method is preferable. On the basis of this study it is recommended that Bottema and Roth’s method be used if uncertainty exists in the data, since it can provide a solution efficiently, accurately and it is the least sensitive to data error.

Rigid-Body Parameters for Molecular Docking Applications

2014 ◽  
Author(s):  
Gregory S. Chirikjian
Keyword(s):  
Molecular Docking ◽  
Rigid Body ◽  
Body Position ◽  
Rigid Body Motion ◽  
The Other ◽  
Body Motion ◽  
Robot Hand ◽  
Position And Orientation ◽  
Body Parameters ◽  
And Robotics

In mechanisms and robotics it is common to describe motions relative to a ground link, or robot base, and the position and orientation of the distal link (or robot hand) is viewed as a rigid-body motion relative to this fixed world frame. Assessing preferred relative rigid-body position and orientation in interacting biomolecules (such as proteins) often uses this approach as well by artificially calling one molecule the ground, and considering the motions of another molecule relative to it. But since both molecules are floating, it is not as natural to take this perspective as it is in the field of mechanisms and robotics. Therefore, this paper introduces a ‘symmetrical’ parameterization of relative biomolecular motions in which the structure of the equations is the same when each molecule views the other. In this way, there is no bias in terms of labeling one molecule as being fixed and the other as moving. The properties of this new parameterization are evaluated and compared with traditional ones known to the kinematics community.

scholarly journals Stabilization of a Rigid Body Payload With Multiple Cooperative Quadrotors

2016 ◽  
Vol 138 (12) ◽  
Author(s):  
Farhad A. Goodarzi ◽  
Taeyoung Lee
Keyword(s):  
Rigid Body ◽  
Arbitrary Number ◽  
Equations Of Motion ◽  
Vertical Direction ◽  
Free Form ◽  
Nonlinear Controller ◽  
Dynamics And Control ◽  
And Control ◽  
Flexible Cables ◽  
Quadrotor Unmanned Aerial Vehicles

Abstract This paper presents the full dynamics and control of arbitrary number of quadrotor unmanned aerial vehicles (UAVs) transporting a rigid body. The rigid body is connected to the quadrotors via flexible cables where each flexible cable is modeled as a system of arbitrary number of serially connected links. It is shown that a coordinate-free form of equations of motion can be derived for the complete model without any simplicity assumptions that commonly appear in other literature, according to Lagrangian mechanics on a manifold. A geometric nonlinear controller is presented to transport the rigid body to a fixed desired position while aligning all of the links along the vertical direction. A rigorous mathematical stability proof is given and the desirable features of the proposed controller are illustrated by numerical examples and experimental results.

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