Modeling of Multibody Flexible Articulated Structures With Mutually Coupled Motions: Part II — Application and Results

1992 ◽  
Author(s):  
Jiechi Xu ◽  
Joseph R. Baumgarten
Keyword(s):  
Experimental Data ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Open Loop ◽  
Body Motion ◽  
Universal Joint ◽  
Open Loop System ◽  
Numerical Examples ◽  
Kinematic Properties ◽  
Good Agreement

Abstract The application of the systematic procedures in the derivation of the equations of motion proposed in Part I of this work is demonstrated and implemented in detail. The equations of motion for each subsystem are derived individually and are assembled under the concept of compatibility between the local kinematic properties of the elastic degrees of freedom of those connected elastic members. The specific structure under consideration is characterized as an open loop system with spherical unconstrained chains being capable of rotating about a Hooke’s or universal joint. The rigid body motion, due to two unknown rotations, and the elastic degrees of freedom are mutually coupled and influence each other. The traditional motion superposition approach is no longer applicable herein. Numerical examples for several cases are presented. These simulations are compared with the experimental data and good agreement is indicated.

Dynamic Modeling of the Three-Degrees-of-Freedom Planar Platform-Type Manipulator

1997 ◽  
Author(s):  
Maher G. Mohamed ◽  
Hazem A. Attia
Keyword(s):  
Dynamic Modeling ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Open Loop ◽  
Loop System ◽  
Constraint Forces ◽  
Open Loop System ◽  
Joint Coordinates ◽  
Joint Constraints ◽  
Three Degrees Of Freedom

Abstract In this paper, the dynamic Modeling of the planar three-degrees of freedom platform-type manipulator is presented. A kinematic analysis is carried out initially, to evaluate and correct the initial coordinates and velocities. The dynamic model of the manipulator is formulated using a two-step transformation. Initially, the dynamic formulation is written in terms of the Cartesian coordinates of a dynamically equivalent system of particles. Since a particle does not have rotational motion, the differential equations of motion are derived by applying Newton’s second law to study the translational motion of the particles. A system of nine primary particles replaces the whole manipulator and the system mass matrix is derived. The equations of motion are then transformed to a more manipulator oriented variables; relative joint coordinates. This leads to efficient solution and integration of the equations of motion. Since the multibody system under consideration contains two independent closed kinematic loops, each of the two closed loops is cut at a suitable joints in order to produce a reduced open loop system with additional constraint equations. When the two cut joints are reassembled, the defined relative joint coordinates are no longer independent. They are related by the cut joint constraints. The constraint forces associated with the cut joint constraints are expressed in terms of Lagrange multipliers. Both cut joint constraints and constraint forces are then introduced into the equations of motion for the reduced open loop system to produce the resulting equations of motions of manipulator. A numerical example is presented and a computer program is developed.

Lagrangian Formulation of the Equations of Motion for Elastic Mechanisms With Mutual Dependence Between Rigid Body and Elastic Motions: Part I—Element Level Equations

1990 ◽  
Vol 112 (2) ◽  
pp. 203-214 ◽  
Author(s):  
S. Nagarajan ◽  
David A. Turcic
Keyword(s):  
Rigid Body ◽  
High Speed ◽  
Degrees Of Freedom ◽  
Nonlinear Differential Equations ◽  
Equations Of Motion ◽  
Realistic Model ◽  
Open Loop ◽  
Rigid Body Motion ◽  
Body Motion ◽  
Elastic Links

Equations of motion are derived using Lagrange’s equation for elastic mechanism systems. The elastic links are modeled using the finite element method. Both rigid body degrees of freedom and the elastic degrees of freedom are considered as generalized coordinates in the derivation. Previous work in the area of analysis of general elastic mechanisms usually involve the assumption that the rigid body motion or the nominal motion of the system is unaffected by the elastic motion. The nonlinear differential equations of motion derived in this work do not make this assumption and thus allow for the rigid body motion and the elastic motion to influence each other. Also the equations obtained are in closed form for the entire mechanism system, in terms of a minimum number of variables, which are the rigid body and the elastic degrees of freedom. These equations represent a more realistic model of light-weight high-speed mechanisms, having closed and open loop multi degree of freedom chains, and geometrically complex elastic links.

scholarly journals Response of a Warped Flexible Rotor with a Fluid Bearing

2008 ◽  
Vol 2008 ◽  
pp. 1-9 ◽  
Author(s):  
Jim Meagher ◽  
Xi Wu ◽  
Chris Lencioni
Keyword(s):  
Experimental Data ◽  
Analytical Model ◽  
Degrees Of Freedom ◽  
Journal Bearing ◽  
Equation Of Motion ◽  
Diagnostic Information ◽  
Flexible Rotor ◽  
Vibration Data ◽  
Rotor Model ◽  
Good Agreement

A two-complex-degrees-of-freedom model is developed and compared to experimental data for various amounts of rotor bow and its orientation to mass imbalance of the rotor. The equation of motion is developed by adding constant forces that rotate with the rotor to a Bently-Muszynska two-mode isotropic rotor model with a plane journal bearing. Diagnostic information discernable from probes at the bearing is explored and compared to midspan response, where previous research has concentrated. The model presented also extends earlier work by representing the effect of a nonrigid bearing. Good agreement between the analytical model and experiment demonstrates that the analysis presented can be useful to diagnose and balance residual shaft bow from probes located at the bearings, where vibration data are typically more available than midspan probes.

Methods of Using a Vibratory System to Measure Small Rates of Turn

1969 ◽  
Vol 11 (5) ◽  
pp. 526-533 ◽  
Author(s):  
J. A. Linnett
Keyword(s):  
Angular Velocity ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Exciting Force ◽  
Velocity Curve ◽  
Alternative Methods ◽  
Vibratory System ◽  
Mass System ◽  
The One ◽  
Good Agreement

The equations of motion for a vibratory two-degrees-of-freedom spring mass system subjected to rotation about an axis perpendicular to its plane of vibration are considered, taking into account the various couplings that may be present. The rate of turn can be measured by three alternative methods, two of which involve an exciting force in the sensing direction in addition to the one vibrating the system. The shape of the phase angle against angular velocity curve is shown to be independent of damping, enabling the transient performance to be improved without affecting the sensitivity of the device. Experimental work shows good agreement with the developed theory.

scholarly journals Dynamic modeling of ships towed by kite

2018 ◽  
pp. 8-10 ◽  
Author(s):  
Nedeleg Bigi ◽  
Morgann Behrel ◽  
Kostia Roncin ◽  
Jean-Baptiste Leroux ◽  
Alain Neme ◽  
...  
Keyword(s):  
Experimental Data ◽  
Strong Coupling ◽  
Dynamic Modeling ◽  
Equations Of Motion ◽  
Critical Conditions ◽  
Ship Motions ◽  
Zero Mass ◽  
Coupling Methods ◽  
Good Agreement

A dynamic kite flight can affect ship motions. Ship equations of motion associated with the analytical zero-mass kite model are developed. Aiming a realistic amplitude modeling of the kite excitation, a linear modification of the aerodynamic kite specs with the turning rate of the kite velocity heading is proposed. A good agreement with experimental data is obtained. Equations of motion are solved on a reaching path alternatively with a weak and a strong coupling between the ship and the kite. Differences between the two coupling methods become significant when a harmonic of the kite excitation approaches the natural roll frequency of the ship. For the presented case of study, these critical conditions can be avoided with longer tethers or larger kite trajectories.

Application of Generalized Newton-Euler Equations and Recursive Projection Methods to Dynamics of Deformable Multibody Systems

1989 ◽  
Author(s):  
R. A. Wehage ◽  
A. A. Shabana
Keyword(s):  
Euler Equations ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Coupled System ◽  
Projection Methods ◽  
Open Loop ◽  
System Of Equations ◽  
Kinematic Chains ◽  
Deformable Bodies ◽  
Generalized Newton

Abstract A general symbolic-based method is presented for solving equations of motion for open-loop kinematic chains consisting of interconnected rigid and deformable bodies. The method utilizes matrix partitioning, recursive projection based on optimal block U-L factorization and generalized Newton-Euler equations to obtain an order n solution for the constrained equations of motion. Kinematic relationships between the absolute reference, joint and elastic coordinates are used with the generalized Newton-Euler equations for deformable bodies to obtain a large, loosely coupled system of equations. Taking advantage of the inertia matrix structure associated with elastic coordinates yields a recursive solution algorithm whose dimension is independent of the elastic degrees of freedom. The above solution techniques applied to this system of equations yield a much smaller operations count and can more effectively exploit vectorization and parallel processing. The algorithms presented in this paper are illustrated with the aid of cylindrical joints which are easily extended to revolute, prismatic, rigid and other joint types.

Modeling and Validation of a Roll Simulator for Recreational Off-Highway Vehicles

2011 ◽  
Author(s):  
Scott B. Zagorski ◽  
Dennis A. Guenther ◽  
Gary J. Heydinger ◽  
Anmol S. Sidhu ◽  
Dale A. Andreatta
Keyword(s):  
Experimental Data ◽  
Degrees Of Freedom ◽  
Close Agreement ◽  
Energy Equation ◽  
Equations Of Motion ◽  
Excellent Correlation ◽  
Motor Systems ◽  
Non Linear ◽  
Entrapped Air ◽  
Three Degrees Of Freedom

A model of a roll simulator for recreational off-highway vehicles (ROV) is presented. Models of each sub-system are described including the equations of motion, the braking, hydraulic and roll motor systems. Derivation of the equations of motion, obtained using Lagrange’s energy equation, demonstrates that they have three degrees-of-freedom (two dynamic, one static) and are coupled and highly non-linear. Results from the hydraulic sub-system illustrated that the amount of entrapped air in the system can significantly influence the response. Comparisons of the model with experimental data from the actual roll simulator showed close agreement. The greatest difference was with motor pressure. The acceleration levels and roll motions for both the model and experimental data showed excellent correlation.

Application of the Surge Model to Radial Compressor System Cycle Optimization

2013 ◽  
Author(s):  
Viktor Kilchyk ◽  
Ahmed Abdelwahab ◽  
Andrew Rosinski
Keyword(s):  
Experimental Data ◽  
Open Loop ◽  
Time Dependent ◽  
Design Parameters ◽  
Radial Compressor ◽  
Lumped Parameter ◽  
Compressor Design ◽  
Compressor Efficiency ◽  
Good Agreement ◽  
Variable Coupling

Surge avoidance and minimization of power consumption in the design of a radial compressor cycle requires a solution to the complex, time-dependent problem of implicit variable coupling. To solve this problem, a modified lumped parameter surge model was developed and tested using experimental data. The model was expanded to include open-loop, time-dependent (periodic) boundary conditions with added equations representing the effects of heat transfer and flow compressibility. Comparison with experimental data showed good agreement with model-predicted behavior. The developed model of the compressor system was analyzed with respect to the main compressor design parameters. Sensitivity of the compressor system to the valve timing and resistance, wheel diameter, and inertia was also examined. It was demonstrated that the mass flow rate-averaged, or power-averaged compressor efficiency was improved by over 3 percent using the optimum impeller diameter.

Solving for Dynamic Problems in Flexible Manufacturing Systems

2010 ◽  
Vol 156-157 ◽  
pp. 1501-1504
Author(s):  
Yunn Lin Hwang ◽  
Shen Jenn Hwang
Keyword(s):  
Flexible Manufacturing ◽  
Flexible Manufacturing Systems ◽  
Manufacturing Systems ◽  
Equations Of Motion ◽  
Open Loop ◽  
Body Motion ◽  
Recursive Formulation ◽  
Deformable Bodies ◽  
System Equations ◽  
Time Invariant

Generally speaking, the flexible manufacturing systems can be classified into two main groups: open-loop and closed-loop systems. In this investigation, a recursive formulation is developed for the dynamic analysis of open-loop flexible manufacturing systems. The nonlinear generalized Newton-Euler equations are developed for rigid and deformable bodies that undergo large translational and rotational displacements. These equations are formulated in terms of a set of time invariant scalars, vectors and matrices that depend on the spatial coordinates as well as the assumed displacement fields, and these time invariant quantities represent the dynamic coupling between the rigid body motion and elastic deformation. The method to solve equations of motion for open-loop systems consisting of interconnected rigid and deformable bodies is presented in this paper. This method applies recursive method with the Newton-Euler method for deformable bodies to obtain a large, loosely coupled system equations of motion. The solution techniques used to solve for the system equations of motion can be more efficiently implemented in the modern computer systems. The algorithms presented in this paper are demonstrated by using cylindrical joints that can be easily extended to revolute, slider and rigid joints. The recursive formulation developed in this investigation is illustrated by a practical numerical example.

Using Nonlinear Recursive Formulation for the Kinematic Analysis of Human Biomechanical Systems

2012 ◽  
Vol 482-484 ◽  
pp. 938-941
Author(s):  
Yunn Lin Hwang ◽  
Wei Hsin Gau ◽  
Wen Huang Lin ◽  
Shen Jenn Hwang ◽  
Chien Hsin Chen
Keyword(s):  
Kinematic Analysis ◽  
Equations Of Motion ◽  
Open Loop ◽  
Body Motion ◽  
Displacement Fields ◽  
Flexible Bodies ◽  
Recursive Formulation ◽  
Closed Loop Systems ◽  
Generalized Newton ◽  
Time Invariant

Generally speaking, the human biomechanical systems can be classified into two main groups: open-loop and closed-loop systems. In this investigation, the nonlinear recursive formulation is developed for the kinematic analysis of human biomechanical systems. The nonlinear generalized Newton-Euler equations are developed for flexible bodies that undergo large translational and rotational displacements. These equations are formulated in terms of a set of time invariant scalars, vectors and matrices that depend on the spatial coordinates as well as the assumed displacement fields, and these time invariant quantities represent the dynamic coupling between the rigid body motion and elastic deformation. The formulation to solve equations of motion for human biomechanical systems consisting of interconnected rigid and flexible bodies is presented in this paper.

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