Nonlinear Model Based Estimation of Rigid-Body Motion Via an Indirect Measurement of an Elastic Appendage

2010 ◽  
Vol 132 (1) ◽  
Author(s):  
M. Senesh ◽  
A. Wolf ◽  
O. Gottlieb
Keyword(s):  
Nonlinear System ◽  
Rigid Body ◽  
Nonlinear Model ◽  
Estimation Procedure ◽  
Indirect Measurement ◽  
Body Motion ◽  
System Parameters ◽  
Model Based ◽  
Proposed Model ◽  
Linear And Nonlinear

In this paper, we develop and implement a nonlinear model based procedure for the estimation of rigid-body motion via an indirect measurement of an elastic appendage. We demonstrate the procedure by motion analysis of a compound planar pendulum from indirect optoelectronic measurements of markers attached to an elastic appendage that is constrained to slide along the rigid-body axis. We implement a Lagrangian approach to derive a theoretical nonlinear model that consistently incorporates several generalized forces acting on the system. Identification of the governing linear and nonlinear system parameters is obtained by analysis of frequency and damping backbone curves from controlled experiments of the decoupled system elements. The accuracy of the proposed model based procedures is evaluated and its results are compared with those of a previously reported point cluster estimation procedure. Two cases are investigated to yield 1.7% and 3.4% errors between measured motion and its model based estimation for experimental configurations, with a slider mass to pendulum frequency ratios of 12.8 and 2.5, respectively. Motion analysis of system dynamics with the point cluster method reveals a noisy signal with a maximal error of 3.9%. Thus, the proposed model based estimation procedure enables accurate evaluation of linear and nonlinear system parameters that are not directly measured.

Nonlinear Model Based Estimation of Rigid-Body Motion Via an Indirect Measurement of an Elastic Appendage

2007 ◽  
Author(s):  
M. Mor ◽  
A. Wolf ◽  
O. Gottlieb
Keyword(s):  
Rigid Body ◽  
Nonlinear Model ◽  
Rotation Angle ◽  
Estimation Procedure ◽  
Indirect Measurement ◽  
Rigid Body Motion ◽  
Body Motion ◽  
Noninvasive Methods ◽  
System Parameters ◽  
Model Based

In this paper we develop and implement a nonlinear model based procedure for estimation of rigid body motion via an indirect measurement of an elastic appendage. We demonstrate the procedure by motion analysis of a compound planar pendulum from indirect optoelectronic measurements of markers attached to an elastic appendage that is restrained to slide along the rigid-body length. We implement a Lagrangian approach to derive a theoretical nonlinear model that consistently incorporates the generalized forces acting on the system. Identification of the governing linear and nonlinear system parameters is obtained by analysis of frequency and damping backbone curves obtained from controlled experiments of the decoupled system elements. Comparison of an independently measured rotation angle to that obtained by the model-based estimation procedure enables evaluation of the procedure accuracy and its advantages over standard noninvasive methods.

scholarly journals Application of the dynamic Lorentz model to modeling the motion of a rigid body

2021 ◽  
pp. 32-36
Author(s):  
Nikolay Makeyev ◽  
Keyword(s):  
Dynamical System ◽  
Qualitative Research ◽  
Rigid Body ◽  
Body Motion ◽  
Dynamic Equations ◽  
Lorentz Model ◽  
Dissipative Forces ◽  
System Parameters ◽  
Phase Trajectories ◽  
Inertia Forces

A qualitative research of the field of phase trajectories of the system of dynamic equations of an absolutely rigid body was carried out, moving around the selected pole under the influence of gyroscopic, dissipative forces and Coriolis inertia forces. The equations of body motion are reduced to a dynamical system generating a Lorentz attractor. Under parametric constraints imposed on the equations of a dynamical system, the structure of its phase trajectories is described depending on the values of the system parameters.

Modeling the Dynamics of Five-Axis Machine Tool Using the Multibody Approach

2020 ◽  
Vol 143 (2) ◽  
Author(s):  
Hoai Nam Huynh ◽  
Yusuf Altintas
Keyword(s):  
Rigid Body ◽  
Machine Tool ◽  
Dynamic Model ◽  
Degrees Of Freedom ◽  
Dynamic Performance ◽  
Body Motion ◽  
Proposed Model ◽  
Multibody Dynamic ◽  
Machining Operations ◽  
Five Axis

Abstract A systematic modeling of multibody dynamics of five-axis machine tools is presented in this article. The machine is divided into major subassemblies such as spindle, column, bed, tool changer, and longitudinal and rotary drives. The inertias and mass center of each subassembly are calculated from the design model. The subassemblies are connected with elastic springs and damping elements at contact joints to form the complete multibody dynamic model of the machine that considers the rigid body kinematics and structural vibrations of the machine at any point. The unknown elastic joint parameters are estimated from the experimental modal analysis of the machine tool. The resulting position-dependent multibody dynamic model has the minimal number of degrees-of-freedom that is equivalent to the number of measured modes, as opposed to thousands used in finite element models. The frequency response functions of the machine can be predicted at any posture of the five-axis machine, which are compared against the directly measured values to assess the validity of model. The proposed model can predict the combined rigid body motion and vibrations of the machine with computational efficiency, and hence, it can be used as a digital twin to simulate its dynamic performance in machining operations and tracking control tests of the servo drives.

A General Method for the Dynamic Modeling of Ball Bearing–Rotor Systems

2015 ◽  
Vol 137 (2) ◽  
Author(s):  
Yamin Li ◽  
Hongrui Cao ◽  
Linkai Niu ◽  
Xiaoliang Jin
Keyword(s):  
Rigid Body ◽  
Dynamic Modeling ◽  
Ball Bearing ◽  
Elastic Vibration ◽  
Rigid Body Motion ◽  
Rotor System ◽  
Body Motion ◽  
Rotor Systems ◽  
Proposed Model ◽  
Vibration Responses

A general dynamic modeling method of ball bearing–rotor systems is proposed. Gupta's bearing model is applied to predict the rigid body motion of the system considering the three-dimensional motions of each part (i.e., outer ring, inner ring, ball, and rotor), lubrication tractions, and bearing clearances. The finite element method is used to model the elastic deformation of the rotor. The dynamic model of the whole ball bearing–rotor system is proposed by integrating the rigid body motion and the elastic vibration of the rotor. An experiment is conducted on a test rig of rotor supported by two angular contact ball bearings. The simulation results are compared with the measured vibration responses to validate the proposed model. Good agreements show the accuracy of the proposed model and its ability to predict the dynamic behavior of ball bearing–rotor systems. Based on the proposed model, vibration responses of a two bearing–rotor system under different bearing clearances were simulated and their characteristics were discussed. The proposed model may provide guidance for structural optimization, fault diagnosis, dynamic balancing, and other applications.

Analysis of 3D rigid-body motion using photogrammetry: A simple model based on a mechanical analogy

2007 ◽  
Vol 75 (1) ◽  
pp. 56-61 ◽  
Author(s):  
A. Page ◽  
P. Candelas ◽  
F. Belmar ◽  
H. De Rosario
Keyword(s):  
Simple Model ◽  
Rigid Body ◽  
Rigid Body Motion ◽  
Body Motion ◽  
Mechanical Analogy ◽  
Model Based

Analysis and Model-Based Control of Servomechanisms With Friction

2004 ◽  
Vol 126 (4) ◽  
pp. 911-915 ◽  
Author(s):  
Evangelos G. Papadopoulos ◽  
Georgios C. Chasparis
Keyword(s):  
Rigid Body ◽  
Function Analysis ◽  
Friction Model ◽  
Body Motion ◽  
System Response ◽  
Friction Compensation ◽  
Kinetic Friction ◽  
Motion Models ◽  
Model Based ◽  
Best Response

Friction is responsible for several servomechanism limitations, and their elimination is always a challenge for control engineers. In this paper, model-based feedback compensation is studied for servomechanism tracking tasks. Several kinetic friction models are employed and their parameters identified experimentally. The effects of friction compensation on system response are examined using describing function analysis. A number of control laws including classical laws, rigid body motion models, and friction compensation are compared experimentally in large-displacement tasks. Results show that the best response is obtained using a controller that incorporates a rigid body model and a friction model based on an accurate description of identified kinetic friction effects.

Sign in / Sign up

Export Citation Format

Share Document