Plane Motion of a Rigid Body Suspended on Nonlinear Spring-Damper

2018 ◽  
pp. 157-170 ◽  
Author(s):  
Roman Starosta ◽  
Grażyna Sypniewska-Kamińska ◽  
Jan Awrejcewicz
Keyword(s):  
Rigid Body ◽  
Plane Motion ◽  
Nonlinear Spring

Eigenanalysis of the Rigid Body Motion Effect on Elastic Systems

1983 ◽  
Vol 105 (4) ◽  
pp. 461-466 ◽  
Author(s):  
A. Maher ◽  
A. L. Schlack
Keyword(s):  
Eigenvalue Problem ◽  
Rigid Body ◽  
Free Vibration Analysis ◽  
Plane Motion ◽  
Rigid Body Motion ◽  
Body Motion ◽  
Computer Calculations ◽  
Motion Effect ◽  
Ritz Procedure ◽  
The Difference

In this paper, the influence of rigid body motion on the behavior of a vibrating elastic system is treated by the development of a difference eigenvalue problem. The maximum possible changes in eigenfrequencies due to removal of constraints are obtained by the employment of the bound approach [1, 2]. As an application to a structural system the Rayleigh-Ritz procedure is employed for constructing the difference eigenvalue problem. Discussion of the use of the method for various types of engineering problems is outlined. An example of a free vibration analysis of a simply supported beam in plane motion with a nonuniform mass and elasticity distribution is solved. A comparison between computer calculations and previously published results is presented.

scholarly journals Precision, repeatability and accuracy of Optotrak® optical motion tracking systems

2016 ◽  
Author(s):  
Jill Schmidt ◽  
Devin R. Berg
Keyword(s):  
Rigid Body ◽  
Motion Tracking ◽  
Surgical Navigation ◽  
Plane Motion ◽  
Human Motion ◽  
Tracking Systems ◽  
Total Displacement ◽  
Camera Systems ◽  
Optical Motion ◽  
Optical Motion Tracking

In the field of biomechanics, optical motion tracking systems are commonly used to record human motion and assist in surgical navigation. Recently, motion tracking systems have been used to track implant and bone motion on a micron-level. The present study evaluated four different Optotrak® motion tracking systems to determine the precision, repeatability and accuracy under static testing conditions. The distance between the camera systems and the rigid body, as well as the tilt angle of the rigid body, did affect the resulting precision, repeatability and accuracy of the camera systems. The precision and repeatability, calculated as the within-trial and between-trial standard deviations, respectively, were less than 30 µm; with some configurations producing precision and repeatability less than 1 µm. The accuracy was less than 0.53% of the total displacement for the in-plane motion and less than 1.56% of the total displacement for the out-of-plane motion.

On the Motion of Lineal Bodies Subject to Linear Damping

1997 ◽  
Vol 64 (1) ◽  
pp. 227-229 ◽  
Author(s):  
M. F. Beatty
Keyword(s):  
Differential Equation ◽  
Dynamical Systems ◽  
Rigid Body ◽  
General Class ◽  
Plane Motion ◽  
Rigid Bodies ◽  
Degree Of Freedom ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Linear Damping

Wilms (1995) has considered the plane motion of three lineal rigid bodies subject to linear damping over their length. He shows that these plane single-degree-of-freedom systems are governed by precisely the same fundamental differential equation. It is not unusual that several dynamical systems may be formally characterized by the same differential equation, but the universal differential equation for these systems is unusual because it is exactly the same equation for the three very different systems. It is shown here that these problems belong to a more general class of problems for which the differential equation is exactly the same for every lineal rigid body regardless of its geometry.

The Necessary Conditions for Plane Motion of a Rigid Body

1998 ◽  
Vol 26 (1) ◽  
pp. 71-74
Author(s):  
Djordje S. Djukic ◽  
S. E. Jones
Keyword(s):  
Rigid Body ◽  
Necessary Conditions ◽  
Plane Motion ◽  
Fundamental Properties ◽  
External Forces

This paper treats the plane motion of a rigid body under the action of external forces and a couple. Some fundamental properties of the motion are contained in one theorem. The theorem gives the necessary conditions under which the bodies perform plane motion.

Study of Forward Connecting Rod Combined Lifting Mechanism Based on Linear Transformation and Vector Algebra

2012 ◽  
Vol 155-156 ◽  
pp. 505-508
Author(s):  
Ming Qing Wu
Keyword(s):  
Mathematical Model ◽  
Rigid Body ◽  
Linear Transformation ◽  
Plane Motion ◽  
Connecting Rod ◽  
Vector Algebra ◽  
Lift Mechanism ◽  
Four Bar Linkage ◽  
The Mathematical Model

By adopting the method of block analysis,the paper analyzes and calculates the forward connecting rod combined lift mechanism by broking up it into a four-bar linkage and the plane motion of an arm triangle rigid body, constructs the kinematic equations of four-bar linkage and arm triangle and the static equations of four-bar linkage based on linear transformation and vector algebra and establishes the mathematical model of lift mechanism based on linear transformation and vector algebra.

Kinematics of the plane motion of a rigid body

2021 ◽  
pp. 31-38
Author(s):  
P.F. Sevryukov
Keyword(s):  
Rigid Body ◽  
Plane Motion

Kinetics of a rigid body in plane motion

1994 ◽  
pp. 75-89
Author(s):  
H.R. Harrison ◽  
T. Nettleton
Keyword(s):  
Rigid Body ◽  
Plane Motion ◽  
Kinetics Of

Dynamic circle of plane motion

2011 ◽  
Vol 225 (5) ◽  
pp. 1147-1151
Author(s):  
D Radomirovic ◽  
I Kovacic
Keyword(s):  
Rigid Body ◽  
General Equation ◽  
Plane Motion ◽  
Mass Centre ◽  
The One

A rigid body in plane motion is considered. The location of all instantaneous points for which a general equation for moments is of the form equivalent to the one written with respect to the mass centre is determined. It is found that the curve containing all these points is a circle. Two examples are given to illustrate some applications of the findings.

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