Instantaneous center/axis of rotation for planar and three-dimensional motion

2021 ◽  
pp. 030641902110511
Author(s):  
Donald L Kunz
Keyword(s):  
Rigid Body ◽  
Closed Form ◽  
Three Dimensional ◽  
The Body ◽  
Body Motion ◽  
Planar Motion ◽  
Instantaneous Axis Of Rotation ◽  
Axis Of Rotation ◽  
Instantaneous Center ◽  
Instantaneous Axis

This article discusses a direct analytical method for calculating the instantaneous center of rotation and the instantaneous axis of rotation for the two-dimensional and three-dimensional motion, respectively, of rigid bodies. In the case of planar motion, this method produces a closed-form expression for the instantaneous center of rotation based on a single point located on the rigid body. It can also be used to derive closed-form expressions for the body and space centrodes. For three-dimensional, rigid body motion, an extension of the technique used for planar motion locates a point on the instantaneous axis of rotation, which is parallel to the body angular velocity vector. In addition, methods are demonstrated that can be used to map the body and space cones for general rigid body motion, and locate the fixed point for the body.

A Velocity Metric for Rigid-Body Planar Motion

2010 ◽  
Author(s):  
Joseph M. Schimmels ◽  
Luis E. Criales
Keyword(s):  
Rigid Body ◽  
Average Distance ◽  
The Body ◽  
Body Motion ◽  
Length Scale ◽  
Translational Velocity ◽  
Body Velocity ◽  
Assembly Problem ◽  
Instantaneous Center ◽  
Selection Of

A planar rigid-body velocity metric based on the instantaneous velocity of all particles that constitute a rigid body is developed. A measure based on the discrepancy in the translational velocity at each particle for two different planar twists is introduced. The calculation of the measure is simplified to the calculation of the product of: 1) the discrepancy in angular velocity, and 2) the average distance of the body from the instantaneous center associated with the twist discrepancy. It is shown that this measure satisfies the mathematical requirements of a metric and is physically consistent. It does not depend on either the selection of length scale or the frames used to describe the body motion. Although the metric does depend on body geometry, it can be calculated efficiently using body decomposition. An example demonstrating the application of the metric to an assembly problem is presented.

Instantaneous Center of Rotation in Pitch Response of a FPSO Submitted to Head Waves

2018 ◽  
Author(s):  
Daniel de Oliveira Costa ◽  
Antonio Carlos Fernandes ◽  
Joel Sena Sales Junior ◽  
Peyman Asgari
Keyword(s):  
Rigid Body ◽  
Degrees Of Freedom ◽  
Tracking System ◽  
The Body ◽  
Body Motion ◽  
Floating Body ◽  
Wave System ◽  
Center Of Rotation ◽  
Head Waves ◽  
Instantaneous Center

When under influence of an incident wave system, any floating body presents a general motion with all six degrees of freedom, unless it presents some kind of restrains on it. For a free moving body, the center of rotation will depend on the force distribution and might not coincide with its center of gravity. For long and slender floating structures, such as FPSO platforms, a small change in the center of Pitch rotation would result in significant change in the overall motions in its fore and aft regions. Therefore, it is of high importance to obtain a better understating of the instantaneous position of the body center of rotation in Heave and Pitch response. This paper investigates the position of the Instantaneous Center of Rotation in Pitch Response of a scaled down model of a FPSO platform under different regular wave conditions. The investigation uses basic kinematics equations for rigid body, defining the 6 degrees of freedom of the rigid body motion from a finite number of markers installed in the model. A high quality tracking system captures the markers positions in order to define the rigid body at each instant of time. For an initial approach, the study considers the response due to head waves seas with experimental validation.

Cervical Plate Stiffness Affects the Distribution of Loads and the Location of the Instantaneous Axis of Rotation of the Spine In Vitro

2016 ◽  
Vol 16 (10) ◽  
pp. S260-S261 ◽  
Author(s):  
Josh Peterson ◽  
Carolyn Chlebek ◽  
Ashley Clough ◽  
Alexandra Wells ◽  
Eric H. Ledet
Keyword(s):  
Instantaneous Axis Of Rotation ◽  
Axis Of Rotation ◽  
Cervical Plate ◽  
Instantaneous Axis

The Global Motion of a Rigid Body Subject to Periodic Body-Fixed Torques

1995 ◽  
Author(s):  
X. Tong ◽  
B. Tabarrok
Keyword(s):  
Rigid Body ◽  
Equations Of Motion ◽  
Melnikov Method ◽  
The Body ◽  
Body Motion ◽  
Heteroclinic Orbits ◽  
Coordinate Frame ◽  
Global Motion ◽  
Stable And Unstable Manifolds ◽  
Body Subject

Abstract In this paper the global motion of a rigid body subject to small periodic torques, which has a fixed direction in the body-fixed coordinate frame, is investigated by means of Melnikov’s method. Deprit’s variables are introduced to transform the equations of motion into a form describing a slowly varying oscillator. Then the Melnikov method developed for the slowly varying oscillator is used to predict the transversal intersections of stable and unstable manifolds for the perturbed rigid body motion. It is shown that there exist transversal intersections of heteroclinic orbits for certain ranges of parameter values.

Prediction of drag and lift of wings from velocity and vorticity fields

2007 ◽  
Vol 111 (1125) ◽  
pp. 699-704 ◽  
Author(s):  
G. Zhu ◽  
P. W. Bearman ◽  
J. M. R. Graham
Keyword(s):  
Velocity Field ◽  
Closed Form ◽  
Three Dimensional ◽  
Viscous Flows ◽  
The Body ◽  
Rotational Flow ◽  
Inviscid Flows ◽  
Drag And Lift

AbstractThe present paper continues the work of Zhuet al. The closed-form expressions for the evaluation of forces on a body in compressible, viscous and rotational flow derived in the previous paper have been extended to different forms. The expressions require only a knowledge of the velocity field (and its derivatives) in a finite and arbitrarily chosen region enclosing the body. The equations are implemented on three-dimensional inviscid flows over wings and wing/body combinations. Further implementation on three-dimensional viscous flows over wings has also been investigated.

On Saint-Venant's Problem for Helicoidal Beams

2015 ◽  
Vol 83 (2) ◽  
Author(s):  
Shilei Han ◽  
Olivier A. Bauchau
Keyword(s):  
Rigid Body ◽  
Closed Form ◽  
Three Dimensional ◽  
Closed Form Solution ◽  
Fem Analysis ◽  
Original System ◽  
Form Solution ◽  
Hamiltonian Matrix ◽  
Jordan Structure ◽  
Rigid Body Motions

This paper proposes a novel solution strategy for Saint-Venant's problem based on Hamilton's formalism. Saint-Venant's problem focuses on helicoidal beams and its solution hinges upon the determination of the subspace of the system's Hamiltonian matrix associated with its null and pure imaginary eigenvalues. A projection approach is proposed that reduces the system Hamiltonian matrix to a matrix of size 12 × 12, whose eigenvalues are identical to the null and purely imaginary eigenvalues of the original system, with the same Jordan structure. A fundamental theoretical result is established: Saint-Venant's solutions exist because rigid-body motions create no strains. Indeed, the solvability conditions for the governing equations of the problem are satisfied because a matrix identity holds, which expresses the fact that rigid-body motions create no strains. Because it avoids the identification of the Jordan structure of the original system, the implementation of the proposed projection for large, realistic problems is straightforward. Closed-form solutions of the reduced problem are found and three-dimensional stress and strain fields can be recovered from the closed-form solution. Numerical examples are presented to demonstrate the capabilities of the analysis. Predictions are compared to exact solutions of three-dimensional elasticity and three-dimensional FEM analysis.

scholarly journals Using the axis of rotation of polar navigator echoes to rapidly measure 3D rigid-body motion

2004 ◽  
Vol 53 (1) ◽  
pp. 150-158 ◽  
Author(s):  
Andreu F. Costa ◽  
Daniel W. Petrie ◽  
Yi-Fen Yen ◽  
Maria Drangova
Keyword(s):  
Rigid Body ◽  
Rigid Body Motion ◽  
Body Motion ◽  
Axis Of Rotation
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