An Improved Principal Coordinate Frame for use with Spatial Rigid Body Displacement Metrics

2019 ◽  
pp. 319-328
Author(s):  
Pierre Larochelle ◽  
Venkatesh Venkataramanujam
Keyword(s):  
Rigid Body ◽  
Coordinate Frame ◽  
Rigid Body Displacement

A Coordinate Frame Useful for Rigid-Body Displacement Metrics

2010 ◽  
Vol 2 (4) ◽  
Author(s):  
Venkatesh Venkataramanujam ◽  
Pierre M. Larochelle
Keyword(s):  
Rigid Body ◽  
Point Mass ◽  
Coordinate Frame ◽  
Invariant Metric ◽  
Mass Model ◽  
Principal Axes ◽  
System Of Units ◽  
Rigid Body Displacement ◽  
Definition Of

This paper presents the definition of a coordinate frame, entitled the principal frame (PF), that is useful for metric calculations on spatial and planar rigid-body displacements. Given a set of displacements and using a point mass model for the moving rigid-body, the PF is determined from the associated centroid and principal axes. It is shown that the PF is invariant with respect to the choice of fixed coordinate frame as well as the system of units used. Hence, the PF is useful for left invariant metric computations. Three examples are presented to demonstrate the utility of the PF.

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.

Protein–Protein Docking with Simultaneous Optimization of Rigid-body Displacement and Side-chain Conformations

2003 ◽  
Vol 331 (1) ◽  
pp. 281-299 ◽  
Author(s):  
Jeffrey J. Gray ◽  
Stewart Moughon ◽  
Chu Wang ◽  
Ora Schueler-Furman ◽  
Brian Kuhlman ◽  
...  
Keyword(s):  
Rigid Body ◽  
Protein Docking ◽  
Simultaneous Optimization ◽  
Side Chain ◽  
Rigid Body Displacement ◽  
Chain Conformations

The rigid-body displacement observed at the Σ = 5, (310)-[001] symmetric tilt grain boundary in central transition bcc metals

2002 ◽  
Vol 82 (8) ◽  
pp. 1573-1594
Author(s):  
Geoffrey H. Campbell ◽  
Mukul Kumar ◽  
Wayne E. King ◽  
James Belak ◽  
John A. Moriarty ◽  
...  
Keyword(s):  
Grain Boundary ◽  
Rigid Body ◽  
Bcc Metals ◽  
Central Transition ◽  
Symmetric Tilt ◽  
Rigid Body Displacement ◽  
Tilt Grain Boundary

Synthesis of Planar, Shape-Changing Rigid-Body Mechanisms

2006 ◽  
Author(s):  
Brian M. Korte ◽  
Andrew P. Murray ◽  
James P. Schmiedeler
Keyword(s):  
Rigid Body ◽  
Degrees Of Freedom ◽  
Shape Change ◽  
Piecewise Linear ◽  
Single Chain ◽  
Open Chain ◽  
Revolute Joints ◽  
Planar Shape ◽  
Rigid Body Displacement ◽  
Planar Linkages

This paper presents a procedure to synthesize planar linkages, composed of rigid links and revolute joints, capable of approximating a shape change defined by a set of curves. These “morphing curves” differ from each other by a combination of rigid-body displacement and shape change. Rigid link geometry is determined through analysis of piecewise linear curves to achieve shape-change approximation, and increasing the number of links improves the approximation. A mechanism is determined through connecting the rigid links into a single chain and adding dyads to eliminate degrees of freedom. The procedure is applied to two open-chain examples.

The rigid-body displacement observed at the ∑ = 5, (310)-[001] symmetric tilt grain boundary in central transition bcc metals

2002 ◽  
Vol 82 (8) ◽  
pp. 1573-1594 ◽  
Author(s):  
Geoffrey H. Campbell ◽  
Mukul Kumar ◽  
Wayne E. King ◽  
James Belak ◽  
John A. Moriarty ◽  
...  
Keyword(s):  
Grain Boundary ◽  
Rigid Body ◽  
Bcc Metals ◽  
Central Transition ◽  
Symmetric Tilt ◽  
Rigid Body Displacement ◽  
Tilt Grain Boundary
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