Geometric Insight Into the Dynamics of a Rigid Body Using the Spatial Triangle of Screws

2001 ◽  
Author(s):  
Gordon R. Pennock ◽  
Patrick J. Meehan
Keyword(s):  
Rigid Body ◽  
Closed Loop ◽  
Equations Of Motion ◽  
Analytical Techniques ◽  
Rate Of Change ◽  
Time Rate ◽  
Open Chain ◽  
Spatial Mechanisms ◽  
Kinetics Of ◽  
Insight Into

Abstract Geometric relationships between the velocity screw and momentum screw are presented, and the dual angle between these two screws is shown to provide important insight into the kinetics of a rigid body. Then the centripetal screw is defined, and the significance of this screw in a study of the dynamics of a rigid body is explained. The dual-Euler equation, which is the dual form of the Newton-Euler equations of motion, is shown to be a spatial triangle. The vertices of the triangle are the centripetal screw, the time rate of change of momentum screw, and the force screw. The sides of the triangle are three dual angles between the three vertices. The spatial triangle provides valuable geometrical insight into the dynamics of a rigid body and is believed to be a meaningful alternative to existing analytical techniques. The authors believe that the work presented in this paper will prove useful in a dynamic analysis of closed-loop spatial mechanisms and multi-rigid body open-chain systems.

Geometric Insight Into the Dynamics of a Rigid Body Using the Spatial Triangle of Screws

2002 ◽  
Vol 124 (4) ◽  
pp. 684-689 ◽  
Author(s):  
Gordon R. Pennock ◽  
Patrick J. Meehan
Keyword(s):  
Rigid Body ◽  
Closed Loop ◽  
Equations Of Motion ◽  
Analytical Techniques ◽  
Rate Of Change ◽  
Time Rate ◽  
Open Chain ◽  
Spatial Mechanisms ◽  
Kinetics Of ◽  
Insight Into

Geometric relationships between the velocity screw and momentum screw are presented, and the dual angle between these two screws is shown to provide important insight into the kinetics of a rigid body. Then the centripetal screw is defined, and the significance of this screw in a study of the dynamics of a rigid body is explained. The dual-Euler equation, which is the dual form of the Newton-Euler equations of motion, is shown to be a spatial triangle. The vertices of the triangle are the centripetal screw, the time rate of change of momentum screw, and the force screw. The sides of the triangles are three dual angles between the three vertices. The spatial triangle provides valuable geometrical insight into the dynamics of a rigid body and is believed to be a meaningful alternative to existing analytical techniques. The authors believe that the work presented in this paper will prove useful in a dynamic analysis of closed-loop spatial mechanisms and multi-rigid body open-chain systems.

scholarly journals Closed-form time derivatives of the equations of motion of rigid body systems

2021 ◽  
Author(s):  
Andreas Müller ◽  
Shivesh Kumar
Keyword(s):  
Rigid Body ◽  
Closed Form ◽  
Multibody Systems ◽  
Equations Of Motion ◽  
Alternative Formulation ◽  
Dynamics Of Rigid Body ◽  
Control Forces ◽  
And Control ◽  
Derivatives Of ◽  
Insight Into

AbstractDerivatives of equations of motion (EOM) describing the dynamics of rigid body systems are becoming increasingly relevant for the robotics community and find many applications in design and control of robotic systems. Controlling robots, and multibody systems comprising elastic components in particular, not only requires smooth trajectories but also the time derivatives of the control forces/torques, hence of the EOM. This paper presents the time derivatives of the EOM in closed form up to second-order as an alternative formulation to the existing recursive algorithms for this purpose, which provides a direct insight into the structure of the derivatives. The Lie group formulation for rigid body systems is used giving rise to very compact and easily parameterized equations.

scholarly journals Dynamic model of multi-rigid-body systems based on particle dynamics with recursive approach

2005 ◽  
Vol 2005 (4) ◽  
pp. 365-382 ◽  
Author(s):  
Hazem Ali Attia
Keyword(s):  
Rigid Body ◽  
Dynamic Model ◽  
Equations Of Motion ◽  
Particle Dynamics ◽  
Rigid Bodies ◽  
Constrained System ◽  
Open Chain ◽  
Chain System ◽  
Closed Chain ◽  
Serial Chains

A dynamic model for multi-rigid-body systems which consists of interconnected rigid bodies based on particle dynamics and a recursive approach is presented. The method uses the concepts of linear and angular momentums to generate the rigid body equations of motion in terms of the Cartesian coordinates of a dynamically equivalent constrained system of particles, without introducing any rotational coordinates and the corresponding rotational transformation matrix. For the open-chain system, the equations of motion are generated recursively along the serial chains. A closed-chain system is transformed to open-chain by cutting suitable kinematical joints and introducing cut-joint constraints. An example is chosen to demonstrate the generality and simplicity of the developed formulation.

The dynamics of a simple system. I. Observables

1945 ◽  
Vol 41 (1) ◽  
pp. 57-65 ◽  
Author(s):  
F. C. Powell
Keyword(s):  
Quantum Mechanics ◽  
Hamiltonian System ◽  
Algebraic Function ◽  
Equations Of Motion ◽  
Complex Multiplication ◽  
Rate Of Change ◽  
Skew Product ◽  
Hermitian Matrices ◽  
Time Rate ◽  
Physical Content

Any particular form of mechanics (e.g. classical or quantum) makes use of a particular ‘formalism’ or set of rules governing the use of the symbols representing dynamical variables and the symbols (such as +, =) representing relations between dynamical variables. In the present paper an attempt is made to examine the physical content of this formalism, particularly that of quantum mechanics. This is done by building up a formalism as the direct expression of a number of physical postulates having direct operational meaning. It is shown that, in a simple case, with any two observables A and B can be associated a unique sum observable A + B and a unique (real) symmetric product observable A.B (= B.A).It is next shown that, if, like a classical Hamiltonian system, the system has the property that the time rate of change of an observable depends linearly on some observable H when the environment in which the system moves is varied, then a (real) skew product observable A × B (= − B × A) can be defined.Finally, if the equations of motion are ‘of second order', it is possible to express the second rate of change of any observable as an algebraic function of that observable and H. This leads to algebraic identities from which it follows that ‘complex multiplication’, defined by AB = A.B + iA × B, is associative (but not commutative). Observables are thus shown to possess the properties usually ascribed to them in quantum mechanics. These properties make possible a representation by Hermitian matrices.

A symbolic and numeric procedure for manipulator rigid-body dynamic significance analysis and simplification

Robotica ◽  
1998 ◽  
Vol 16 (5) ◽  
pp. 589-594 ◽  
Author(s):  
Peter I. Corke
Keyword(s):  
Rigid Body ◽  
Robot Manipulator ◽  
Equations Of Motion ◽  
Joint Torque ◽  
Serial Link ◽  
Rigid Body Dynamic ◽  
Significance Analysis ◽  
The Many ◽  
Body Dynamic ◽  
Insight Into

This paper describes an automated procedure for analysing the significance of each of the many terms in the equations of motion for a serial-link robot manipulator. Significance analysis provides insight into the rigid-body dynamic effects that are significant locally or globally in the manipulator's state space. Deleting those terms that do not contribute significantly to the total joint torque can greatly reduce the computational burden for online control, and a Monte-Carlo style simulation is used to investigate the errors thus introduced. The procedures, freely available, are a hybrid of symbolic and numeric techniques implemented using a standard computer algebra package.

scholarly journals Point-joint coordinate formulation for the dynamic analysis of generalised planar linkages

2005 ◽  
Vol 46 (4) ◽  
pp. 575-589
Author(s):  
Hazem Ali Attia
Keyword(s):  
Rigid Body ◽  
Dynamic Analysis ◽  
Equations Of Motion ◽  
Translational Motion ◽  
Constraint Forces ◽  
Constrained System ◽  
Open Chain ◽  
Closed Chain ◽  
Efficient Integration ◽  
Planar Linkages

AbstractThis paper presents a two-step formulation for the dynamic analysis of generalised planar linkages. First, a rigid body is replaced by a dynamically equivalent constrained system of particles and Newton's second law is used to study the motion of the particles without introducing any rotational coordinates. The translational motion of the constrained particles represents the general motion of the rigid body both translationally and rotationally. The simplicity and the absence of any rotational coordinates from the final form of the equations of motion are considered the main advantages of this formulation. A velocity transformation is then used to transform the equations of motion to a reduced set in terms of selected relative joint variables. For an open-chain, this process automatically eliminates all of the non-working constraint forces and leads to efficient integration of the equations of motion. For a closed-chain, suitable joints should be cut and some cut-joint constraint equations should be included. An example of a closed-chain is used to demonstrate the generality and efficiency of the proposed method.

scholarly journals Rapid systemic surge of IL-33 after severe human trauma: a prospective observational study

2021 ◽  
Vol 27 (1) ◽  
Author(s):  
Olav Sundnes ◽  
William Ottestad ◽  
Camilla Schjalm ◽  
Peter Lundbäck ◽  
Lars la Cour Poulsen ◽  
...  
Keyword(s):  
High Resolution ◽  
Prospective Observational Study ◽  
Tissue Injury ◽  
Trauma Patients ◽  
Decoy Receptor ◽  
Interleukin 33 ◽  
Injured Patients ◽  
First Time ◽  
Kinetics Of ◽  
Insight Into

Abstract Background Alarmins are considered proximal mediators of the immune response after tissue injury. Understanding their biology could pave the way for development of new therapeutic targets and biomarkers in human disease, including multiple trauma. In this study we explored high-resolution concentration kinetics of the alarmin interleukin-33 (IL-33) early after human trauma. Methods Plasma samples were serially collected from 136 trauma patients immediately after hospital admission, 2, 4, 6, and 8 h thereafter, and every morning in the ICU. Levels of IL-33 and its decoy receptor sST2 were measured by immunoassays. Results We observed a rapid and transient surge of IL-33 in a subset of critically injured patients. These patients had more widespread tissue injuries and a greater degree of early coagulopathy. IL-33 half-life (t1/2) was 1.4 h (95% CI 1.2–1.6). sST2 displayed a distinctly different pattern with low initial levels but massive increase at later time points. Conclusions We describe for the first time early high-resolution IL-33 concentration kinetics in individual patients after trauma and correlate systemic IL-33 release to clinical data. These findings provide insight into a potentially important axis of danger signaling in humans.

scholarly journals Simulation of Folding Kinetics for Aligned RNAs

Genes ◽  
2021 ◽  
Vol 12 (3) ◽  
pp. 347
Author(s):  
Jiabin Huang ◽  
Björn Voß
Keyword(s):  
Evolutionary Conservation ◽  
Folding Kinetics ◽  
New Approach ◽  
Computational Approaches ◽  
Reasonable Time ◽  
Valuable Method ◽  
Kinetics Of ◽  
Insight Into ◽  
Folding Space ◽  
Standing Problem

Studying the folding kinetics of an RNA can provide insight into its function and is thus a valuable method for RNA analyses. Computational approaches to the simulation of folding kinetics suffer from the exponentially large folding space that needs to be evaluated. Here, we present a new approach that combines structure abstraction with evolutionary conservation to restrict the analysis to common parts of folding spaces of related RNAs. The resulting algorithm can recapitulate the folding kinetics known for single RNAs and is able to analyse even long RNAs in reasonable time. Our program RNAliHiKinetics is the first algorithm for the simulation of consensus folding kinetics and addresses a long-standing problem in a new and unique way.

Atomic-level insight into reasonable design of metal-based catalysts for hydrogen oxidation in alkaline electrolytes

2021 ◽  
Author(s):  
Lulu An ◽  
Xu Zhao ◽  
Tonghui Zhao ◽  
Deli Wang
Keyword(s):  
Fuel Cell ◽  
Anion Exchange ◽  
Hydrogen Oxidation ◽  
Anion Exchange Membrane ◽  
Atomic Level ◽  
Alkaline Electrolytes ◽  
Exchange Membrane ◽  
Kinetics Of ◽  
Insight Into ◽  
Hydrogen Utilization

Anion exchange membrane fuel cell (AEMFC) is becoming highly attractive for hydrogen utilization owing to the advantages of employing economic catalysts in alkaline electrolytes. Nevertheless, the kinetics of anodic hydrogen...

Derivatives of isatin in aqueous solution. I. Kinetics of ring opening of Isatin-5-sulfonate

1981 ◽  
Vol 34 (2) ◽  
pp. 365 ◽  
Author(s):  
H Stunzi
Keyword(s):  
Ring Opening ◽  
Rate Of Change ◽  
Spectroscopic Methods ◽  
Ph Values ◽  
Buffer Region ◽  
Pka Value ◽  
Back Titration ◽  
Kinetics Of ◽  
Derivatives Of ◽  
Sulfonate Anion

The reactions of isatin-5-sulfonate anion (si-) which cause a hysteresis in pH titrations were studied by pH-metric and n.m.r, spectroscopic methods. Rapid alkalimetric titrations [I 0.15 M (KNO3),37�] gave the pKa value corresponding to the addition of OH- to si- [pKa(ring) 9.55]. The slow ring opening to the sulfonatoisatate dianion (sia2-) led to a drift of the pH values towards an equilibrium buffer region. Its pKa, value [pKa(eq) 3.44] corresponds to the reaction si-+H2O ↔ sia 2-+H+ Rapid back-titration gave the pKa value of the ring-opened species Hsia- [pKa(open) c. 1.3]. The rate law for the ring opening d[sia]/dt=k2 [siOH](OH)+k1*[si] was obtained from the rate of change of pH. N-Methylisatin-5-sulfonate behaves analogously.

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