Application of Screw Theory to Rigid Body Dynamics

1992 ◽  
Vol 114 (2) ◽  
pp. 262-269 ◽  
Author(s):  
G. R. Pennock ◽  
B. A. Oncu
Keyword(s):  
Rigid Body ◽  
Euler Equation ◽  
Computer Aided Design ◽  
Graphical Representation ◽  
Screw Theory ◽  
Rigid Body Dynamics ◽  
The Body ◽  
Dynamic State ◽  
Disk Rolling ◽  
Insight Into

This paper applies screw theory to the dynamic analysis of a rigid body in general spatial motion. Particular emphasis is placed upon the geometric interpretation of the velocity screw, the momentum screw, and the force screw which provide valuable physical insight into the dynamic behavior of the rigid body. The geometric relation between the velocity screw and the momentum screw is discussed in some detail. The paper shows that the dual angle between the two screws provides insight into the kinetics of the rigid body. The dynamic state of motion of the body is then described by a dual vector equation, referred to as the dual Euler equation. The paper shows that the geometric equivalent of the dual Euler equation is a spatial triangle which can be used as a graphical method of solution, or as a check, of the analytical formulation. The concepts introduced in this paper are illustrated by the well-known example of a thin, homogeneous, circular disk rolling without slipping on a flat horizontal surface. With the widespread use of computer graphics and computer-aided design, the geometric approach presented here will prove useful in the graphical representation of the dynamics of a rigid body.

Modelling lateral manoeuvres in fish

2012 ◽  
Vol 697 ◽  
pp. 1-34 ◽  
Author(s):  
K. Singh ◽  
T. J. Pedley
Keyword(s):  
Rigid Body ◽  
Equations Of Motion ◽  
Rigid Body Dynamics ◽  
The Body ◽  
Body Motion ◽  
Dynamic State ◽  
Parameter Study ◽  
Element Formulation ◽  
Turn Angle ◽  
Impulsive Input

AbstractWe propose a method to model manoeuvres in self-propelled flexible-bodied fish by modelling the hydrodynamics coupled to the body inertia. Flexible body motion is prescribed and the equations of motion are solved for the position of the centre of mass and rotation of the body. The governing equations are formulated by applying the conservation of linear and angular momentum. Two independent methods to model the fluid dynamics are pursued: Model 1 is an extension of elongated-body theory, modified for self-propulsion and flexible motion. Model 2 applies a numerical boundary-element formulation with the fish modelled as an infinitely thin rectangular body. The manoeuvring response to an impulsive input is first examined to understand the rigid-body characteristics of the fish. A flexible bend action is included to model C-bends of the type observed during escapes in fish. Models 1 and 2 are used to cross-verify the respective implementations as well as to develop physical insights into manoeuvring. A parameter study shows that fish of intermediate body depths are best adapted to rapid turns whereas the initial dynamic state of the fish is instrumental in affecting the sign as well as the magnitude of the turn angle, for a prescribed bend deflection. Computations for combined swimming and turning show that the initial rigid-body dynamics of the fish is much more effective than the induced effect of the prior shed wake in enhancing the turning response.

The Forced Oscillations of Submerged Bodies

2003 ◽  
Vol 125 (4) ◽  
pp. 710-715
Author(s):  
Angel Sanz-Andre´s ◽  
Gonzalo Tevar ◽  
Francisco-Javier Rivas
Keyword(s):  
Rigid Body ◽  
Small Amplitude ◽  
Center Of Mass ◽  
Rigid Body Dynamics ◽  
The Body ◽  
Central Point ◽  
Modal Testing ◽  
Forced Oscillations ◽  
Motion Equations ◽  
Marine Applications

The increasing use of very light structures in aerospace applications are given rise to the need of taking into account the effects of the surrounding media in the motion of a structure (as for instance, in modal testing of solar panels or antennae) as it is usually performed in the motion of bodies submerged in water in marine applications. New methods are in development aiming at to determine rigid-body properties (the center of mass position and inertia properties) from the results of oscillations tests (at low frequencies during modal testing, by exciting the rigid-body modes only) by using the equations of the rigid-body dynamics. As it is shown in this paper, the effect of the surrounding media significantly modifies the oscillation dynamics in the case of light structures and therefore this effect should be taken into account in the development of the above-mentioned methods. The aim of the paper is to show that, if a central point exists for the aerodynamic forces acting on the body, the motion equations for the small amplitude rotational and translational oscillations can be expressed in a form which is a generalization of the motion equations for a body in vacuum, thus allowing to obtain a physical idea of the motion and aerodynamic effects and also significantly simplifying the calculation of the solutions and the interpretation of the results. In the formulation developed here the translational oscillations and the rotational motion around the center of mass are decoupled, as is the case for the rigid-body motion in vacuum, whereas in the classical added mass formulation the six motion equations are coupled. Also in this paper the nonsteady motion of small amplitude of a rigid body submerged in an ideal, incompressible fluid is considered in order to define the conditions for the existence of the central point in the case of a three-dimensional body. The results here presented are also of interest in marine applications.

scholarly journals Knowledge and perceptions about the reproductive system by pregnants: A qualitative study

2021 ◽  
pp. 1-7
Author(s):  
Ingridy Kammers ◽  
Fabiana Sperandio ◽  
Cinara Sacomori ◽  
Gessica Moreira ◽  
Fernando Cardoso
Keyword(s):  
Qualitative Study ◽  
Qualitative Analysis ◽  
Pelvic Floor ◽  
Reproductive System ◽  
Graphical Representation ◽  
Self Care ◽  
The Body ◽  
Insight Into ◽  
In Pregnancy ◽  
Structured Questionnaire

  Background: To know pregnant’s perceptions and a critical basis attributed to the body from the perspective of the reproductive system. Methods: This is a qualitative study. We used a semi-structured questionnaire with socioeconomic and gynecological-obstetric information, an A4 sheet for graphical representation of the reproductive system and pelvic floor and an interview, questioning the meanings of the reproductive system in the pregnancy context. Then, a qualitative analysis of the interviews was produced. Results: Five categories were identified: recognition began in adolescence, health-disease relationship, process of being pregnant, insight into sexuality, and lack of recognition of its importance in pregnancy. Conclusion: This perception had different meanings and roles in adolescence, changing with pregnancy, becoming a cradle of affection through self-care.

Investigating Rigidity of Military Vehicle Body Using Operating Deflection Shape (ODS) Analysis

2006 ◽  
Vol 49 (2) ◽  
pp. 16-24 ◽  
Author(s):  
Mark Bounds ◽  
George White
Keyword(s):  
Rigid Body ◽  
Dynamic Models ◽  
The Body ◽  
Vehicle Body ◽  
Rigid Body Dynamic ◽  
Military Vehicle ◽  
Acceleration Data ◽  
Specific Frequency ◽  
Body Dynamic ◽  
Insight Into

The Army has many rigid-body dynamic models of various vehicle platforms. The adequacy of these rigid-body models has been questioned. In an effort to gain insight into the significance of flexibility in the development of dynamic vehicle models, operating deflection shape (ODS) techniques were applied to acceleration data gathered from the body of a wheeled military vehicle. The data were analyzed in an effort to determine a specific frequency range over which the assumption of rigidity would be valid. For the particular platform examined in this study, the assumption of rigidity would apply up to approximately 14 Hz. Future efforts include using operational modal analysis (OMA) to further examine the problem.

Rigid Body Dynamics, Constraints, and Inverses

2005 ◽  
Vol 74 (1) ◽  
pp. 47-56 ◽  
Author(s):  
Hooshang Hemami ◽  
Bostwick F. Wyman
Keyword(s):  
Rigid Body ◽  
State Space ◽  
Tracking Error ◽  
Feedback System ◽  
Rigid Body Dynamics ◽  
The Body ◽  
Contact Forces ◽  
Constraint Forces ◽  
Inverse Systems ◽  
Body Dynamics

Rigid body dynamics are traditionally formulated by Lagrangian or Newton-Euler methods. A particular state space form using Euler angles and angular velocities expressed in the body coordinate system is employed here to address constrained rigid body dynamics. We study gliding and rolling, and we develop inverse systems for estimation of internal and contact forces of constraint. A primitive approximation of biped locomotion serves as a motivation for this work. A class of constraints is formulated in this state space. Rolling and gliding are common in contact sports, in interaction of humans and robots with their environment where one surface makes contact with another surface, and at skeletal joints in living systems. This formulation of constraints is important for control purposes. The estimation of applied and constraint forces and torques at the joints of natural and robotic systems is a challenge. Direct and indirect measurement methods involving a combination of kinematic data and computation are discussed. The basic methodology is developed for one single rigid body for simplicity, brevity, and precision. Computer simulations are presented to demonstrate the feasibility and effectiveness of the approaches presented. The methodology can be applied to a multilink model of bipedal systems where natural and/or artificial connectors and actuators are modeled. Estimation of the forces is accomplished by the inverse of the nonlinear plant designed by using a robust high gain feedback system. The inverse is shown to be stable, and bounds on the tracking error are developed. Lyapunov stability methods are used to establish global stability of the inverse system.

A variational principle for three-dimensional interactions between water waves and a floating rigid body with interior fluid motion

2019 ◽  
Vol 866 ◽  
pp. 630-659 ◽  
Author(s):  
Hamid Alemi Ardakani
Keyword(s):  
Variational Principle ◽  
Rigid Body ◽  
Water Waves ◽  
Fluid Motion ◽  
Three Dimensional ◽  
Rigid Body Dynamics ◽  
The Body ◽  
Three Dimensions ◽  
Fluid Sloshing ◽  
Gravity Driven

A variational principle is given for the motion of a rigid body dynamically coupled to its interior fluid sloshing in three-dimensional rotating and translating coordinates. The fluid is assumed to be inviscid and incompressible. The Euler–Poincaré reduction framework of rigid body dynamics is adapted to derive the coupled partial differential equations for the angular momentum and linear momentum of the rigid body and for the motion of the interior fluid relative to the body coordinate system attached to the moving rigid body. The variational principle is extended to the problem of interactions between gravity-driven potential flow water waves and a freely floating rigid body dynamically coupled to its interior fluid motion in three dimensions.

Intrinsic Time Integration Procedures for Rigid Body Dynamics

2012 ◽  
Vol 8 (1) ◽  
Author(s):  
Olivier A. Bauchau ◽  
Hao Xin ◽  
Shiyu Dong ◽  
Zhiheng Li ◽  
Shilei Han
Keyword(s):  
Angular Velocity ◽  
Rigid Body ◽  
Equations Of Motion ◽  
Time Integration ◽  
Rigid Body Dynamics ◽  
The Body ◽  
Rotation Tensor ◽  
Intrinsic Nature ◽  
Intrinsic Form ◽  
Angular Velocities

The treatment of rotations in rigid body and Cosserat solids dynamics is challenging. In most cases, at some point in the formulation, a parameterization of rotation is introduced and the intrinsic nature of the equations of motions is lost. Typically, this step considerably complicates the form of the equations and increases the order of the nonlinearities. Clearly, it is desirable to bypass parameterization of rotation, leaving the equations of motion in their original, intrinsic form. This has prompted the development of rotationless and intrinsic formulations. This paper focuses on the latter approach. The most famous example of intrinsic formulation is probably Euler’s second law for the motion of a rigid body rotating about an inertial point. This equation involves angular velocities solely, with algebraic nonlinearities of the second-order at most. Unfortunately, this intrinsic equation also suffers serious drawbacks: the angular velocity of the body is computed, but not its orientation, the body is “unaware” of its inertial orientation. This paper presents an alternative approach to the problem by proposing discrete statements of the rotation kinematic compatibility equation, which provide solutions for both rotation tensor and angular velocity without relying on a parameterization of rotation. The formulation is also generalized using the motion formalism, leading to very simple discretized equations of motion.

Dynamics of Flexible Body Negotiating a Curve

2016 ◽  
Vol 11 (4) ◽  
Author(s):  
Huailong Shi ◽  
Liang Wang ◽  
Ahmed A. Shabana
Keyword(s):  
Rigid Body ◽  
Equations Of Motion ◽  
Rigid Body Dynamics ◽  
The Body ◽  
Flexible Body ◽  
Motion Trajectory ◽  
Centrifugal Forces ◽  
Coriolis Forces ◽  
Body Dynamics ◽  
Body Reference

When a rigid body negotiates a curve, the centrifugal force takes a simple form which is function of the body mass, forward velocity, and the radius of curvature of the curve. In this simple case of rigid body dynamics, curve negotiation does not lead to Coriolis forces. In the case of a flexible body negotiating a curve, on the other hand, the inertia of the body becomes function of the deformation, curve negotiations lead to Coriolis forces, and the expression for the deformation-dependent centrifugal forces becomes more complex. In this paper, the nonlinear constrained dynamic equations of motion of a flexible body negotiating a circular curve are used to develop a systematic procedure for the calculation of the centrifugal forces during curve negotiations. The floating frame of reference (FFR) formulation is used to describe the body deformation and define the nonlinear centrifugal and Coriolis forces. The algebraic constraint equations which define the motion trajectory along the curve are formulated in terms of the body reference and elastic coordinates. It is shown in this paper how these algebraic motion trajectory constraint equations can be used to define the constraint forces that lead to a systematic definition of the resultant centrifugal force in the case of curve negotiations. The embedding technique is used to eliminate the dependent variables and define the equations of motion in terms of the system degrees of freedom. As demonstrated in this paper, the motion trajectory constraints lead to constant generalized forces associated with the elastic coordinates, and as a consequence, the elastic velocities and accelerations approach zero in the steady state. It is also shown that if the motion trajectory constraints are imposed on the coordinates of a flexible body reference that satisfies the mean-axis conditions, the centrifugal forces take the same form as in the case of rigid body dynamics. The resulting flexible body dynamic equations can be solved numerically in order to obtain the body coordinates and evaluate numerically the constraint and centrifugal forces. The results obtained for a flexible body negotiating a circular curve are compared with the results obtained for the rigid body in order to have a better understanding of the effect of the deformation on the centrifugal forces and the overall dynamics of the body.

On Singularity of Rigid-Body Dynamics Using Quaternion-Based Models

2012 ◽  
Vol 79 (2) ◽  
Author(s):  
Homin Choi ◽  
Bingen Yang
Keyword(s):  
Dynamic Response ◽  
Rigid Body ◽  
Dynamic Modeling ◽  
Degrees Of Freedom ◽  
Rigid Bodies ◽  
Rigid Body Dynamics ◽  
The Body ◽  
Applied Torque ◽  
Body Dynamics

It is well known that use of quaternions in dynamic modeling of rigid bodies can avoid the singularity due to Euler rotations. This paper shows that the dynamic response of a rigid body modeled by quaternions may become unbounded when a torque is applied to the body. A theorem is derived, relating the singularity to the axes of the rotation and applied torque, and to the degrees of freedom of the body in rotation. To avoid such singularity, a method of equivalent couples is proposed.

scholarly journals Mesoscopic Rigid Body Modelling of the Extracellular Matrix Self-Assembly

2018 ◽  
Vol 15 (2) ◽  
Author(s):  
Hua Wong ◽  
Jessica Prévoteau-Jonquet ◽  
Stéphanie Baud ◽  
Manuel Dauchez ◽  
Nicolas Belloy
Keyword(s):  
Extracellular Matrix ◽  
Rigid Body ◽  
Self Assembly ◽  
Rigid Bodies ◽  
Rigid Body Dynamics ◽  
Biological Molecules ◽  
Body Dynamics ◽  
Technological Limitations ◽  
Insight Into ◽  
Prime Target

AbstractThe extracellular matrix (ECM) plays an important role in supporting tissues and organs. It even has a functional role in morphogenesis and differentiation by acting as a source of active molecules (matrikines). Many diseases are linked to dysfunction of ECM components and fragments or changes in their structures. As such it is a prime target for drugs. Because of technological limitations for observations at mesoscopic scales, the precise structural organisation of the ECM is not well-known, with sparse or fuzzy experimental observables. Based on the Unity3D game and physics engines, along with rigid body dynamics, we propose a virtual sandbox to model large biological molecules as dynamic chains of rigid bodies interacting together to gain insight into ECM components behaviour in the mesoscopic range. We have preliminary results showing how parameters such as fibre flexibility or the nature and number of interactions between molecules can induce different structures in the basement membrane. Using the Unity3D game engine and virtual reality headset coupled with haptic controllers, we immerse the user inside the corresponding simulation. Untrained users are able to navigate a complex virtual sandbox crowded with large biomolecules models in a matter of seconds.

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