Rolling Condition and Gyroscopic Moments in Curve Negotiations

2012 ◽  
Author(s):  
Ahmed A. Shabana ◽  
Martin B. Hamper ◽  
James J. O’Shea
Keyword(s):  
Coordinate System ◽  
Degrees Of Freedom ◽  
The Body ◽  
Contact Forces ◽  
Body Motion ◽  
Global Coordinate System ◽  
Gyroscopic Moment ◽  
Absolute Angular Velocity ◽  
Pure Rolling ◽  
The Stability

In vehicle system dynamics, the effect of the gyroscopic moments can be significant during curve negotiations. The absolute angular velocity of the body can be expressed as the sum of two vectors; one vector is due to the curvature of the curve, while the second vector is due to the rate of changes of the angles that define the orientation of the body with respect to a coordinate system that follows the body motion. In this paper, the configuration of the body in the global coordinate system is defined using the trajectory coordinates in order to examine the effect of the gyroscopic moments in the case of curve negotiations. These coordinates consist of arc length, two relative translations and three relative angles. The relative translations and relative angles are defined with respect to a trajectory coordinate system that follows the motion of the body on the curve. It is shown that when the yaw and roll angles relative to the trajectory coordinate system are constrained and the motion is predominantly rolling, the effect of the gyroscopic moment on the motion becomes negligible, and in the case of pure rolling and zero yaw and roll angles, the generalized gyroscopic moment associated with the system degrees of freedom becomes identically zero. The analysis presented in this investigation sheds light on the danger of using derailment criteria that are not obtained using laws of motion, and therefore, such criteria should not be used in judging the stability of railroad vehicle systems. Furthermore, The analysis presented in this paper shows that the roll moment which can have a significant effect on the wheel/rail contact forces depends on the forward velocity in the case of curve negotiations. For this reason, roller rigs that do not allow for the wheelset forward velocity cannot capture these moment components, and therefore, cannot be used in the analysis of curve negotiations. A model of a suspended railroad wheelset is used in this investigation to study the gyroscopic effect during curve negotiations.

Rolling Condition and Gyroscopic Moments in Curve Negotiations

2012 ◽  
Vol 8 (1) ◽  
Author(s):  
Ahmed A. Shabana ◽  
Martin B. Hamper ◽  
James J. O’Shea
Keyword(s):  
Coordinate System ◽  
Degrees Of Freedom ◽  
Rate Of Change ◽  
The Body ◽  
Contact Forces ◽  
Body Motion ◽  
Global Coordinate System ◽  
Gyroscopic Moment ◽  
Absolute Angular Velocity ◽  
The Stability

In vehicle system dynamics, the effect of the gyroscopic moments can be significant during curve negotiations. The absolute angular velocity of the body can be expressed as the sum of two vectors; one vector is due to the curvature of the curve, while the second vector is due to the rate of change of the angles that define the orientation of the body with respect to a coordinate system that follows the body motion. In this paper, the configuration of the body in the global coordinate system is defined using the trajectory coordinates in order to examine the effect of the gyroscopic moments in the case of curve negotiations. These coordinates consist of arc length, two relative translations, and three relative angles. The relative translations and relative angles are defined with respect to a trajectory coordinate system that follows the motion of the body on the curve. It is shown that when the yaw and roll angles relative to the trajectory coordinate system are constrained and the motion is predominantly rolling, the effect of the gyroscopic moment on the motion becomes negligible and, in the case of pure rolling and zero yaw and roll angles, the generalized gyroscopic moment associated with the system degrees of freedom becomes identically zero. The analysis presented in this investigation sheds light on the danger of using derailment criteria that are not obtained using laws of motion and, therefore, such criteria should not be used in judging the stability of railroad vehicle systems. Furthermore, the analysis presented in this paper shows that the roll moment, which can have a significant effect on the wheel/rail contact forces, depends on the forward velocity in the case of curve negotiations. For this reason, roller rigs that do not allow for the wheelset forward velocity cannot capture these moment components and, therefore, should not be used in the analysis of curve negotiations. A model of a suspended railroad wheelset is used in this investigation to study the gyroscopic effect during curve negotiations.

Interpretation of Ankle Joint Moments during the Stance Phase of Walking: A Comparison of Two Orthogonal Axes Systems

2001 ◽  
Vol 17 (2) ◽  
pp. 173-180 ◽  
Author(s):  
Adrienne E. Hunt ◽  
Richard M. Smith
Keyword(s):  
Coordinate System ◽  
Ankle Joint ◽  
Stance Phase ◽  
Reaction Force ◽  
Frontal Plane ◽  
Transverse Plane ◽  
The Body ◽  
Global Coordinate System ◽  
Coordinate Systems ◽  
Joint Moments

Three-dimensional ankle joint moments were calculated in two separate coordinate systems, from 18 healthy men during the stance phase of walking, and were then compared. The objective was to determine the extent of differences in the calculated moments between these two commonly used systems and their impact on interpretation. Video motion data were obtained using skin surface markers, and ground reaction force data were recorded from a force platform. Moments acting on the foot were calculated about three orthogonal axes, in a global coordinate system (GCS) and also in a segmental coordinate system (SCS). No differences were found for the sagittal moments. However, compared to the SCS, the GCS significantly (p < .001) overestimated the predominant invertor moment at midstance and until after heel rise. It also significantly (p < .05) underestimated the late stance evertor moment. This frontal plane discrepancy was attributed to sensitivity of the GCS to the degree of abduction of the foot. For the transverse plane, the abductor moment peaked earlier (p < .01) and was relatively smaller (p < .01) in the GCS. Variability in the transverse plane was greater for the SCS, and attributed to its sensitivity to the degree of rearfoot inversion. We conclude that the two coordinate systems result in different calculations of nonsagittal moments at the ankle joint during walking. We propose that the body-based SCS provides a more meaningful interpretation of function than the GCS and would be the preferred method in clinical research, for example where there is marked abduction of the foot.

scholarly journals Investigation of the dynamic stability of bending-torsional deformations of the pipeline

2021 ◽  
Vol 23 (1) ◽  
pp. 72-81
Author(s):  
Petr A. Velmisov ◽  
Yuliya A. Tamarova ◽  
Yuliya V. Pokladova
Keyword(s):  
Dynamic Stability ◽  
Degrees Of Freedom ◽  
Deformable Body ◽  
Nonlinear Partial Differential Equations ◽  
Bending Moment ◽  
The Body ◽  
Initial Moment ◽  
Torsional Vibrations ◽  
Small Deviations ◽  
The Stability

Nonlinear mathematical models are proposed that describe the dynamics of a pipeline with a fluid flowing in it: a) the model of bending-torsional vibrations with two degrees of freedom; b) the model describing flexural-torsional vibrations taking into account the nonlinearity of the bending moment and centrifugal force; c) the model that takes into account joint longitudinal, bending (transverse) and torsional vibrations. All proposed models are described by nonlinear partial differential equations for unknown strain functions. To describe the dynamics of a pipeline, the nonlinear theory of a rigid deformable body is used, which takes into account the transverse, tangential and longitudinal deformations of the pipeline. The dynamic stability of bending-torsional and longitudinal-flexural-torsional vibrations of the pipeline is investigated. The definitions of the stability of a deformable body adopted in this work correspond to the Lyapunov concept of stability of dynamical systems. The problem of studying dynamic stability, namely, stability according to initial data, is formulated as follows: at what values of the parameters characterizing the gas-body system, small deviations of the body from the equilibrium position at the initial moment of time will correspond to small deviations and at any moment of time. For the proposed models, positive definite functionals of the Lyapunov type are constructed, on the basis of which the dynamic stability of the pipeline is investigated. Sufficient stability conditions are obtained that impose restrictions on the parameters of a mechanical system.

Numerical Study on Scale Effect of KCS

2019 ◽  
Author(s):  
Yujie Zhou ◽  
Liwei Liu ◽  
Xiao Cai ◽  
Dakui Feng ◽  
Bin Guo
Keyword(s):  
Scale Effect ◽  
Degrees Of Freedom ◽  
Control Method ◽  
Numerical Study ◽  
The Body ◽  
The Self ◽  
Body Motion ◽  
Propulsion Performance ◽  
Calm Water ◽  
Unsteady Rans

Abstract The key objective of this paper is to perform a fully nonlinear unsteady RANS simulation to predict the self-propulsion performance of KCS at two different scales. This simulations are performed at design speeds in calm water, using inhouse computational fluid dynamics (CFD) to solve RANS equation coupled with two degrees of freedom (2DOF) solid body motion equations including heave and pitch. The SST k-ω turbulence equation is discretized by finite difference method. The velocity pressure coupling is solved by PISO algorithm. Computations have used structured grid with overset technology. The single-phase level-set method is used to capture the free surface. The simulations of self-propulsion are based on the body-force method. The PID control method is applied to match the speed of KCS by changing the propeller rotation speed automatically. In this paper, the self-propulsion factors of KCS at two scales are predicted and the results from inhouse CFD code are compared with the EFD date, and then the reasons for the scale effect have been discussed.

A Finite Element Formulation of Flexible Slider Crank Mechanism Using Local Coordinates

1994 ◽  
Author(s):  
Behrooz Fallahi ◽  
S. Lai ◽  
C. Venkat
Keyword(s):  
Rigid Body ◽  
Coordinate System ◽  
High Speed ◽  
Displacement Vector ◽  
Lagrange Equation ◽  
Local Coordinate System ◽  
Body Motion ◽  
Elastic Displacement ◽  
Global Coordinate System ◽  
Element Formulation

Abstract The need for higher productivity has lead to the design of machines operating at higher speeds. At high speed the rigid body assumption is no longer valid and the links should be considered flexible. In this work a method which is based on Modified Lagrange Equation for modeling flexible mechanism is presented. The method posses a more computational efficiency for not requiring the transformation from the local coordinate system to the global coordinate system. Also an approach using the homogeneous coordinate for element matrices generation is presented. The approach leads to a formalism where the displacement vector is expressed as a product of two matrices and a vector. The first matrix is a function of rigid body motion. The second matrix is a function of rigid body configuration. The vector is a function of elastic displacement. This formal separation helps to facilitate the generation of element matrices using symbolic manipulations.

A Finite Element Formulation of a Flexible Slider Crank Mechanism Using Local Coordinates

1995 ◽  
Vol 117 (3) ◽  
pp. 329-335 ◽  
Author(s):  
Behrooz Fallahi ◽  
S. Lai ◽  
C. Venkat
Keyword(s):  
Rigid Body ◽  
Coordinate System ◽  
Displacement Vector ◽  
Lagrange Equation ◽  
Local Coordinate System ◽  
Body Motion ◽  
Elastic Displacement ◽  
Global Coordinate System ◽  
Element Formulation ◽  
Crank Mechanism

The need for higher manufacturing throughput has lead to the design of machines operating at higher speeds. At higher speeds, the rigid body assumption is no longer valid and the links should be considered flexible. In this work, a method based on the Modified Lagrange Equation for modeling a flexible slider-crank mechanism is presented. This method possesses the characteristic of not requiring the transformation from the local coordinate system to the global coordinate system. An approach using the homogeneous coordinate for element matrices generation is also presented. This approach leads to a formalism in which the displacement vector is expressed as a product of two matrices and a vector. The first matrix is a function of rigid body motion. The second matrix is a function of rigid body configuration. The vector is a function of the elastic displacement. This formal separation helps to facilitate the generation of element matrices using symbolic manipulators.

Extended Kalman Filter for Stereo Vision-Based Localization and Mapping Applications

2017 ◽  
Vol 140 (3) ◽  
Author(s):  
Xue Iuan Wong ◽  
Manoranjan Majji
Keyword(s):  
Coordinate System ◽  
Relative Motion ◽  
Image Features ◽  
Body Motion ◽  
Image Feature ◽  
Recursive Least Squares ◽  
Global Coordinate System ◽  
Error Statistics ◽  
Extended Kalman Filtering ◽  
Localization And Mapping

Image feature-based localization and mapping applications useful in field robotics are considered in this paper. Exploiting the continuity of image features and building upon the tracking algorithms that use point correspondences to provide an instantaneous localization solution, an extended Kalman filtering (EKF) approach is formulated for estimation of the rigid body motion of the camera coordinates with respect to the world coordinate system. Recent results by the authors in quantifying uncertainties associated with the feature tracking methods form the basis for deriving scene-dependent measurement error statistics that drive the optimal estimation approach. It is shown that the use of certain relative motion models between a static scene and the moving target can be recast as a recursive least squares problem and admits an efficient solution to the relative motion estimation problem that is amenable to real-time implementations on board mobile computing platforms with computational constraints. The utility of the estimation approaches developed in the paper is demonstrated using stereoscopic terrain mapping experiments carried out using mobile robots. The map uncertainties estimated by the filter are utilized to establish the registration of the local maps into the global coordinate system.

Flight performance and visual control of flight of the free-flying housefly ( Musca domestica L.) I. Organization of the flight motor

1986 ◽  
Vol 312 (1158) ◽  
pp. 527-551 ◽  
Keyword(s):  
Coordinate System ◽  
Degrees Of Freedom ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Rigid Bodies ◽  
The Body ◽  
Midsagittal Plane ◽  
Torque Vector ◽  
Translation Velocity ◽  
Flight Motor

Free-flying houseflies have been filmed simultaneously from two sides. The orientation of the flies’ body axes in three-dimensional space can be seen on the films. A method is presented for the reconstruction of the flies’ movements in a fly-centred coordinate system, relative to an external coordinate system and relative to the airstream. The flies are regarded as three-dimensionally rigid bodies. They move with respect to the six degrees of freedom they thus possess. The analysis of the organization of the flight motor from the kinematic data leads to the following conclusions: the sideways movements can, at least qualitatively, be explained by taking into account the sideways forces resulting from rolling the body about the long axis and the influence of inertia. Thus, the force vector generated by the flight motor is most probably located in the fly’s midsagittal plane. The direction of this vector can be varied by the fly in a restricted range only. In contrast, the direction of the torque vector can be freely adjusted by the fly. No coupling between the motor force and the torques is indicated. Changes of flight direction may be explained by changes in the orientation of the body axes: straight flight at an angle of sideslip differing from zero is due to rolling. Sideways motion during the banked turns as well as the decrease of translation velocity observed in curves are a consequence of the inertial forces and rolling. The results are discussed with reference to studies about the aerodynamic performance of insects and the constraints for aerial pursuit.

Effects of Pubertal Maturation on ACL Forces During a Landing Task in Females

2021 ◽  
pp. 036354652110383
Author(s):  
Azadeh Nasseri ◽  
David G. Lloyd ◽  
Clare Minahan ◽  
Timothy A. Sayer ◽  
Kade Paterson ◽  
...  
Keyword(s):  
Body Mass ◽  
Statistical Parametric Mapping ◽  
Acl Injury ◽  
The Body ◽  
Contact Forces ◽  
Body Motion ◽  
Adolescent And Young Adult ◽  
Medium Effect ◽  
Muscle Forces ◽  
Pubertal Maturation

Background: Rates of anterior cruciate ligament (ACL) rupture in young people have increased by >70% over the past two decades. Adolescent and young adult females are at higher risk of ACL injury as compared with their prepubertal counterparts. Purpose: To determine ACL loading during a standardized drop-land-lateral jump in females at different stages of pubertal maturation. Study Design: Controlled laboratory study. Methods: On the basis of the Tanner classification system, 19 pre-, 19 early-/mid-, and 24 late-/postpubertal females performed a standardized drop-land-lateral jump while 3-dimensional body motion, ground-reaction forces, and surface electromyography data were acquired. These data were used to model external biomechanics, lower limb muscle forces, and knee contact forces, which were subsequently used in a validated computational model to estimate ACL loading. Statistical parametric mapping analysis of variance was used to compare ACL force and its causal contributors among the 3 pubertal maturation groups during stance phase of the task. Results: When compared with pre- and early-/midpubertal females, late-/postpubertal females had significantly higher ACL force with mean differences of 471 and 356 N during the first 30% and 48% to 85% of stance, and 343 and 274 N during the first 24% and 59% to 81% of stance, respectively, which overlapped peaks in ACL force. At the point of peak ACL force, contributions from sagittal and transverse plane loading mechanisms to ACL force were higher in late-/postpubertal compared with pre- and early-/midpubertal groups (medium effect sizes from 0.44 to 0.77). No differences were found between pre- and early-/midpubertal groups in ACL force or its contributors. Conclusion: The highest ACL forces were observed in late-/postpubertal females, consistent with recently reported rises of ACL injury rates in females aged 15 to 19 years. It is important to quantify ACL force and its contributors during dynamic tasks to advance our understanding of the loading mechanism and thereby provide guidance to injury prevention. Clinical Relevance: Growth of ACL volume plateaus around 10 years of age, before pubertal maturation, meaning that a late-/postpubertal female could have an ACL of similar size to their less mature counterparts. However, late-/postpubertal females have higher body mass requiring higher muscle forces to accelerate the body during dynamic tasks, which may increase ACL loading. Thus, if greater forces develop in these females, in part because of their increased body mass, these higher forces will be applied to an ACL that is not proportionally larger. This may partially explain the higher rates of ACL injury in late-/postpubertal females.

A Low Computational Cost Nonlinear Formulation for Multibody Railroad Vehicle Systems

2007 ◽  
Author(s):  
Graham G. Sanborn ◽  
Jason R. Heineman ◽  
Ahmed A. Shabana
Keyword(s):  
Coordinate System ◽  
Degrees Of Freedom ◽  
Dynamic Models ◽  
Computational Cost ◽  
Space Curve ◽  
The Body ◽  
Degree Of Freedom ◽  
Arbitrary Body ◽  
Resistance Forces ◽  
Low Computational Cost

In this investigation, a multibody system formulation for the nonlinear dynamics of railroad vehicles is developed. This formulation, which permits developing simplified models for the forces acting on rail cars, allows the analysis of long trains at a low computational cost. In the dynamic models developed using the formulation proposed in this investigation, each rail car can be represented as a single rigid body. The configurations of the bodies in a train model are defined with respect to trajectory coordinate systems which follow a space curve whose geometry is defined at a preprocessing stage. In the formulation presented in this study, the number of degrees of freedom of an arbitrary body can be varied from one to six degrees of freedom. The principal degree of freedom of an arbitrary body is the arc length along the space curve. This degree of freedom defines the location of the origin and the orientation of the body trajectory coordinate system. The other five degrees of freedom define the location and orientation of the body with respect to the body trajectory coordinate system. The nonlinear equations of motion of the bodies in a train model are developed using the three-dimensional Newton-Euler equations. These equations are then expressed in terms of the trajectory coordinates and their derivatives. To this end, a velocity transformation is obtained by expressing the Cartesian and angular velocities of the bodies in terms of the time derivatives of the trajectory coordinates. Various force element models particular to rail cars are developed in this study. These forces include tractive effort, and air brake and dynamic brake forces, as well as a model of available wheel-rail adhesion. Additionally, various types of couplers are formulated as force elements, allowing the modeling of connections between cars. Resistance forces are also modeled in order to be able to simulate rolling, curve, and air resistance forces that may act on the cars during the train operations.

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