On the Regulus Associated With the General Displacement of a Line

2007 ◽  
Author(s):  
Chintien Huang ◽  
Wuchang Kuo ◽  
Bahram Ravani
Keyword(s):  
Rigid Body ◽  
The Body ◽  
Line Geometry ◽  
Hyperbolic Paraboloid ◽  
General Displacement ◽  
Computational Kinematics

In the two position theory of finite kinematics, we are concerned with not only the displacement of a rigid body, but also with the displacement of a certain element of the body. This paper deals with the displacement of a line and reveals the regulus that characterizes such a displacement. Residing on a special hyperbolic paraboloid, the regulus is obtained by the intersection of three linear line complexes corresponding to a specific set of basis screws of a 3-system. The degeneration of the regulus when two positions of a line intersect is also discussed. In this paper, the regulus of intersection is obtained geometrically as well as analytically. The discovery of the regulus lays a geometric foundation for dealing with line-based problems in computational kinematics and computational line geometry.

On the Regulus Associated With the General Displacement of a Line and Its Application in Determining Displacement Screws

2010 ◽  
Vol 2 (4) ◽  
Author(s):  
Chintien Huang ◽  
Wuchang Kuo ◽  
Bahram Ravani
Keyword(s):  
Rigid Body ◽  
Measurement Errors ◽  
The Body ◽  
Hyperbolic Paraboloid ◽  
Line Complex ◽  
General Displacement ◽  
Basic Entity ◽  
Best Fit

In the two position theory of finite kinematics, we are concerned with not only the displacement of a rigid body, but also with the displacement of a certain element of the body. This paper deals with the displacement of a line and unveils the regulus that corresponds to such a displacement. The regulus is then used as a basic entity to determine the displacements of a rigid body from line specifications. Residing on a special hyperbolic paraboloid, the regulus is obtained by the intersection of three linear line complexes corresponding to a specific set of basis screws of a three-system. When determining the displacements of a rigid body from line specifications, a displacement screw is obtained by fitting a linear line complex to two or more line reguli. When two exact pairs of homologous lines are specified, we obtain a unique linear line complex, which determines the corresponding displacement screw. When more than two pairs of homologous lines with measurement errors are specified, it becomes a redundantly specified problem, and a linear line complex that has the best fit to more than two reguli is determined.

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.

Does a rigid body limit maneuverability?

2000 ◽  
Vol 203 (22) ◽  
pp. 3391-3396 ◽  
Author(s):  
J.A. Walker
Keyword(s):  
Rigid Body ◽  
The Body ◽  
Alternative Measure ◽  
Pectoral Fin ◽  
Caudal Fin ◽  
Minimum Radius ◽  
Current Definition ◽  
Theoretical Minimum

Whether a rigid body limits maneuverability depends on how maneuverability is defined. By the current definition, the minimum radius of the turn, a rigid-bodied, spotted boxfish Ostracion meleagris approaches maximum maneuverability, i.e. it can spin around with minimum turning radii near zero. The radius of the minimum space required to turn is an alternative measure of maneuverability. By this definition, O. meleagris is not very maneuverable. The observed space required by O. meleagris to turn is slightly greater than its theoretical minimum but much greater than that of highly flexible fish. Agility, the rate of turning, is related to maneuverability. The median- and pectoral-fin-powered turns of O. meleagris are slow relative to the body- and caudal-fin-powered turns of more flexible fish.

MULTIBODY DYNAMIC MODELING AND FLUTTER ANALYSIS OF A FLEXIBLE SLENDER VEHICLE

2012 ◽  
Vol 12 (06) ◽  
pp. 1250049 ◽  
Author(s):  
A. RASTI ◽  
S. A. FAZELZADEH
Keyword(s):  
Differential Equations ◽  
Rigid Body ◽  
Dynamic Modeling ◽  
Equations Of Motion ◽  
The Body ◽  
Elastic Deformations ◽  
Strip Theory ◽  
Multibody Dynamic ◽  
Flutter Analysis ◽  
Rigid Body Motions

In this paper, multibody dynamic modeling and flutter analysis of a flexible slender vehicle are investigated. The method is a comprehensive procedure based on the hybrid equations of motion in terms of quasi-coordinates. The equations consist of ordinary differential equations for the rigid body motions of the vehicle and partial differential equations for the elastic deformations of the flexible components of the vehicle. These equations are naturally nonlinear, but to avoid high nonlinearity of equations the elastic displacements are assumed to be small so that the equations of motion can be linearized. For the aeroelastic analysis a perturbation approach is used, by which the problem is divided into a nonlinear flight dynamics problem for quasi-rigid flight vehicle and a linear extended aeroelasticity problem for the elastic deformations and perturbations in the rigid body motions. In this manner, the trim values that are obtained from the first problem are used as an input to the second problem. The body of the vehicle is modeled with a uniform free–free beam and the aeroelastic forces are derived from the strip theory. The effect of some crucial geometric and physical parameters and the acting forces on the flutter speed and frequency of the vehicle are investigated.

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.

A Parameterization of the Central Axis Congruence Associated with Four Positions of a Rigid Body in Space

1993 ◽  
Vol 115 (3) ◽  
pp. 547-551 ◽  
Author(s):  
J. M. McCarthy
Keyword(s):  
Rigid Body ◽  
The Body ◽  
Central Axis ◽  
Spatial Mechanisms ◽  
Center Point ◽  
Point Curve ◽  
Screw Surface ◽  
Computer Based

Given four positions of a rigid body in space, there is a congruence of lines that can be used as the central axes of cylindric cranks to guide the body through the four positions. This “central axis congruence” is a generalization of the center point curve of planar kinematics. It is known that this congruence is identical to the screw congruence which arises in the study of complementary screw quadrilateral. It is less well-known that the screw congruence is the “screw surface” of the 4C linkage formed by the complementary screw quadrilateral, and it is this relationship that we use to obtain a parameterization for the screw congruence and in turn, the central axis congruence. This parameterization should facilitate the use of this congruence in computer based design of spatial mechanisms.

scholarly journals Disc starts: the pectoral disc of stingrays promotes omnidirectional fast starts across the substrate

2019 ◽  
Vol 97 (7) ◽  
pp. 597-605 ◽  
Author(s):  
S.G. Seamone ◽  
T.M. McCaffrey ◽  
D.A. Syme
Keyword(s):  
Rigid Body ◽  
The Body ◽  
Similar Performance ◽  
Yaw Rate ◽  
Benthic Environment ◽  
Fast Start ◽  
Escape Responses ◽  
Turning Radius ◽  
Longitudinal Flexibility ◽  
Translational Speed

We explored how the flattened and rounded pectoral disc of the ocellate river stingray (Potamotrygon motoro (Müller and Henle, 1841)) enables them to use the benthic plane during fast-start escape. Escape responses were elicited via prodding different locations around the pectoral disc and were recorded using video. Modulation of pectoral-fin movements that power swimming enabled omnidirectional escape across the substrate, with similar performance in all directions of escape. Hence, translation of the body did not necessarily have to follow the orientation of the head, overcoming the constraint of a rigid body axis. An increase in prod speed was associated with an increase in initial translational speed and acceleration away from the prod. As prod location shifted towards the snout, yaw rotation increased, eventually reorienting the fish into a forward swimming position away from the prod. Furthermore, P. motoro yawed with essentially zero turning radius, allowing reorientation of the head with simultaneous rapid translation away from the prod, and yaw rate during escape was substantially greater than reported during routine swimming for stingrays. We conclude that stingrays employ a distinctive approach to escape along the substrate, which we have termed disc starts, that results in effective manoeuvrability across the benthic environment despite limited longitudinal flexibility of the body and that challenges the concept of manoeuvrability typically used for fishes.

scholarly journals Angular velocity of rotation of extended bodies in general relativity

1996 ◽  
Vol 172 ◽  
pp. 309-320
Author(s):  
S.A. Klioner
Keyword(s):  
General Relativity ◽  
Angular Velocity ◽  
Rigid Body ◽  
Rotational Motion ◽  
The Body ◽  
Astronomical Observations ◽  
Newtonian Approximation ◽  
Accurate Definition ◽  
Principal Axes ◽  
Definition Of

We consider rotational motion of an arbitrarily composed and shaped, deformable weakly self-gravitating body being a member of a system of N arbitrarily composed and shaped, deformable weakly self-gravitating bodies in the post-Newtonian approximation of general relativity. Considering importance of the notion of angular velocity of the body (Earth, pulsar) for adequate modelling of modern astronomical observations, we are aimed at introducing a post-Newtonian-accurate definition of angular velocity. Not attempting to introduce a relativistic notion of rigid body (which is well known to be ill-defined even at the first post-Newtonian approximation) we consider bodies to be deformable and introduce the post-Newtonian generalizations of the Tisserand axes and the principal axes of inertia.

scholarly journals The Dynamical Behavior of a Rigid Body Relative Equilibrium Position

2017 ◽  
Vol 2017 ◽  
pp. 1-13 ◽  
Author(s):  
T. S. Amer
Keyword(s):  
Rigid Body ◽  
Degrees Of Freedom ◽  
Numerical Solutions ◽  
Equations Of Motion ◽  
Relative Equilibrium ◽  
Dynamical Behavior ◽  
Vertical Plane ◽  
The Body ◽  
Physical Parameters ◽  
Pendulum Model

In this paper, we will focus on the dynamical behavior of a rigid body suspended on an elastic spring as a pendulum model with three degrees of freedom. It is assumed that the body moves in a rotating vertical plane uniformly with an arbitrary angular velocity. The relative periodic motions of this model are considered. The governing equations of motion are obtained using Lagrange’s equations and represent a nonlinear system of second-order differential equations that can be solved in terms of generalized coordinates. The numerical solutions are investigated using the fourth-order Runge-Kutta algorithms through Matlab packages. These solutions are represented graphically in order to describe and discuss the behavior of the body at any instant for different values of the physical parameters of the body. The obtained results have been discussed and compared with some previous published works. Some concluding remarks have been presented at the end of this work. The importance of this work is due to its numerous applications in life such as the vibrations that occur in buildings and structures.

Topology Optimization of Rigid-Body Systems Considering Collision Avoidance

2020 ◽  
Vol 142 (8) ◽  
Author(s):  
Fritz Stöckli ◽  
Kristina Shea
Keyword(s):  
Topology Optimization ◽  
Rigid Body ◽  
Collision Avoidance ◽  
Optimization Problems ◽  
Computational Design ◽  
Optimization Method ◽  
The Body ◽  
Graph Grammar ◽  
Automated Synthesis ◽  
Inertia Properties

Abstract Passive dynamic mechanisms can perform simple robotic tasks without requiring actuators and control. In previous research, a computational design method was introduced that integrates dynamic simulation to evaluate and evolve configurations of such mechanisms. It was shown to find multiple solutions of passive dynamic brachiating robots (Stöckli and Shea, 2017, “Automated Synthesis of Passive Dynamic Brachiating Robots Using a Simulation-Driven Graph Grammar Method,” J. Mech. Des. 139(9), p. 092301). However, these solutions are limited, since bodies are modeled only by their inertia properties and thus lack a shape embodiment. This paper presents a method to generate rigid-body topologies based on given inertia properties. The rule-based topology optimization method presented guarantees that the topology is manifold, meaning that it has no disconnected parts, while still connecting all joints that need to be part of the body. Furthermore, collisions with the environment, as well as with other bodies, during their predefined motion trajectories are avoided. A collision matrix enables efficient collision detection as well as the calculation of the swept area of one body in the design space of another body by only one matrix–vector multiplication. The presented collision avoidance method proves to be computationally efficient and can be adopted for other topology optimization problems. The method is shown to solve different tasks, including a reference problem as well as passive dynamic brachiating mechanisms. Combining the presented methods with the simulation-driven method from Stöckli and Shea (2017, “Automated Synthesis of Passive Dynamic Brachiating Robots Using a Simulation-Driven Graph Grammar Method,” J. Mech. Des. 139(9), p. 092301), the computational design-to-fabrication of passive dynamic systems is now possible and solutions are provided as STL files ready to be 3D-printed directly.

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