scholarly journals Maneuvering Hydrodynamics of Ellipsoidal Forms

1979 ◽  
Vol 23 (01) ◽  
pp. 66-75
Author(s):  
Touvia Miloh
Keyword(s):  
Closed Form ◽  
Degrees Of Freedom ◽  
Major Axis ◽  
The Body ◽  
Time Dependent ◽  
Triaxial Ellipsoid ◽  
Inviscid Fluid ◽  
Six Degrees Of Freedom ◽  
Ellipsoidal Harmonics ◽  
Unbounded Medium

The hydrodynamical forces and moments acting on a triaxial ellipsoid moving in an incompressible and inviscid fluid are analyzed. The rigid ellipsoid is allowed to move in the most general manner with time-dependent velocity and six degrees of freedom. The force and moment expressions are obtained by applying the Lagally theorem to the image singularities system representing the body in the presence of exterior disturbances. First, expressions for the Lagally force and moment acting on a maneuvering ellipsoid in an unbounded medium are derived and then these expressions are generalized to include the effect of an exterior source moving in an arbitrary manner. It is also shown how the Lagally expressions for an exterior source can be used to obtain closed-form expressions for the hydrodynamical forces and moments acting on a maneuvering ellipsoid in the presence of an arbitrary exterior disturbance. The analysis, which is based on the application of ellipsoidal harmonics, is demonstrated in a simple case of propeller-hull interaction. Here the motion of the ellipsoid is restricted to the major axis, and the propeller at the stern is represented by an isolated sink in accordance with Dickmann's model. 'Practical expressions for the thrust-deduction coefficient, wake fraction, and propeller-induced vibration are then derived for ellipsoidal, spheroidal and spherical hulls..

scholarly journals Ring dynamics around an oblate body with an inclined satellite: the case of Haumea

2020 ◽  
Vol 643 ◽  
pp. A67
Author(s):  
Francesco Marzari
Keyword(s):  
Equatorial Plane ◽  
Protective Factor ◽  
Central Body ◽  
Orbital Plane ◽  
Major Axis ◽  
The Body ◽  
Triaxial Ellipsoid ◽  
Semi Major Axis ◽  
Short Timescale ◽  
The Impact

Context. The recent discovery of rings and massive satellites around minor bodies and dwarf planets suggests that they may often coexist, as for example around Haumea. Aims. A ring perturbed by an oblate central body and by an inclined satellite may disperse on a short timescale. The conditions under which a ring may survive are explored both analytically and numerically. Methods. The trajectories of ring particles are integrated under the influence of the gravitational field of a triaxial ellipsoid and (a) massive satellite(s), including the effects of collisions. Results. A ring initially formed in the equatorial plane of the central body will be disrupted if the satellite has an inclination in the Kozai–Lidov regime (39.2° < i < 144.8). For lower inclinations, the ring may relax to the satellite orbital plane thanks to an intense collisional damping. On the other hand, a significant J2 term easily suppresses the perturbations of an inclined satellite within a critical semi-major axis, even in the case of Kozai–Lidov cycles. However, if the ring is initially inclined with respect to the equatorial plane, the same J2 perturbations are not a protective factor but instead disrupt the ring on a short timescale. The ring found around Haumea is stable despite the rise in the impact velocities that is due to the asymmetric shape of the body and the presence of a 3:1 resonance with the rotation of the central body. Conclusions. A ring close to an oblate central body should be searched for in the proximity of the equatorial plane, where the J2 perturbations protect it against the perturbations of an external inclined satellites. In an inclined configuration, the J2 term is itself disruptive.

3D Modeling and Closed-Form Inverse Kinematics Solution for 6dof Surgical Robot

2013 ◽  
Vol 455 ◽  
pp. 533-538
Author(s):  
Edris Farah ◽  
Shao Gang Liu
Keyword(s):  
Closed Form ◽  
Inverse Kinematics ◽  
Degrees Of Freedom ◽  
Closed Form Solution ◽  
Inverse Kinematic ◽  
Form Solution ◽  
Surgical Robot ◽  
Decoupling Method ◽  
Six Degrees Of Freedom ◽  
Inverse Kinematics Problem

Since robots began to inter the medical fields, more research efforts and more attention have been given to this kind of robots. In this paper six degrees of freedom surgical robot was studied. The Denavit-Hartenberg parameters of the robot have been computed and 3D model has been built by using open source robotics toolbox. The paper also discussed a closed form solution for the inverse kinematics problem by using inverse kinematic decoupling method.

The Hexapodopter: A Hybrid Flying Hexapod—Holonomic Flying Analysis

2018 ◽  
Vol 10 (5) ◽  
Author(s):  
Daniel Soto-Guerrero ◽  
José Gabriel Ramírez-Torres
Keyword(s):  
Degrees Of Freedom ◽  
The Body ◽  
Design Criteria ◽  
Control Law ◽  
Two Degrees Of Freedom ◽  
Main Design ◽  
Walking Machine ◽  
Six Degrees Of Freedom ◽  
Thrust Vector ◽  
Thrust Forces

This document introduces the holonomic flying capabilities of the Hexapodopter, a six-legged walking machine capable of vertical take-off and landing. For ground locomotion, each limb has two degrees-of-freedom (2DoF); while the thrust required for flying is provided by six motors mounted close to every knee, so the thrust vector can be reoriented depending on the configuration of each limb. The capacity of reorienting the thrust forces makes the Hexapodopter a true holonomic vehicle, capable of individually controlling its six degrees-of-freedom (6DoF) on the air without reorienting any of the thrust motors nor the body. The main design criteria and validation will be discussed on this paper, as well as a control law for the vehicle.

Vibration of a Spring-Supported Body

1965 ◽  
Vol 7 (2) ◽  
pp. 185-192 ◽  
Author(s):  
P. Grootenhuis ◽  
D. J. Ewins
Keyword(s):  
Rigid Body ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Vertical Axis ◽  
The Body ◽  
Stiffness Ratio ◽  
Six Degrees Of Freedom ◽  
Centre Of Gravity ◽  
Longitudinal Stiffness ◽  
The Matrix

The equations of motion for a rigid body supported on four springs are derived for the general case of the centre-of-gravity being anywhere within the body and allowing for the sideways as well as the longitudinal stiffnesses of the springs. This constitutes a six-degrees-of-freedom case with three degrees of asymmetry. Coupling between motions in all directions occurs even when the centre-of-gravity is at the geometric centre with the exception then of vertical oscillations and rotation about the vertical axis. Any number of additional springs can be allowed for by adding terms to the expression for the potential energy stored in the springs. Allowance is made in the expression for kinetic energy for the products of inertia which arise with an offset centre-of-gravity. The real case is simulated for purposes of analysis by replacing the rigid body by a rectangular box with a light framework and all the mass concentrated at the eight corners. The matrix solution is changed into dimensionless parameters and the effect of an offset centre-of-gravity upon the eigenvalues and eigenvectors studied. Only the proportions of the box and the stiffness ratio between sideways to longitudinal stiffness of the springs remain as factors. The numerical example given is for proportions of height to width to length of 3/4/5 and for a stiffness ratio of 5. Small amounts of offset of the centre-of-gravity from the geometric centre do not alter the dynamic behaviour of the system much but displacing the total mass towards either a lower or an upper corner has marked effects. Some of the natural frequencies associated with motion in rotation when the system is symmetric become less than the frequencies connected with motion in translation for the centre-of-gravity being close to a corner connected to a spring. A large region free from any natural frequency arises when the centre-of-gravity is moved towards a corner furthest removed from the plane containing the springs. The asymptotic conditions for the position of the centre-of-gravity are also considered.

Spatial Mechanism-Environment Contact Geometric Models

2021 ◽  
Author(s):  
Nina Robson ◽  
Aaron Lee
Keyword(s):  
Degrees Of Freedom ◽  
Theoretical Foundation ◽  
Kinematic Chain ◽  
The Body ◽  
Order Effects ◽  
Six Degrees Of Freedom ◽  
Spatial Mechanism ◽  
Motion Constraints ◽  
Spherical Surfaces ◽  
Proposed Model

Abstract This work proposes a theoretical foundation for a general spatial geometric mechanism-environment contact model. In the proposed model the curvature of the environment in the vicinity of the contact is approximated by a number of spherical surfaces with known radii of curvature that constrain/define the movement of the body. We show how the modeled body-environment contact and curvature constraints can be transformed into conditions on spatial velocity and acceleration (i.e. first and second order effects) of certain points of the moving body that can be incorporated in the kinematic task for designing spatial mechanisms. Further, we explore the exact synthesis of a spatial six degrees-of-freedom TPS kinematic chain which end-effector maintains contact with objects in the environment and varies orientation in the vicinity of a contact location. It is discussed how the higher order motion constraints allow for the introduction of kinematic task variations in the vicinity of a contact, resulting in different behaviors of the designed spatial mechanism. The theoretical foundation presented in this paper is crucial in gaining understanding of the constraints in describing mechanism-environment interactions in the vicinity of a contact and is a new contribution.

Generalization of Taylor’s Added-Mass Formula for Two Bodies

1989 ◽  
Vol 33 (01) ◽  
pp. 1-9
Author(s):  
L. Landweber ◽  
A. T. Chwang
Keyword(s):  
Degrees Of Freedom ◽  
Added Mass ◽  
Simple Relation ◽  
The Body ◽  
Taylor Formula ◽  
Offshore Structure ◽  
Six Degrees Of Freedom ◽  
Moving Body ◽  
Added Masses ◽  
Two Bodies

A previous generalization of the Taylor formula, which expresses the added masses of a single body, moving with six degrees of freedom, in terms of the system of hydrodynamic singularities which generate the irrotational flow about the body, is further generalized for the case when another moving body is present. This work was stimulated by a study of the hydrodynamic interactions between an ice mass and a ground-based offshore structure. The results are applied to calculate the variation of the added masses as a rectangular cylinder approaches a circular one. A new simple relation between the added masses of a rectangle moving parallel to its longer or shorter side, and a more complete table of the added-mass coefficients for various thickness-length ratios than was previously available, is presented in the Appendix.

Closed-Form Inverse Kinematics for Interventional C-Arm X-Ray Imaging With Six Degrees of Freedom: Modeling and Application

2012 ◽  
Vol 31 (5) ◽  
pp. 1086-1099 ◽  
Author(s):  
Lejing Wang ◽  
Pascal Fallavollita ◽  
Rui Zou ◽  
Xin Chen ◽  
Simon Weidert ◽  
...  
Keyword(s):  
Closed Form ◽  
Inverse Kinematics ◽  
Degrees Of Freedom ◽  
X Ray ◽  
Six Degrees Of Freedom ◽  
X Ray Imaging

Closed-form inverse kinematics for intra-operative mobile C-arm positioning with six degrees of freedom

2011 ◽  
Author(s):  
Lejing Wang ◽  
Rui Zou ◽  
Simon Weidert ◽  
Juergen Landes ◽  
Ekkehard Euler ◽  
...  
Keyword(s):  
Closed Form ◽  
Inverse Kinematics ◽  
Degrees Of Freedom ◽  
Six Degrees Of Freedom

The motion of a lunar orbiter

1966 ◽  
Vol 25 ◽  
pp. 373
Author(s):  
Y. Kozai
Keyword(s):  
Degrees Of Freedom ◽  
Dimensional Space ◽  
Artificial Satellite ◽  
Equations Of Motion ◽  
Triaxial Ellipsoid ◽  
The Moon ◽  
Secular Motion ◽  
The Earth ◽  
Close Satellite ◽  
The Mean

The motion of an artificial satellite around the Moon is much more complicated than that around the Earth, since the shape of the Moon is a triaxial ellipsoid and the effect of the Earth on the motion is very important even for a very close satellite.The differential equations of motion of the satellite are written in canonical form of three degrees of freedom with time depending Hamiltonian. By eliminating short-periodic terms depending on the mean longitude of the satellite and by assuming that the Earth is moving on the lunar equator, however, the equations are reduced to those of two degrees of freedom with an energy integral.Since the mean motion of the Earth around the Moon is more rapid than the secular motion of the argument of pericentre of the satellite by a factor of one order, the terms depending on the longitude of the Earth can be eliminated, and the degree of freedom is reduced to one.Then the motion can be discussed by drawing equi-energy curves in two-dimensional space. According to these figures satellites with high inclination have large possibilities of falling down to the lunar surface even if the initial eccentricities are very small.The principal properties of the motion are not changed even if plausible values ofJ3andJ4of the Moon are included.This paper has been published in Publ. astr. Soc.Japan15, 301, 1963.

Representing utility and deploying the body

2020 ◽  
Vol 43 ◽  
Author(s):  
David Spurrett
Keyword(s):  
Functional Activity ◽  
Degrees Of Freedom ◽  
The Body ◽  
Target Article ◽  
Processing Demands ◽  
The Many

Abstract Comprehensive accounts of resource-rational attempts to maximise utility shouldn't ignore the demands of constructing utility representations. This can be onerous when, as in humans, there are many rewarding modalities. Another thing best not ignored is the processing demands of making functional activity out of the many degrees of freedom of a body. The target article is almost silent on both.

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