Completely Specified Displacements of a Rigid Body and Their Application in the Direct Kinematics of In-Parallel Mechanisms

1999 ◽  
Vol 121 (4) ◽  
pp. 485-491
Author(s):  
C. Mavroidis
Keyword(s):  
Rigid Body ◽  
The Body ◽  
Algebraic Solution ◽  
Final Position ◽  
Parallel Mechanisms ◽  
Direct Kinematics

In this paper we study the type of completely specified displacements of a rigid body where the distances of six points on the body, between their final and initial positions, have been specified. A method is presented to calculate the screws associated with these displacements. It is shown that there are 24 different screws at the most that will bring the rigid body from the initial to its final position to satisfy the six distances. If the six points are co-planar or symmetrical with respect to a plane then the number of screws reduces to 16. The method to calculate the screws associated with these completely specified displacements, is used to obtain a simple algebraic solution to the direct kinematics problem of a special type of in-parallel mechanisms: the mechanisms where the moving and the fixed platforms are the same.

Completely Specified Displacements of a Rigid Body and Their Application in the Direct Kinematics of In-Parallel Mechanisms

1998 ◽  
Author(s):  
Constantinos Mavroidis
Keyword(s):  
Rigid Body ◽  
The Body ◽  
Algebraic Solution ◽  
Final Position ◽  
Parallel Mechanisms ◽  
Direct Kinematics

Abstract In this paper we study the type of completely specified displacements of a rigid body where the distances of six points on the body, between their final and initial positions, have been specified. A method is presented to calculate the screws associated with these displacements. It is shown that there are 24 different screws at the most that will bring the rigid body from the initial to its final position to satisfy the six distances. If the six points are co-planar or symmetrical with respect to a plane then the number of screws reduces to 16. The method to calculate the screws associated with these completely specified displacements, is used to obtain a simple algebraic solution to the direct kinematics problem of a special type of in-parallel mechanisms: the mechanisms where the moving and the fixed platforms are the same.

A Linear Algebra Approach to the Analysis of Rigid Body Displacement From Initial and Final Position Data

1982 ◽  
Vol 49 (1) ◽  
pp. 213-216 ◽  
Author(s):  
A. J. Laub ◽  
G. R. Shiflett
Keyword(s):  
Rigid Body ◽  
Linear Algebra ◽  
Initial Position ◽  
The Body ◽  
Final Position ◽  
Explicit Formulas ◽  
Algebra Approach ◽  
Other Information ◽  
Position Data ◽  
Rigid Body Displacement

The location and orientation of a rigid body in space can be defined in terms of three noncollinear points in the body. As the rigid body is moved through space, the motion may be described by a series of rotations and translations. The sequence of displacements may be conveniently represented in matrix form by a series of displacement matrices that describe the motion of the body between successive positions. If the rotations and translations (and hence the displacement matrix) are known then succeeding positions of a rigid body may be easily calculated in terms of the initial position. Conversely, if successive positions of three points in the rigid body are known, it is possible to calculate the parameters of the corresponding rotation and translation. In this paper, a new solution is presented which provides explicit formulas for the rotation and translation of a rigid body in terms of the initial and final positions of three points fixed in the rigid body. The rotation matrix is determined directly whereupon appropriate rotation angles and other information can subsequently be calculated if desired.

Direct Kinematic Analysis of a Hexapod Spider-Like Mobile Robot

2011 ◽  
Vol 403-408 ◽  
pp. 5053-5060 ◽  
Author(s):  
Mostafa Ghayour ◽  
Amir Zareei
Keyword(s):  
Angular Velocity ◽  
Mobile Robot ◽  
Time Variation ◽  
Kinematic Analysis ◽  
The Body ◽  
Specific Time ◽  
Centre Of Gravity ◽  
Joint Variable ◽  
Direct Kinematics ◽  
Robot Platform

In this paper, an appropriate mechanism for a hexapod spider-like mobile robot is introduced. Then regarding the motion of this kind of robot which is inspired from insects, direct kinematics of position and velocity of the centre of gravity (C.G.) of the body and noncontact legs are analysed. By planning and supposing a specific time variation for each joint variable, location and velocity of the C.G. of the robot platform and angular velocity of the body are obtained and the results are shown and analysed.

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.

Three-Position Rigid Body Guidance Using Specified Moving Pivots for a Four-Bar Mechanism With Variable Topology

2018 ◽  
Author(s):  
Brian J. Slaboch
Keyword(s):  
Rigid Body ◽  
Algebraic Solution ◽  
Graphical Approach ◽  
Practical Applications ◽  
Joint Geometry ◽  
Topological State ◽  
Variable Topology

This paper provides an algorithm allowing a designer to perform three position rigid body guidance with specified moving pivots for a 4R-RRRP mechanism with variable topology (MVT). A mechanism with variable topology is a mechanism that changes from one topological state to another due to a change in joint geometry. Both a graphical approach and an algebraic solution are presented. An example is provided in which a circuit defect in a 4R mechanism can be avoided using a 4R-RRRP mechanism. Two additional examples are provided that show the results of this new theory. Practical applications for this theory are found in many industries including manufacturing, aerospace, and healthcare.

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.

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