Physical Restrictions on the Impulse Acting During Three-Dimensional Impact of Two “Rigid” Bodies

1998 ◽  
Vol 65 (2) ◽  
pp. 464-469 ◽  
Author(s):  
M. B. Rubin
Keyword(s):  
Constitutive Equation ◽  
Abrupt Change ◽  
Three Dimensional ◽  
Friction Angle ◽  
Coefficient Of Restitution ◽  
Rigid Bodies ◽  
General Nature ◽  
Physical Conditions ◽  
Finite Spheres ◽  
Two Bodies

It is well known that the impulse of the contact force acting during impact of two rigid bodies determines the abrupt change in the motions of the two bodies. Much recent work has been focused on determining a constitutive equation for this impulse which models the complicated phenomena occurring during the actual deformations of the two bodies. The objective of this paper is to discuss a set of physical conditions which impose nontrivial restrictions on general constitutive equations for the impulse. Due to the general nature of these restrictions they can be used to determine the range of validity of various proposals for the impulse. For the general case of three-dimensional impact, the impulse depends on an energetic coefficient of restitution and two angles defining its direction. However, when there are no directional properties of the roughness of the two impacting bodies, it is reasonable to propose a simpler form for the direction of the impulse which depends only on this coefficient of restitution and a single friction angle. An example of impact of two finite spheres is considered which shows that the condition that the two bodies have a tendency to separate after impact imposes nontrivial bounds on this friction angle.

Rigid Body Collisions

1989 ◽  
Vol 56 (1) ◽  
pp. 133-138 ◽  
Author(s):  
Raymond M. Brach
Keyword(s):  
Energy Loss ◽  
Classical Problem ◽  
Negative Energy ◽  
Coefficient Of Restitution ◽  
Rigid Bodies ◽  
Interaction Process ◽  
Energy Losses ◽  
Conservation Of Energy ◽  
Special Case ◽  
Two Bodies

A general approach is presented for solving the problem of the collision of two rigid bodies at a point. The approach overcomes the difficulties encountered by others on the treatment of contact velocity reversals and negative energy losses. A classical problem is solved; the initial velocities are presumed known and the final velocities unknown. The interaction process between the two bodies is modeled using two coefficients. These are the classical coefficient of restitution, e, and the ratio, μ, of tangential to normal impulses. The latter quantity can be a coefficient of friction as a special case. The paper reveals that these coefficients have a much broader intepretation than previously recognized in the solution of collision problems. The appropriate choice of values for μ is related to the energy loss of the collision. It is shown that μ is bounded by values which correspond to no sliding at separation and conservation of energy. Another bound on μ combined with limits on the coefficient e, provides an overall bound on the energy loss of a collision. Examples from existing mechanics literature are solved to illustrate the significance of the coefficients and their relationship to the energy loss of collisions.

Velocity and Acceleration Analysis of Contact Between Three-Dimensional Rigid Bodies

1996 ◽  
Vol 63 (4) ◽  
pp. 974-984 ◽  
Author(s):  
N. Sankar ◽  
V. Kumar ◽  
Xiaoping Yun
Keyword(s):  
Rigid Body ◽  
Relative Motion ◽  
Three Dimensional ◽  
Rigid Bodies ◽  
Local Surface ◽  
Contact Points ◽  
Pure Rolling ◽  
Acceleration Analysis ◽  
Rigid Body Motions ◽  
Two Bodies

During manipulation and locomotion tasks encountered in robotics, it is often necessary to control the relative motion between two contacting rigid bodies. In this paper we obtain the equations relating the motion of the contact points on the pair of contacting bodies to the rigid-body motions of the two bodies. The equations are developed up to the second order. The velocity and acceleration constraints for contact, for rolling, and for pure rolling are derived. These equations depend on the local surface properties of each contacting body. Several examples are presented to illustrate the nature of the equations.

Velocity and Acceleration Analysis of Contact Between Three-Dimensional Rigid Bodies

1994 ◽  
Author(s):  
Nilanjan Sarkar ◽  
Vijay Kumar ◽  
Xiaoping Yun
Keyword(s):  
Rigid Body ◽  
Relative Motion ◽  
Three Dimensional ◽  
Rigid Bodies ◽  
Local Surface ◽  
Contact Points ◽  
Pure Rolling ◽  
Acceleration Analysis ◽  
Rigid Body Motions ◽  
Two Bodies

Abstract During manipulation and locomotion tasks encountered in robotics, it is often necessary to control the relative motion between two contacting rigid bodies. In this paper we obtain the equations relating the motion of the contact points on the pair of contacting bodies to the rigid body motions of the two bodies. The equations are developed up to the second order. The velocity and acceleration constraints for contact, for rolling, and for pure rolling are derived. These equations depend on the local surface properties of each contacting body. Several examples are presented to illustrate the nature of the equations.

Effect of Material and Geometric Parameters on the Steady-State Belt Stresses and Belt Slip for Flat Belt-Drives

2015 ◽  
Author(s):  
Cagkan Yildiz ◽  
Tamer M. Wasfy ◽  
Hatem M. Wasfy ◽  
Jeanne M. Peters
Keyword(s):  
Steady State ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Flexible Multibody Dynamics ◽  
Friction Model ◽  
Rigid Bodies ◽  
Geometric Parameters ◽  
Rubber Matrix ◽  
Axial Stiffness ◽  
Belt Drive

In order to accurately predict the fatigue life and wear life of a belt, the various stresses that the belt is subjected to and the belt slip over the pulleys must be accurately calculated. In this paper, the effect of material and geometric parameters on the steady-state stresses (including normal, tangential and axial stresses), average belt slip for a flat belt, and belt-drive energy efficiency is studied using a high-fidelity flexible multibody dynamics model of the belt-drive. The belt’s rubber matrix is modeled using three-dimensional brick elements and the belt’s reinforcements are modeled using one dimensional truss elements. Friction between the belt and the pulleys is modeled using an asperity-based Coulomb friction model. The pulleys are modeled as cylindrical rigid bodies. The equations of motion are integrated using a time-accurate explicit solution procedure. The material parameters studied are the belt-pulley friction coefficient and the belt axial stiffness and damping. The geometric parameters studied are the belt thickness and the pulleys’ centers distance.

Kinematics of Meshing Surfaces Using Geometric Algebra

2003 ◽  
Author(s):  
Scott M. Miller
Keyword(s):  
Geometric Algebra ◽  
Screw Theory ◽  
Three Dimensional ◽  
Normal Vector ◽  
The Past ◽  
Geometric Concepts ◽  
Vector Algebra ◽  
The Common ◽  
Two Bodies ◽  
Theoretical Developments

As is well known, analysis of two surfaces in mesh plays a fundamental role in gear theory. In the past, special coordinate systems, vector algebra, or screw theory was used to analyze the kinematics of meshing. The approach here instead relies on geometric algebra, an extension of conventional vector algebra. The elegance of geometric algebra for theoretical developments is demonstrated by examining the so-called “equation of meshing,” which requires that the relative velocity of two bodies at a point of contact be perpendicular to the common surface normal vector. With surprisingly little effort, several alternative forms of the equation of meshing are generated and, subsequently, interpreted geometrically. Via straightforward algebraic manipulations, the results of screw theory and vector algebra are unified. Due to the simplicity with which complex geometric concepts are expressed and manipulated, the effort required to grasp the general three-dimensional meshing of surfaces is minimized.

Three-Dimensional Kinematics of Rigid Bodies

1997 ◽  
pp. 657-698
Author(s):  
Bichara B. Muvdi ◽  
Amir W. Al-Khafaji ◽  
J. W. McNabb
Keyword(s):  
Three Dimensional ◽  
Rigid Bodies

scholarly journals Three-dimensional oblique water-entry problems at small deadrise angles

2012 ◽  
Vol 711 ◽  
pp. 259-280 ◽  
Author(s):  
M. R. Moore ◽  
S. D. Howison ◽  
J. R. Ockendon ◽  
J. M. Oliver
Keyword(s):  
Three Dimensional ◽  
Oblique Impact ◽  
Water Entry ◽  
Rigid Bodies ◽  
Normal Impact ◽  
Displacement Potential ◽  
Pressure Profiles ◽  
The Relationship ◽  
Wagner Theory ◽  
The Ideal

AbstractThis paper extends Wagner theory for the ideal, incompressible normal impact of rigid bodies that are nearly parallel to the surface of a liquid half-space. The impactors considered are three-dimensional and have an oblique impact velocity. A formulation in terms of the displacement potential is used to reveal the relationship between the oblique and corresponding normal impact solutions. In the case of axisymmetric impactors, several geometries are considered in which singularities develop in the boundary of the effective wetted region. We present the corresponding pressure profiles and models for the splash sheets.

Radula-centric and odontophore-centric kinematic models of swallowing inAplysia californica

2002 ◽  
Vol 205 (14) ◽  
pp. 2029-2051 ◽  
Author(s):  
Richard F. Drushel ◽  
Greg P. Sutton ◽  
David M. Neustadter ◽  
Elizabeth V. Mangan ◽  
Benjamin W. Adams ◽  
...  
Keyword(s):  
Kinematic Model ◽  
Three Dimensional ◽  
Rigid Bodies ◽  
High Temporal Resolution ◽  
Buccal Mass ◽  
Kinematic Models ◽  
Dimensional Shape ◽  
Position Parameter ◽  
Three Dimensional Shape

SUMMARYTwo kinematic models of the radula/odontophore of the marine mollusc Aplysia californica were created to characterize the movement of structures inside the buccal mass during the feeding cycle in vivo. Both models produce a continuous range of three-dimensional shape changes in the radula/odontophore, but they are fundamentally different in construction. The radulacentric model treats the radular halves as rigid bodies that can pitch, yaw and roll relative to a fixed radular stalk, thus creating a three-dimensional shape. The odontophore-centric model creates a globally convex solid representation of the radula/odontophore directly, which then constrains the positions and shapes of internal structures. Both radula/odontophore models are placed into a pre-existing kinematic model of the I1/I3 and I2 muscles to generate three-dimensional representations of the entire buccal mass. High-temporal-resolution, mid-sagittal magnetic resonance(MR) images of swallowing adults in vivo are used to provide non-invasive, artifact-free shape and position parameter inputs for the models. These images allow structures inside the buccal mass to be visualized directly, including the radula, radular stalk and lumen of the I1/I3 cavity. Both radula-centric and odontophore-centric models were able to reproduce two-dimensional, mid-sagittal radula/odontophore and buccal mass kinematics,but the odontophore-centric model's predictions of I1/I3, I2 and I7 muscle dimensions more accurately matched data from MR-imaged adults and transilluminated juveniles.

Closed-Form Determination of the Location of a Rigid Body by Seven In-Parallel Linear Transducers

1996 ◽  
Author(s):  
Carlo Innocenti
Keyword(s):  
Rigid Body ◽  
Linear Equations ◽  
Parallel Manipulators ◽  
Rigid Bodies ◽  
Body Location ◽  
Position And Orientation ◽  
General Geometry ◽  
Two Bodies

Abstract The paper presents an original analytic procedure for unambiguously determining the relative position and orientation (location) of two rigid bodies based on the readings from seven linear transducers. Each transducer connects two points arbitrarily chosen on the two bodies. The sought-for rigid-body location simply results by solving linear equations. The proposed procedure is suitable for implementation in control of fully-parallel manipulators with general geometry. A numerical example shows application of the reported results to a case study.

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