# Lund University Publications

## LUND UNIVERSITY LIBRARIES

### Kinematics for unilateral constraints in multibody dynamics

(2017) In Mathematics and Mechanics of Solids 22(8). p.1654-1687
Abstract

This paper is concerned with the kinematics of unilateral constraints in multibody dynamics. These constraints are related to the contact between parts and the principle of impenetrability of matter and have the property that they may be active, in which case they give rise to constraint forces, or passive, in which case they do not give rise to constraint forces. In order to check whether the constraint is active or passive a distance function between parts of the multibody is required. The paper gives a rigorous definition of the distance function and derives certain of its properties. The unilateral constraint may then be expressed in terms of this distance function. The paper analyses the transitions from passive constraints to... (More)

This paper is concerned with the kinematics of unilateral constraints in multibody dynamics. These constraints are related to the contact between parts and the principle of impenetrability of matter and have the property that they may be active, in which case they give rise to constraint forces, or passive, in which case they do not give rise to constraint forces. In order to check whether the constraint is active or passive a distance function between parts of the multibody is required. The paper gives a rigorous definition of the distance function and derives certain of its properties. The unilateral constraint may then be expressed in terms of this distance function. The paper analyses the transitions from passive constraints to active and vice versa. Sufficient regularity of the transplacements of the parts and their boundary surfaces will lead to specific properties of the time derivative of the distance function. When the unilateral constraint is active then the parts are geometrically in contact and there is a certain contact surface that, in specific cases, may degenerate into a point. If the parts are in mechanical contact over the contact surface then there will be an interaction between the parts given by contact forces, such as normal and friction forces. Parts in contact may be at rest relative to one another, over the contact surface, or they may be in relative sliding motion. The transition from non-sliding contact to sliding and from sliding to non-sliding is discussed and necessary conditions on the relative velocity and the traction vector are derived. Appropriate complementary conditions are then formulated. These are instrumental when the technique of linear complementarity is used in order to find solutions to the equations of motion.

(Less)
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
complementary conditions, distance function, kinematics, Multibody dynamics, unilateral constraints
in
Mathematics and Mechanics of Solids
volume
22
issue
8
pages
34 pages
publisher
SAGE Publications Inc.
external identifiers
• scopus:85026881832
• wos:000407176200002
ISSN
1081-2865
DOI
10.1177/1081286516642270
language
English
LU publication?
yes
id
bb0d82c0-0779-4de7-8097-d58424bb7f68
2017-08-29 14:40:26
date last changed
2018-01-07 12:16:28
```@article{bb0d82c0-0779-4de7-8097-d58424bb7f68,
abstract     = {<p>This paper is concerned with the kinematics of unilateral constraints in multibody dynamics. These constraints are related to the contact between parts and the principle of impenetrability of matter and have the property that they may be active, in which case they give rise to constraint forces, or passive, in which case they do not give rise to constraint forces. In order to check whether the constraint is active or passive a distance function between parts of the multibody is required. The paper gives a rigorous definition of the distance function and derives certain of its properties. The unilateral constraint may then be expressed in terms of this distance function. The paper analyses the transitions from passive constraints to active and vice versa. Sufficient regularity of the transplacements of the parts and their boundary surfaces will lead to specific properties of the time derivative of the distance function. When the unilateral constraint is active then the parts are geometrically in contact and there is a certain contact surface that, in specific cases, may degenerate into a point. If the parts are in mechanical contact over the contact surface then there will be an interaction between the parts given by contact forces, such as normal and friction forces. Parts in contact may be at rest relative to one another, over the contact surface, or they may be in relative sliding motion. The transition from non-sliding contact to sliding and from sliding to non-sliding is discussed and necessary conditions on the relative velocity and the traction vector are derived. Appropriate complementary conditions are then formulated. These are instrumental when the technique of linear complementarity is used in order to find solutions to the equations of motion.</p>},
author       = {Lidström, P.},
issn         = {1081-2865},
keyword      = {complementary conditions,distance function,kinematics,Multibody dynamics,unilateral constraints},
language     = {eng},
month        = {08},
number       = {8},
pages        = {1654--1687},
publisher    = {SAGE Publications Inc.},
series       = {Mathematics and Mechanics of Solids},
title        = {Kinematics for unilateral constraints in multibody dynamics},
url          = {http://dx.doi.org/10.1177/1081286516642270},
volume       = {22},
year         = {2017},
}

```