An Efficient Method for a Category of Contact/Impact Problems in Multibody Systems: Tree Topologies

2005 ◽  
Author(s):  
Michael J. Sadowski ◽  
Kurt S. Anderson
Keyword(s):  
Rigid Body ◽  
Dynamic Systems ◽  
Equations Of Motion ◽  
Momentum Balance ◽  
Unilateral Constraints ◽  
Constraint Forces ◽  
Rigid Body Dynamic ◽  
Tree Topologies ◽  
Contact Impact ◽  
Impact Problems

This paper presents an algorithm for the efficient numerical analysis and simulation of a category of contact/impact problems in multi-rigid-body dynamic systems with tree topologies. The algorithm can accommodate the jumps in structure which occur in the equations of motion of general multi-rigid-body systems due to a contact/impact event between bodies, or due to the locking of joints as long as the resulting system is a tree topology. The presented method uses a generalized momentum balance approach to determine the velocity jumps which take place across impacts in such multibody dynamic systems where event constraint forces are of the “non-working” category. The presented method does not suffer from the performance (speed) penalty encountered by most other momentum balance methods given its O(n) overall cost, and exact direct embedded consideration of all the constraints. Due to these characteristics, the presented algorithm offers superior computing performance relative to other methods in situations involving both large n and potentially many unilateral constraints.

An Efficient Method for Contact/Impact Problems in Multibody Systems: Tree Topologies

2003 ◽  
Author(s):  
Kurt S. Anderson ◽  
Michael J. A. Sadowski
Keyword(s):  
Rigid Body ◽  
Dynamic Systems ◽  
Equations Of Motion ◽  
Momentum Balance ◽  
Unilateral Constraints ◽  
Rigid Body Dynamic ◽  
Large N ◽  
Generalized Momentum ◽  
Contact Impact ◽  
Impact Problems

This paper presents an algorithm for the efficient numerical analysis and simulation of contact/impact problems in tree topology multi-rigid-body dynamic systems. The algorithm can accommodate the jumps in structure which occur in the equations of motion of general multi-rigid-body tree systems due to a contact/impact event between bodies, or due to the locking of joints. The presented method uses a generalized momentum balance approach to determine the velocity jumps which take place across impacts in such multibody dynamic systems, and where necessary explicitly determines impact impulsive loads (both working and non-working). The presented method does not suffer from the performance (speed) penalty encountered by most other momentum balance methods given its O(n) overall cost, and exact direct embedded consideration of the all constraints. Due to these characteristics, the presented algorithm offers superior computing performance relative to other methods in situations involving both large n and potentially many unilateral constraints.

An Efficient Method for Contact/Impact Problems in Multibody Systems: Topologies With Many Loops

2003 ◽  
Author(s):  
Kurt S. Anderson ◽  
Michael J. A. Sadowski
Keyword(s):  
Dynamic Systems ◽  
Momentum Balance ◽  
Closed Loops ◽  
Rigid Body Dynamic ◽  
Large N ◽  
Multibody Dynamic ◽  
Generalized Momentum ◽  
Contact Impact ◽  
Impact Problems ◽  
Algebraic Constraints

This paper presents an algorithm for the efficient numerical analysis and simulation of contact/impact problems in modest to heavily constrained multi-rigid-body dynamic systems. The algorithm can accommodate the spatial motion of general multirigid-body systems containing arbitrarily many closed loops in O(n+m) operations overall for systems containing n generalized coordinates, and m independent algebraic constraints. The presented method uses a generalized momentum balance approach to determine the velocity jumps which take place across impacts in such constrained multibody dynamic systems. The presented method does not suffer from the performance (speed) penalty encountered by most other momentum balance methods given its O(n + m) cost, and exact direct embedded consideration of the all constraints. Due to these characteristics, the presented algorithm offers superior computing performance relative to other methods in situations involving both large n and m.

A Hybrid Highly Parallelizable Algorithm for the Dynamics of Rigid Body Chain Systems

1999 ◽  
Author(s):  
Shanzhong Duan ◽  
Kurt S. Anderson
Keyword(s):  
Rigid Body ◽  
Degrees Of Freedom ◽  
High Efficiency ◽  
Equations Of Motion ◽  
Constraint Forces ◽  
Dynamics Of Rigid Body ◽  
A Chain ◽  
Explicit Determination ◽  
Order Algorithm

Abstract The paper presents a new hybrid parallelizable low order algorithm for modeling the dynamic behavior of multi-rigid-body chain systems. The method is based on cutting certain system interbody joints so that largely independent multibody subchain systems are formed. These subchains interact with one another through associated unknown constraint forces f¯c at the cut joints. The increased parallelism is obtainable through cutting the joints and the explicit determination of associated constraint loads combined with a sequential O(n) procedure. In other words, sequential O(n) procedures are performed to form and solve equations of motion within subchains and parallel strategies are used to form and solve constraint equations between subchains in parallel. The algorithm can easily accommodate the available number of processors while maintaining high efficiency. An O[(n+m)Np+m(1+γ)Np+mγlog2Np](0<γ<1) performance will be achieved with Np processors for a chain system with n degrees of freedom and m constraints due to cutting of interbody joints.

Kinematics for unilateral constraints in multibody dynamics

2016 ◽  
Vol 22 (8) ◽  
pp. 1654-1687
Author(s):  
P Lidström
Keyword(s):  
Multibody Dynamics ◽  
Distance Function ◽  
Contact Surface ◽  
Equations Of Motion ◽  
Time Derivative ◽  
Unilateral Constraint ◽  
Contact Forces ◽  
Unilateral Constraints ◽  
Constraint Forces ◽  
Friction Forces

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.

scholarly journals New Aspects Concerning Dynamics of Rigid Solid Body in Plane-Parallel Motion Subjected to Real Constraints. Part One

2019 ◽  
Vol 24 (2) ◽  
pp. 175-180
Author(s):  
Vladimir Dragoş Tătaru ◽  
Mircea Bogdan Tătaru
Keyword(s):  
Differential Equations ◽  
Rigid Body ◽  
Dynamic Analysis ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Original Method ◽  
Horizontal Force ◽  
Constraint Forces ◽  
Inclined Plane ◽  
Parallel Motion

Abstract The present paper approaches in an original manner the dynamic analysis of a wheel which climbs on an inclined plane under the action of a horizontal force. The wheel rolls and slides in the same time. The two movements, rolling and sliding are considered to be independent of each other. Therefore we are dealing with a solid rigid body with two degrees of freedom. The difficulty of approaching the problem lies in the fact that in the differential equations describing the motion of the solid rigid body are also present the constraint forces and these are unknown. For this reason they must be eliminated from the differential equations of motion. The paper presents as well an original method of the constraint forces elimination.

Improved “Order-N” Performance Algorithm for the Simulation of Constrained Multi-Rigid-Body Dynamic Systems

2001 ◽  
Author(s):  
Kurt S. Anderson
Keyword(s):  
Rigid Body ◽  
Dynamic Systems ◽  
Constraint Violation ◽  
Closed Loops ◽  
Rigid Body Dynamic ◽  
Large N ◽  
Computing Performance ◽  
Algebraic Constraints ◽  
Coordinate Partitioning ◽  
Body Dynamic

Abstract This paper presents an algorithm for the efficient numerical analysis and simulation of modest to heavily constrained multi-rigid-body dynamic systems. The algorithm can accommodate the spatial motion of general multi-rigid-body systems containing arbitrarily many closed loops in O(n + m) operations overall for systems containing n generalized coordinates, and m independent algebraic constraints. The presented approach does not suffer from the performance (speed) penalty encountered by most other of the so-called “O(n)” state-space formulations, when dealing with constraints which tend to actually show O(n + m + nm + nm2 + m3) performance. Additionally, these latter formulations may require additional constraint violation stablization procedures (e.g. Baumgarte’s method, coordinate partitioning, etc.) which can contribute significant additional computation. The presented method suffers less from this difficulty because the loop closure constraints at both the velocity and acceleration level are directly embedded within the formulation. Due to these characteristics, the presented algorithm should offer superior computing performance relative to other methods in situations involving both large n and m.

Recursive Coordinate Reduction: An Addendum

2005 ◽  
Author(s):  
Michael J. Sadowski ◽  
Kurt S. Anderson
Keyword(s):  
Rigid Body ◽  
Dynamic Systems ◽  
Closed Loops ◽  
Rigid Body Dynamic ◽  
Large N ◽  
Computing Performance ◽  
Algebraic Constraints ◽  
Coordinate Reduction ◽  
Coordinate Partitioning ◽  
Body Dynamic

This paper presents an addendum to the Recursive Coordinate Reduction (RCR) algorithm for the efficient numerical analysis and simulation of modest to heavily constrained multi-rigid-body dynamic systems. The RCR algorithm can accommodate the spatial motion of broad categories of multi-rigid-body systems containing arbitrarily many closed loops in O(n + m) operations overall for systems containing n generalized coordinates, and m independent algebraic constraints. The presented approach does not suffer from the performance (speed) penalty encountered by most other of the so-called “(n)” state-space formulations, and does not require additional constraint violation stabilization procedures (e.g. Baumgartes method, coordinate partitioning, etc.). Due to these characteristics, the presented algorithm should offer superior computing performance relative to other methods in many situations involving both large n and m. This paper will specifically address an unpublished recursive step in the handling of “floating” loop base bodies, as well as present an extension to “spur” topologies.

A symbolic and numeric procedure for manipulator rigid-body dynamic significance analysis and simplification

Robotica ◽  
1998 ◽  
Vol 16 (5) ◽  
pp. 589-594 ◽  
Author(s):  
Peter I. Corke
Keyword(s):  
Rigid Body ◽  
Robot Manipulator ◽  
Equations Of Motion ◽  
Joint Torque ◽  
Serial Link ◽  
Rigid Body Dynamic ◽  
Significance Analysis ◽  
The Many ◽  
Body Dynamic ◽  
Insight Into

This paper describes an automated procedure for analysing the significance of each of the many terms in the equations of motion for a serial-link robot manipulator. Significance analysis provides insight into the rigid-body dynamic effects that are significant locally or globally in the manipulator's state space. Deleting those terms that do not contribute significantly to the total joint torque can greatly reduce the computational burden for online control, and a Monte-Carlo style simulation is used to investigate the errors thus introduced. The procedures, freely available, are a hybrid of symbolic and numeric techniques implemented using a standard computer algebra package.

scholarly journals Point-joint coordinate formulation for the dynamic analysis of generalised planar linkages

2005 ◽  
Vol 46 (4) ◽  
pp. 575-589
Author(s):  
Hazem Ali Attia
Keyword(s):  
Rigid Body ◽  
Dynamic Analysis ◽  
Equations Of Motion ◽  
Translational Motion ◽  
Constraint Forces ◽  
Constrained System ◽  
Open Chain ◽  
Closed Chain ◽  
Efficient Integration ◽  
Planar Linkages

AbstractThis paper presents a two-step formulation for the dynamic analysis of generalised planar linkages. First, a rigid body is replaced by a dynamically equivalent constrained system of particles and Newton's second law is used to study the motion of the particles without introducing any rotational coordinates. The translational motion of the constrained particles represents the general motion of the rigid body both translationally and rotationally. The simplicity and the absence of any rotational coordinates from the final form of the equations of motion are considered the main advantages of this formulation. A velocity transformation is then used to transform the equations of motion to a reduced set in terms of selected relative joint variables. For an open-chain, this process automatically eliminates all of the non-working constraint forces and leads to efficient integration of the equations of motion. For a closed-chain, suitable joints should be cut and some cut-joint constraint equations should be included. An example of a closed-chain is used to demonstrate the generality and efficiency of the proposed method.

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