Dynamics of Multibody Systems With Known Configuration Changes

1991 ◽  
Vol 58 (1) ◽  
pp. 215-221 ◽  
Author(s):  
J. J. McPhee ◽  
R. N. Dubey
Keyword(s):  
Numerical Simulation ◽  
Computer Program ◽  
Multibody Systems ◽  
Equations Of Motion ◽  
Rigid Bodies ◽  
Rotation Vector ◽  
Dynamic Effects ◽  
Physical Systems ◽  
Dynamics Of Multibody Systems ◽  
Configuration Changes

The equations of motion are derived for a system with inertial properties that are varying in time as a result of known relative motions between the rigid bodies comprising the system. This vector-dyadic formulation has been encoded into a computer program, making use of the conformal rotation vector for the representation of rotations. The numerical simulation of two different physical systems is presented in order to illustrate the dynamic effects of the changing inertial properties, and the usefulness of the encoded formulation for modeling these effects.

Numerical Simulation of Multibody Systems With Time Dependant Structure

1993 ◽  
Author(s):  
Pierre Joli ◽  
Madeleine Pascal ◽  
René Gibert
Keyword(s):  
Numerical Simulation ◽  
Multibody Systems ◽  
Computational Algorithm ◽  
Rigid Bodies ◽  
Three Dimensions ◽  
Integration Step ◽  
General Systems ◽  
Articulated Systems ◽  
Jump Velocity ◽  
Assembly Tasks

Abstract Current dynamic simulation programs are able to calculate the continuous motions of articulated systems or more general systems of rigid bodies in the absence of contact between members of the system or between the system and its environment. Some are able to simulate the effects of isolated contacts and impacts but none are able to simulate the motion with unrestricted multiple concurrent contacts. However, in special robotic programs such as robots performing assembly tasks or walking, it would be very interesting to simulate appropriate commands before implementing them on the robots. This paper develops intrinsic problems of collision to produce an efficient computational algorithm. This algorithm handles the detection of collision in three dimensions, the reduction of the integration step in order to avoid interpenetration between the bodies before impact, the jump velocity caused by a new collision and indicator magnitudes which determine the addition or deletion of constraints.

Dynamics of Serial Multibody Systems Using the Decoupled Natural Orthogonal Complement Matrices

1999 ◽  
Vol 66 (4) ◽  
pp. 986-996 ◽  
Author(s):  
S. K. Saha
Keyword(s):  
Multibody Systems ◽  
Degrees Of Freedom ◽  
Inverse Dynamics ◽  
Equations Of Motion ◽  
Kinematic Chain ◽  
Rigid Bodies ◽  
Dynamic Equations ◽  
Orthogonal Complement ◽  
Forward Dynamics ◽  
Velocity Constraints

Constrained dynamic equations of motion of serial multibody systems consisting of rigid bodies in a serial kinematic chain are derived in this paper. First, the Newton-Euler equations of motion of the decoupled rigid bodies of the system at hand are written. Then, with the aid of the decoupled natural orthogonal complement (DeNOC) matrices associated with the velocity constraints of the connecting bodies, the Euler-Lagrange independent equations of motion are derived. The De NOC is essentially the decoupled form of the natural orthogonal complement (NOC) matrix, introduced elsewhere. Whereas the use of the latter provides recursive order n—n being the degrees-of-freedom of the system at hand—inverse dynamics and order n3 forward dynamics algorithms, respectively, the former leads to recursive order n algorithms for both the cases. The order n algorithms are desirable not only for their computational efficiency but also for their numerical stability, particularly, in forward dynamics and simulation, where the system’s accelerations are solved from the dynamic equations of motion and subsequently integrated numerically. The algorithms are illustrated with a three-link three-degrees-of-freedom planar manipulator and a six-degrees-of-freedom Stanford arm.

Generalized Vector-Network Formulation for the Dynamic Simulation of Multibody Systems

1986 ◽  
Vol 108 (4) ◽  
pp. 322-329 ◽  
Author(s):  
M. J. Richard ◽  
R. Anderson ◽  
G. C. Andrews
Keyword(s):  
Multibody Systems ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Rigid Bodies ◽  
New Approach ◽  
System Description ◽  
Nonlinear Equations Of Motion ◽  
Systematic Formulation ◽  
Multi Body ◽  
Entire Procedure

This paper describes the vector-network approach which is a comprehensive mathematical model for the systematic formulation of the nonlinear equations of motion of dynamic three-dimensional constrained multi-body systems. The entire procedure is a basic application of concepts of graph theory in which laws of vector dynamics have been combined. The main concepts of the method have been explained in previous publications but the work described herein is an appreciable extension of this relatively new approach. The method casts simultaneously the three-dimensional inertia equations associated with each rigid body and the geometrical expressions corresponding to the kinematic restrictions into a symmetrical format yielding the differential equations governing the motion of the system. The algorithm is eminently well suited for the computer-aided simulation of arbitrary interconnected rigid bodies; it serves as the basis for a “self-formulating” computer program which can simulate the response of a dynamic system, given only the system description.

Generalized Modeling of Dynamic Cam-follower Pairs in Mechanisms

1991 ◽  
Vol 113 (2) ◽  
pp. 102-109 ◽  
Author(s):  
B. S. Bagepalli ◽  
T. L. Haskins ◽  
I. Imam
Keyword(s):  
Multibody Systems ◽  
Surface Profile ◽  
General Purpose ◽  
Mechanism Analysis ◽  
Dynamic Effects ◽  
Dynamics Of Multibody Systems ◽  
Multibody Dynamic ◽  
Cam Follower ◽  
2D And 3D ◽  
Multibody Dynamic System

This paper deals with the application of homogeneous (4 × 4) transformations to the generalizing modeling of cam-follower pairs. The procedure adopted is generic, in that it suggests a method of incorporating the modeling of cam-follower pairs in a general purpose program, such as MAP (Mechanism Analysis Program, © General Electric Co.) capable of solving the dynamics of multibody systems, in which any of the bodies could be cams, or followers. This development covers both 2D and 3D cam-follower pairs: XY cams, rotary cams, and drum cams. The cams could be dynamic—with single, or two surfaces (or tracked), with the possibility of impacts between the follower and these surfaces, or, kinematic, with the follower being guided exactly in a slot. This generalized procedure allows one to model several cam-follower pairs in a multibody dynamic system. This is useful in studying, for instance, the dynamic effects that tend to bounce a follower off of a cam surface, the contact force generated, etc. The procedure, also, just as easily, allows for the easy studying of the effects of varying the cam surface profile. Several examples have been tried, and some correlations have been obtained with experimental observations.

Modeling a Robot With Flexible Joints and Decoupling its Equations of Motion

1997 ◽  
Author(s):  
Ali Meghdari ◽  
Farbod Fahimi
Keyword(s):  
Rigid Body ◽  
Multibody Systems ◽  
Equations Of Motion ◽  
Degree Of Freedom ◽  
Flexible Joints ◽  
Kane’S Equations ◽  
Kane's Equations ◽  
Recent Advances ◽  
Dynamics Of Multibody Systems ◽  
Two Degree Of Freedom

Abstract Recent advances in the study of dynamics of multibody systems indicate the need for decoupling of the equations of motion. In this paper, our efforts are focused on this issue, and we have tried to expand the existing methods for multi-rigid body systems to include systems with some kind of flexibility. In this regard, the equations of motion for a planar two-degree-of-freedom robot with flexible joints is carried out using Lagrange’s equations and Kane’s equations with congruency transformations. The method of decoupling the equations of motion using Kane’s equations with congruency transformations is presented. Finally, the results obtained from both methods are compared.

Developing a Numerical Simulation Software for 3D Multibody Systems Based on a Unified Computational Modeling Technique

2009 ◽  
Author(s):  
Shahram Shokouhfar ◽  
Sayyid Mahdi Khorsandijou
Keyword(s):  
Numerical Simulation ◽  
Multibody Systems ◽  
Dynamic Models ◽  
Initial Conditions ◽  
Rigid Bodies ◽  
Simulation Software ◽  
Computational Technique ◽  
Main Task ◽  
Algebraic Equations ◽  
Time Step

This article represents the features and capabilities of a newly developed application namely MASS (Mechanisms Analysis and Simulation Software) and the formulation and techniques therein. MASS is a general C++ application program whose main task is to construct and solve the governing algebraic differential motion equations of 3D multibody systems automatically in matrix forms complying with the computational algorithms required for numerical simulation. Newton-Raphson and SVD methods have been used for kinematical assembling and producing consistent initial conditions. Adaptive time-step Runge-Kutta-Fehlberg numerical integration methods might be used for forward dynamics problems. The governing equations perfectly describe the kinematics and dynamics of multibody systems within which 3D kinematical joints and collisions between rigid bodies might be taken into consideration. The unified computational technique for mathematical modeling of kinematical joints is the most important concept on top of which MASS has been implemented. It has occurred due to the existence of thirteen basic kinematical constraint equations. Each kinematical joint might be defined by a set of algebraic equations being selected from the mentioned basic equations. The unified dynamic models for collisions and impulsive loads have been also achieved using the mentioned technique. Simulation results obtained from MASS have been compared with that of the corresponding software of Working Model ver. 6 and a discussion about the coincidences and differences has been exposed.

Explicit Time Integration of Multibody Systems Modelled With Three Rotation Parameters

2020 ◽  
Author(s):  
Stefan Holzinger ◽  
Johannes Gerstmayr
Keyword(s):  
Lie Group ◽  
Multibody Systems ◽  
Degrees Of Freedom ◽  
Time Integration ◽  
Rigid Bodies ◽  
Rotation Vector ◽  
Body Motion ◽  
Euler Parameters ◽  
Time Step ◽  
Rotation Parameters

Abstract Rigid bodies are an essential part of multibody systems. As there are six degrees of freedom in rigid bodies, it is natural but also precarious to use three parameters for the displacement and three parameters for the rotation parameters — since there is no singularity-free description of spatial rotations based on three rotation parameters. Standard formulations based on three rotation parameters avoid singularities, e.g. by applying reparameterization strategies during the time integration of the rotational kinematic equations. Alternatively, Euler parameters are commonly used to avoid singularities. State of the art approaches use Lie group methods, specifically integrators, to model rigid body motion without the need for the above mentioned solutions. However, the methods so far have been based on additional information, e.g., the rotation matrix, which has to been computed in each step. The latter procedure is thus difficult to be implemented in existing codes that are based on three rotation parameters. In this paper, we use the rotation vector to model large rotations. Whereby Lie group integration methods are used to compute consistent updates for the rotation vector in every time step. The resulting rotation vector update is finite, while the derivative of the rotation vector in the singularity becomes unbounded. The advantages of this method are shown in an example of a gyro. Additionally, the method is applied to a multibody system and the effects of crossing singularities are presented.

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