An Efficient Dynamic Formulation for Solving Rigid and Flexible Multibody Systems Based on Semirecursive Method and Implicit Integration

2016 ◽  
Vol 11 (5) ◽  
Author(s):  
Francisco Javier Funes ◽  
Javier García de Jalón
Keyword(s):  
Multibody Systems ◽  
Dynamic Equations ◽  
Integration Process ◽  
Implicit Integration ◽  
Flexible Bodies ◽  
Velocity Transformation ◽  
Dynamic Formulation ◽  
Variable Stepsizes ◽  
Tangent Manifold ◽  
Stability Issues

This paper presents a method for solving the dynamic equations of multibody systems containing both rigid and flexible bodies. The proposed method uses independent coordinates and projects the dynamic equations on the constraint tangent manifold by means of a velocity transformation matrix. It can be used with a wide variety of integration formulae, considering both fixed and variable stepsizes. Topological semirecursive methods are used to take advantage of the relatively small number of parameters needed. An in depth implementation analysis is performed in order to evaluate the terms involved in the integration process. Numerical and stability issues are also discussed.

Spatial Dynamics of Deformable Multibody Systems With Variable Kinematic Structure: Part 2—Velocity Transformation

1990 ◽  
Vol 112 (2) ◽  
pp. 160-167 ◽  
Author(s):  
C. W. Chang ◽  
A. A. Shabana
Keyword(s):  
Multibody Systems ◽  
Robot Manipulator ◽  
Spatial Dynamics ◽  
Dynamic Equations ◽  
Velocity Transformation ◽  
Joint Forces ◽  
Joint Coordinates ◽  
Deformable Bodies ◽  
Spatial System ◽  
Velocity Transformation Technique

In Part 1 of these two companion papers, the spatial system kinematic and dynamic equations are developed using the Cartesian and elastic coordinates in order to maintain the generality of the formulation. This allows introducing general forcing functions and adding and/or deleting kinematic constraints. In control applications, however, it is desirable to determine the joint forces associated with the joint variables. On the other hand the use of the joint coordinates to formulate the dynamic equations leads to a complex recursive formulation based on loop closure equations. In this paper a velocity transformation technique applicable to spatial multibody systems that consist of interconnected rigid and deformable bodies is developed. The Cartesian variables are expressed in terms of the joint and elastic variables. The resulting kinematic relationships are then employed to determine the joint forces associated with the joint variables. A spatial robot manipulator that manipulates an object is presented as a numerical example to exemplify the development presented in this paper.

Recursive Method for the Dynamic Analysis of Open-Loop Flexible Multibody Systems

2003 ◽  
Author(s):  
Yunn-Lin Hwang
Keyword(s):  
Dynamic Analysis ◽  
Multibody Systems ◽  
Equations Of Motion ◽  
Open Loop ◽  
Flexible Multibody Systems ◽  
Recursive Method ◽  
Flexible Bodies ◽  
System Equations ◽  
Generalized Newton ◽  
Time Invariant

The main objective of this paper is to develop a recursive method for the dynamic analysis of open-loop flexible multibody systems. The nonlinear generalized Newton-Euler equations are used for flexible bodies that undergo large translational and rotational displacements. These equations are formulated in terms of a set of time invariant scalars, vectors and matrices that depend on the spatial coordinates as well as the assumed displacement fields, and these time invariant quantities represent the dynamic coupling between the rigid body motion and elastic deformation. The method to solve for the equations of motion for open-loop systems consisting of interconnected rigid and flexible bodies is presented in this investigation. This method applies recursive method with the generalized Newton-Euler method for flexible bodies to obtain a large, loosely coupled system equations of motion. The solution techniques used to solve for the system equations of motion can be more efficiently implemented in the vector or digital computer systems. The algorithms presented in this investigation are illustrated by using cylindrical joints that can be easily extended to revolute, slider and rigid joints. The basic recursive formulations developed in this paper are demonstrated by two numerical examples.

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.

Simplification of manipulator dynamic formulations utilizing a dimensionless method

Robotica ◽  
1993 ◽  
Vol 11 (2) ◽  
pp. 139-147 ◽  
Author(s):  
Yueh-Jaw Lin ◽  
Hai-Yan Zhang
Keyword(s):  
Dynamic Model ◽  
Inverse Dynamics ◽  
Equations Of Motion ◽  
Dynamics Simulation ◽  
Dynamic Equations ◽  
New Approach ◽  
Magnitude Comparison ◽  
Dynamic Formulation ◽  
Order Of Magnitude ◽  
Physical Quantities

SUMMARYThis paper presents a new approach for simplifying dynamic equations of motion of robot manipulators by using a nondimensionalization scheme. With this approach the dynamic analysis is done in a nondimensional space. That is, it is required to establish a dimensionless coordinate system in which the dynamic equations of motion of manipulators are formulated. The characteristic parameters of the manipulators are then defined by choosing proper physical quantities as basic units for nondimensionalization. Within the nondimensional space the Lagrange method is applied to the manipulator to obtain a set of general dimensionless equations of motion. This dimensionless dynamic formulation of manipulators leads to an easier way to simplify the dynamic formulation by neglecting insignificant terms using the order of magnitude comparison. The dimensionless dynamic model and its simplified version of PUMA 560 robot are implemented using the proposed approach. It is found that the simplified dynamic model greatly reduces the computation burden of the inverse dynamics. Simulation results also show that the simplified model is extremely accurate. This implies that the proposed nondimensional simplification emethod is reliable.

An Open Code for the Dynamic Simulation of Multibody Systems

2004 ◽  
Author(s):  
Pietro Fanghella ◽  
Carlo Galletti ◽  
Giorgio Torre
Keyword(s):  
Control Systems ◽  
Multibody Systems ◽  
Object Oriented ◽  
General Purpose ◽  
External Control ◽  
Common Environment ◽  
Flexible Bodies ◽  
Kinematic Chains ◽  
Dynamic Simulator ◽  
User Friendly

The paper presents several features of a dynamic simulator for multibody systems. Its main characteristics are the following: it can deal with mechanisms with open and closed kinematic chains, allows definitions of rigid and flexible bodies, permits definitions of complex non-standard dynamic actions by a powerful and well-known general-purpose simulation package, and provides links to user-friendly interfaces for result displaying and interfacing with external control systems. In order to perform all these actions, a common environment based on Matlab has been established. The software is implemented using the Matlab object-oriented language. The first part of the paper provides a basic discussion of the mathematical approach followed to model multibody systems, then the actual software implementation is described. The designed software architecture is open and allows great model generality; moreover, the software can be optimized and tailored to specific multibody models in order to obtain good computational efficiency. Integration aspects in Simulink and VRML environments are analyzed.

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