Inverse Dynamics of Constrained Multibody Systems

1990 ◽  
Vol 57 (3) ◽  
pp. 750-757 ◽  
Author(s):  
J. T. Wang
Keyword(s):  
Multibody Systems ◽  
Inverse Dynamics ◽  
Multibody System ◽  
Coefficient Matrix ◽  
Force Term ◽  
Constraint Forces ◽  
Kinematic Constraints ◽  
Constrained Multibody Systems ◽  
Orthogonal Complement Matrix ◽  
Partial Velocity

A method for analyzing constrained multibody systems is presented. The method is applicable to a class of problems in which the multibody system is subjected to both force and kinematic constraints. This class of problems cannot be solved by using the classical methods. The method is based upon the concept of partial velocity and generalized forces of Kane’s method to permit the choice of constraint forces for fulfilling both kinematic and force constraints. Thus, the constraint forces or moments at convenient points or bodies may be specified in any desired form. For many applications, the method also allows analysts to choose a constant coefficient matrix for the undetermined force term to greatly reduce the burden of repeatedly computing its orthogonal complement matrix in solving the differential algebraic dynamic equations. Two examples illustrating the concepts are presented.

A Vector Bond Graph Method of Kineto-Static Analysis for Spatial Multibody Systems

2013 ◽  
Vol 321-324 ◽  
pp. 1725-1729 ◽  
Author(s):  
Zhong Shuang Wang ◽  
Yang Yang Tao ◽  
Quan Yi Wen
Keyword(s):  
Static Analysis ◽  
Multibody Systems ◽  
Degrees Of Freedom ◽  
Multibody System ◽  
Graph Model ◽  
Bond Graph ◽  
Constraint Forces ◽  
Decoupling Method ◽  
Complete Form ◽  
Three Degrees Of Freedom

In order to increase the reliability and efficiency of the kineto-static analysis of complex multibody systems, the corresponding vector bond graph procedure is proposed. By the kinematic constraint condition, spatial multibody systems can be modeled by vector bond graph. For the algebraic difficulties brought by differential causality in system automatic kineto-static analysis, the effective decoupling method is proposed, thus the differential causalities in system vector bond graph model can be eliminated. In the case of considering EJS, the unified formulae of driving moment and constraint forces at joints are derived based on vector bond graph, which are easily derived on a computer in a complete form and very suitable for spatial multibody systems. As a result, the automatic kineto-static analysis of spatial multibody system on a computer is realized, its validity is illustrated by the spatial multibody system with three degrees of freedom.

A Self-Stabilized Algorithm for Enforcing Constraints in Multibody Systems

2003 ◽  
Author(s):  
Olivier A. Bauchau
Keyword(s):  
Multibody Systems ◽  
Convergence Rates ◽  
Multibody System ◽  
Flexible Multibody System ◽  
Constraint Forces ◽  
High Frequencies ◽  
Elastic Forces ◽  
Element Approach ◽  
Index 2 ◽  
Work Done

A new algorithm is developed for the enforcement of constraints within the framework of nonlinear, flexible multibody system modeled with the finite element approach. The proposed algorithm exactly satisfies the constraints at the displacement and velocity levels, and furthermore, it achieves nonlinear unconditional stability by imposing the vanishing of the work done by the constraint forces when combined with specific discretizations of the inertial and elastic forces. Identical convergence rates are observed for the displacements, velocities, and Lagrange multipliers. The proposed algorithm is closely related to the stabilized index-2 or GGL method, although no additional multipliers are introduced in the present approach. These desirable characteristics are obtained without resorting to numerically dissipative algorithms. If high frequencies are present in the system, i.e. the system +is physically stiff, dissipative schemes become necessary; the proposed algorithm is extended to deal with this situation.

Udwadia-Kalaba Approach for Parallel Manipulator Dynamics

2013 ◽  
Vol 135 (6) ◽  
Author(s):  
Jin Huang ◽  
Y. H. Chen ◽  
Zhihua Zhong
Keyword(s):  
Closed Form ◽  
Dynamic Model ◽  
Parallel Manipulator ◽  
Inverse Dynamics ◽  
Equation Of Motion ◽  
Dynamics Analysis ◽  
Constraint Forces ◽  
Kinematic Constraints ◽  
Manipulator Dynamics ◽  
Stewart Gough Platform

A novel Udwadia-Kalaba approach for parallel manipulator dynamics analysis is presented. The approach segments a parallel manipulator system into several leg-subsystems and the platform subsystem, which are connected by kinematic constraints. The Udwadia-Kalaba equation is then used to calculate the constraint forces due to the constraints. Based on this, the equation of motion, which is an explicit (i.e., closed) form, can be formulated. The method allows a systematic procedure to generate the dynamic model for both direct dynamics and inverse dynamics without invoking additional variables (such as multipliers or quasi-variables), nor does it require projection. A classical parallel Stewart-Gough platform is chosen to demonstrate the feasibility and advantages of this approach.

scholarly journals An Orthogonal Complement Matrix Formulation for Constrained Multibody Systems

1994 ◽  
Vol 116 (2) ◽  
pp. 423-428 ◽  
Author(s):  
W. Blajer ◽  
D. Bestle ◽  
W. Schiehlen
Keyword(s):  
Dynamic Analysis ◽  
Multibody Systems ◽  
Reference Frames ◽  
Automatic Generation ◽  
Orthogonal Complement ◽  
Matrix Formulation ◽  
Constraint Matrix ◽  
Constrained Multibody Systems ◽  
Local Reference ◽  
Orthogonal Complement Matrix

A method is proposed for the automatic generation of an orthogonal complement matrix to the constraint matrix for the dynamic analysis of constrained multibody systems. The clue for this method lies in the determination of local constraint matrices and their orthogonal complements relative to the local reference frames of particular constrained points. These matrices are then transformed into the system’s configuration space in order to form the final constraint matrix and its orthogonal complement. The avoidance of singularities in the formulation is discussed. The method is especially suited for the dynamic analysis of multibody systems with many constraints and/or closed-loops.

scholarly journals Recursive Dynamic Algorithm of Open-Chain Multibody System

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Ming Lu ◽  
Wenbin Gu ◽  
Jianqing Liu ◽  
Zhenxiong Wang ◽  
Zhisheng Jing ◽  
...  
Keyword(s):  
Multibody Systems ◽  
Multibody System ◽  
Structural Characteristics ◽  
Open Chain ◽  
Widespread Application ◽  
Dynamic Algorithm ◽  
Generalized Coordinates ◽  
The Relationship ◽  
Kane Method ◽  
Partial Velocity

Open-chain multibody systems have been extensively studied because of their widespread application. Based on the structural characteristics of such a system, the relationship between its hinged bodies was transformed into recursive constraint relationships among the position, velocity, and acceleration of the bodies. The recursive relationships were used along with the Huston-Kane method to select the appropriate generalized coordinates and determine the partial velocity of each body and to develop an algorithm of the entire system. The algorithm was experimentally validated; it has concise steps and low susceptibility to error. Further, the algorithm can readily solve and analyze open-chain multibody systems.

Linearizing the Equations of Motion for Multibody Systems Using an Orthogonal Complement Method

2005 ◽  
Vol 11 (1) ◽  
pp. 51-66 ◽  
Author(s):  
B. Minaker ◽  
P. Frise
Keyword(s):  
Stiffness Matrix ◽  
Multibody Systems ◽  
Multibody System ◽  
Equations Of Motion ◽  
Orthogonal Complement ◽  
Computer Implementation ◽  
Constraint Forces ◽  
Coordinate Vector

The equations of motion of a multibody system are linearized and reduced to independent coordinates, using an orthogonal complement method. The orthogonal complement is used to eliminate the terms that result from a variation of the constraint forces. The resulting equations contain the derivative of the constraint Jacobian with respect to the coordinate vector in the stiffness matrix. The technique is suitable for a computer implementation. Examples are used to illustrate the process.

Optimal Design of Lightweight Machines Using Flexible Multibody System Dynamics

2012 ◽  
Author(s):  
Robert Seifried ◽  
Alexander Held
Keyword(s):  
Energy Efficiency ◽  
Multibody Systems ◽  
Multibody System ◽  
Tracking Error ◽  
Dynamic Loads ◽  
Crucial Issue ◽  
Flexible Multibody ◽  
Dynamical Simulations ◽  
Tracking Behavior ◽  
Robotic Applications

In many machine and robotic applications energy efficiency is an increasingly crucial issue. In order to achieve energy efficiency lightweight structural designs are necessary. However, undesired elastic deformations might occur due to the light wight design. In order to achieve good system performance the actual dynamic loads must be taken into account in the design of the system’s components. In this paper optimization approaches for lightweight machine designs are employed to improve the tracking behavior the systems. Thereby, fully dynamical simulations of flexible multibody systems are coupled with both shape or topology optimization for the elastic members of the multibody system. It is shown, that by these approaches the end-effector trajectory tracking error of light wight manipulators can be decreased significantly.

Trajectory Tracking of Underactuated Multibody Systems

2011 ◽  
Author(s):  
Stefan Reichl ◽  
Wolfgang Steiner
Keyword(s):  
Trajectory Tracking ◽  
Multibody Systems ◽  
Degrees Of Freedom ◽  
Inverse Dynamics ◽  
Feedforward Control ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Differential Algebraic Equations ◽  
State Variables ◽  
Algebraic Equations

This work presents three different approaches in inverse dynamics for the solution of trajectory tracking problems in underactuated multibody systems. Such systems are characterized by less control inputs than degrees of freedom. The first approach uses an extension of the equations of motion by geometric and control constraints. This results in index-five differential-algebraic equations. A projection method is used to reduce the systems index and the resulting equations are solved numerically. The second method is a flatness-based feedforward control design. Input and state variables can be parameterized by the flat outputs and their time derivatives up to a certain order. The third approach uses an optimal control algorithm which is based on the minimization of a cost functional including system outputs and desired trajectory. It has to be distinguished between direct and indirect methods. These specific methods are applied to an underactuated planar crane and a three-dimensional rotary crane.

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