Generalized coordinate partitioning for complex mechanisms based on kinematic substructuring

2015 ◽  
Vol 92 ◽  
pp. 464-483 ◽  
Author(s):  
Kristopher T. Wehage ◽  
Roger A. Wehage ◽  
Bahram Ravani
Keyword(s):  
Complex Mechanisms ◽  
Coordinate Partitioning ◽  
Generalized Coordinate

Efficient Dynamic Computer Simulation of Simple-Closed Spatial Linkages

1990 ◽  
Author(s):  
L. T. Wang
Keyword(s):  
Computer Simulation ◽  
Computational Algorithm ◽  
Equations Of Motion ◽  
Joint Space ◽  
Kinematic Chains ◽  
Spatial Linkages ◽  
Dynamic Computer Simulation ◽  
The Stability ◽  
Coordinate Partitioning ◽  
Generalized Coordinate

Abstract A new method of formulating the generalized equations of motion for simple-closed (single loop) spatial linkages is presented in this paper. This method is based on the generalized principle of D’Alembert and the use of the transformation Jacobian matrices. The number of the differential equations of motion is minimized by performing the method of generalized coordinate partitioning in the joint space. Based on this formulation, a computational algorithm for computer simulation the dynamic motions of the linkage is developed, this algorithm is not only numerically stable but also fully exploits the efficient recursive computational schemes developed earlier for open kinematic chains. Two numerical examples are presented to demonstrate the stability and efficiency of the algorithm.

Design Sensitivity Analysis of Large-Scale Constrained Dynamic Mechanical Systems

1984 ◽  
Vol 106 (2) ◽  
pp. 156-162 ◽  
Author(s):  
E. J. Haug ◽  
R. A. Wehage ◽  
N. K. Mani
Keyword(s):  
Sensitivity Analysis ◽  
Large Scale ◽  
Equations Of Motion ◽  
Design Sensitivity ◽  
Differential Algebraic Equations ◽  
Adjoint Equations ◽  
Design Sensitivity Analysis ◽  
Integration Algorithm ◽  
Coordinate Partitioning ◽  
Generalized Coordinate

A method for computer-aided design sensitivity analysis of large-scale constrained dynamic systems is presented. A generalized coordinate partitioning method is used for assembling and solving sets of mixed differential-algebraic equations of motion and adjoint equations required for calculation of derivatives of dynamic response measures with respect to design variables. The reduction in dimension of the equations of motion and associated adjoint equations obtained through use of generalized coordinate partitioning significantly reduces the computational burden, as compared to methods previously employed. Use of predictor-corrector numerical integration algorithms, rather than an implicit integration algorithm used in the past is shown to greatly simplify the equations that must be formulated and solved. Two examples are presented to illustrate accuracy of the design sensitivity analysis method developed.

A Computational Method for Formulation and Solution of Dynamical Equations for Complex Mechanisms and Multibody Systems

2017 ◽  
Author(s):  
Kristopher Wehage ◽  
Bahram Ravani
Keyword(s):  
Multibody Systems ◽  
Sparse Matrix ◽  
Equations Of Motion ◽  
Schur Complement ◽  
Computational Method ◽  
Dynamical Equations ◽  
Multibody Dynamic ◽  
Sparse Matrix Techniques ◽  
Complex Mechanisms ◽  
Coordinate Partitioning

This paper presents a computational method for formulating and solving the dynamical equations of motion for complex mechanisms and multibody systems. The equations of motion are formulated in a preconditioned form using kinematic substructuring with a heuristic application of Generalized Coordinate Partitioning (GCP). This results in an optimal split of dependent and independent variables during run time. It also allows reliable handling of end-of-stroke conditions and bifurcations in mechanisms, thereby facilitating dynamic simulation of paradoxical linkages such as Bricard’s mechanism that has been known to cause problems with some multibody dynamic codes. The new Preconditioned Equations of Motion are then solved using a recursive formulation of the Schur Complement Method combined with Sparse Matrix Techniques. In this fashion the Preconditioned Equations of Motion are recursively uncoupled and solved one kinematic substructure at a time. The results are demonstrated using examples.

Implicit Numerical Integration of Constrained Equations of Motion Via Generalized Coordinate Partitioning

1992 ◽  
Vol 114 (2) ◽  
pp. 296-304 ◽  
Author(s):  
E. J. Haug ◽  
Jeng Yen
Keyword(s):  
Numerical Integration ◽  
Equations Of Motion ◽  
Integration Algorithm ◽  
Differentiation Formula ◽  
Generalized Coordinates ◽  
Multibody Dynamic ◽  
Constrained Equations ◽  
Automated Simulation ◽  
Coordinate Partitioning ◽  
Generalized Coordinate

An implicit, stiffly stable numerical integration algorithm is developed and demonstrated for automated simulation of multibody dynamic systems. The concept of generalized coordinate partitioning is used to parameterize the constraint set with independent generalized coordinates. A stiffly stable, Backward Differentiation Formula (BDF) numerical integration algorithm is used to integrate independent generalized coordinates and velocities. Dependent generalized coordinates, velocities, and accelerations, as well as Lagrange multipliers that account for constraints, are explicitly retained in the formulation to satisfy all of the governing kinematic and dynamic equations. The algorithm is shown to be valid and accurate, both theoretically and through solution of an example.

A Hybrid Numerical Integration Method for Machine Dynamic Simulation

1986 ◽  
Vol 108 (2) ◽  
pp. 211-216 ◽  
Author(s):  
T. W. Park ◽  
E. J. Haug
Keyword(s):  
Mechanical System ◽  
Dynamic Simulation ◽  
Error Control ◽  
Integration Method ◽  
Differential Algebraic Equations ◽  
Numerical Integration Method ◽  
Algebraic Equations ◽  
Stable Method ◽  
Coordinate Partitioning ◽  
Generalized Coordinate

An efficient and stable method for solving mixed-differential algebraic equations of constrained mechanical system dynamics is presented. The algorithm combines constraint stabilization and generalized coordinate partitioning methods, taking advantage of their attractive speed and error control characteristics, respectively. Three examples are studied to demonstrate efficiency and stability of the method.

Spatial Transient Analysis of Inertia-Variant Flexible Mechanical Systems

1984 ◽  
Vol 106 (2) ◽  
pp. 172-178 ◽  
Author(s):  
A. A. Shabana ◽  
R. A. Wehage
Keyword(s):  
Differential Equations ◽  
Transient Analysis ◽  
Large Scale ◽  
Equations Of Motion ◽  
Integration Algorithm ◽  
System Equations ◽  
Element Technique ◽  
Coordinate Partitioning ◽  
Mode Technique ◽  
Generalized Coordinate

An analytical method for transient dynamic simulation of large-scale inertia-variant spatial mechanical and structural systems is presented. Multibody systems consisting of interconnected rigid and flexible substructures which may undergo large angular rotations are analyzed. A finite element technique is used to characterize the elastic properties of deformable substructures. A component mode technique is then employed to eliminate insignificant substructure modes. Nonlinear holonomic constraint equations are used to define joints between different substructures. The system equations of motion are written in terms of a mixed set of modal and physical coordinates. A generalized coordinate partitioning technique is then employed to eliminate redundant differential equations. An implicit-explicit numerical integration algorithm solves the remaining set of differential equations and the approximate physical system state is recovered. The transient analysis of a spatial vehicle with flexible chassis is presented to demonstrate the method.

Implicit Numerical Integration of Constrained Equations of Motion via Generalized Coordinate Partitioning

1989 ◽  
Author(s):  
E. J. Haug ◽  
J. Yen
Keyword(s):  
Numerical Integration ◽  
Equations Of Motion ◽  
Integration Algorithm ◽  
Generalized Coordinates ◽  
Multibody Dynamic ◽  
Constraint Set ◽  
Constrained Equations ◽  
Automated Simulation ◽  
Coordinate Partitioning ◽  
Generalized Coordinate

Abstract An implicit, stiffly stable numerical integration algorithm is developed and demonstrated for automated simulation of multibody dynamic systems. The concept of generalized coordinate partitioning is used to parameterize the constraint set with independent generalized coordinates. A stiffly stable, backward difference numerical integration algorithm is applied to determine independent generalized coordinates and velocities. Dependent generalized coordinates, velocities, and accelerations, as well as Lagrange multipliers that account for constraints, are explicitly retained in the formulation to satisfy all of the governing kinematic and dynamic equations. The algorithm is shown to be valid and accurate, both theoretically and through solution of a numerical example.

Exneriana – II – The Scientific Legacy of John E. Exner, Jr. 1Part of this paper was presented at the XIXth International Congress of Rorschach and Projective Methods, July 22–26, 2008, Louvain, Belgium.

2008 ◽  
Vol 29 (2) ◽  
pp. 81-107 ◽  
Author(s):  
Anne Andronikof
Keyword(s):  
Clinical Studies ◽  
Experimental Studies ◽  
Scientific Work ◽  
International Congress ◽  
Response Process ◽  
Scientific Legacy ◽  
Projective Test ◽  
Projective Methods ◽  
Comprehensive Picture ◽  
Complex Mechanisms

Based on an analysis of John Exner’s peer-reviewed published work from 1959 to 2007, plus a brief comment for an editorial in Rorschachiana, the author draws a comprehensive picture of the scientific work of this outstanding personality. The article is divided into three sections: (1) the experimental studies on the Rorschach, (2) the clinical studies using the Rorschach, and (3) Exner’s “testament,” which we draw from the last paper he saw published before his death (Exner, 2001/2002). The experimental studies were aimed at better understanding the nature of the test, in particular the respective roles of perception and projection in the response process. These fundamental studies led to a deeper understanding of the complex mechanisms involved in the Rorschach responses and introduced some hypotheses about the intentions of the author of the test. The latter were subsequently confirmed by the preparatory sketches and documents of Hermann Rorschach, which today can be seen at the H. Rorschach Archives and Museum in Bern (Switzerland). Exner’s research has evidenced the notion that the Rorschach is a perceptive-cognitive-projective test.

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