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.

Automatic Generation of Equations of Motion of Mechanical Systems

2014 ◽  
Vol 611 ◽  
pp. 40-45
Author(s):  
Darina Hroncová ◽  
Jozef Filas
Keyword(s):  
Computer Simulation ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Automatic Generation ◽  
Lagrange Equations ◽  
Kinematic Chains ◽  
Transformation Matrices

The paper describes an algorithm for automatic compilation of equations of motion. Lagrange equations of the second kind and the transformation matrices of basic movements are used by this algorithm. This approach is useful for computer simulation of open kinematic chains with any number of degrees of freedom as well as any combination of bonds.

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.

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.

Efficient Dynamic Computer Simulation of Robotic Mechanisms

1982 ◽  
Vol 104 (3) ◽  
pp. 205-211 ◽  
Author(s):  
M. W. Walker ◽  
D. E. Orin
Keyword(s):  
Computer Simulation ◽  
Computational Complexity ◽  
Execution Time ◽  
Digital Computer ◽  
Equations Of Motion ◽  
Kinematic Chain ◽  
Open Loop ◽  
Dynamic Computer Simulation ◽  
Joint Variable

The Newton-Euler formulation of the equations of motion of an open-loop kinematic chain is used within a dynamic computer simulation of a robotic mechanism. Four different methods are presented for obtaining the joint variable accelerations given the joint positions, velocities, and input torques or forces. Each of these methods was programmed in FORTRAN and then executed on a CYBER 175 digital computer. This paper contains a comparison of the computational complexity of these methods and the execution time of the programs which implement them.

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.

Concept development for the optimisation of the Hamburg Wastewater Treatment Plants

2000 ◽  
Vol 41 (9) ◽  
pp. 89-95 ◽  
Author(s):  
G. Ladiges ◽  
N-P. Bertram ◽  
R. Otterpohl
Keyword(s):  
Computer Simulation ◽  
Wastewater Treatment ◽  
Simulation Study ◽  
Storage Capacity ◽  
Wastewater Treatment Plants ◽  
Concept Development ◽  
Final Solution ◽  
Effluent Standards ◽  
Dynamic Computer Simulation ◽  
Traditional Manner

The Hamburger Stadtentwässerung (HSE) is planning to take on a further approximately 250,000 PE in addition to the 1.85 m PE already served by its combined wastewater treatment plants at Köhlbrandhöft/Dradenau. To cope with the increased load, a concept for the extension of the plants had to be developed. Various concepts were compared and evaluated using a dynamic computer simulation. The very wide-ranging simulation study showed that the required effluent standards can still be achieved after the volume of the sludge liquor storage capacity has been increased. As many concepts had been assessed in detail, the final solution chosen was considerably less expensive than if the wastewater treatment plants had been extended in a traditional manner.

scholarly journals A Study of the Stability of a Plate-Like Load Towed beneath a Helicopter

1971 ◽  
Vol 13 (5) ◽  
pp. 330-343 ◽  
Author(s):  
D. F. Sheldon
Keyword(s):  
Equations Of Motion ◽  
Physical Parameters ◽  
Recent Experience ◽  
Wind Tunnel Testing ◽  
Stability Derivatives ◽  
Direct Indication ◽  
Metric Dimensions ◽  
Set Up ◽  
The Stability ◽  
Derivative Information

Recent experience has shown that a plate-like load suspended beneath a helicopter moving in horizontal forward flight has unstable characteristics at both low and high forward speeds. These findings have prompted a theoretical analysis to determine the longitudinal and lateral dynamic stability of a suspended pallet. Only the longitudinal stability is considered here. Although it is strictly a non-linear problem, the usual assumptions have been made to obtain linearized equations of motion. The aerodynamic derivative data required for these equations have been obtained, where possible, for the appropriate ranges of Reynolds and Strouhal number by means of static and dynamic wind tunnel testing. The resulting stability equations (with full aerodynamic derivative information) have been set up and solved, on a digital computer, to give direct indication of a stable or unstable system for a combination of physical parameters. These results have indicated a longitudinal unstable mode for all practical forward speeds. Simultaneously the important stability derivatives were found for this instability and modifications were made subsequently in the suspension system to eliminate the instabilities in the longitudinal sense. Throughout this paper, all metric dimensions are given approximately.

Stability Analysis of a Hydrodynamic Journal Bearing With Rotating Herringbone Grooves

2003 ◽  
Vol 125 (2) ◽  
pp. 291-300 ◽  
Author(s):  
G. H. Jang ◽  
J. W. Yoon
Keyword(s):  
Journal Bearing ◽  
Equations Of Motion ◽  
Fourier Series Expansion ◽  
Algebraic Equations ◽  
High Rotational Speed ◽  
Dynamic Coefficients ◽  
Stiffness Coefficients ◽  
Hydrodynamic Journal Bearing ◽  
The Stability ◽  
Herringbone Grooves

This paper presents an analytical method to investigate the stability of a hydrodynamic journal bearing with rotating herringbone grooves. The dynamic coefficients of the hydrodynamic journal bearing are calculated using the FEM and the perturbation method. The linear equations of motion can be represented as a parametrically excited system because the dynamic coefficients have time-varying components due to the rotating grooves, even in the steady state. Their solution can be assumed as a Fourier series expansion so that the equations of motion can be rewritten as simultaneous algebraic equations with respect to the Fourier coefficients. Then, stability can be determined by solving Hill’s infinite determinant of these algebraic equations. The validity of this research is proved by the comparison of the stability chart with the time response of the whirl radius obtained from the equations of motion. This research shows that the instability of the hydrodynamic journal bearing with rotating herringbone grooves increases with increasing eccentricity and with decreasing groove number, which play the major roles in increasing the average and variation of stiffness coefficients, respectively. It also shows that a high rotational speed is another source of instability by increasing the stiffness coefficients without changing the damping coefficients.

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