Dynamic Analysis of Mechanical Systems With Time-Varying Topologies: Part 1 — Dynamic Model and Stability Analysis

1990 ◽  
Author(s):  
Yu Wang
Keyword(s):  
Stability Analysis ◽  
Dynamic Model ◽  
Local Stability ◽  
Global Analysis ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Time Varying ◽  
Discrete Equations ◽  
Local Stability Analysis ◽  
Multiple Collisions

Abstract A model is developed for analyzing mechanical systems with a pair of bodies with topological changes in their kinematic constraints. It is built upon the concept of Poincaré map rather than following the traditional methods of differential equations. The model provides a set of well-defined and naturally-discrete equations of motion and is capable of giving physical insights of dynamic characteristics of deadbeat convergence of multiple collisions and periodic or chaotic responses. The development of dynamic model and a local stability analysis are presented in Part 1, and the global analysis and numerical simulation are discussed in Part 2.

scholarly journals Dynamic Modeling and Stability Analysis of Mechanical Systems with Time-Varying Topologies

1993 ◽  
Vol 115 (4) ◽  
pp. 808-816 ◽  
Author(s):  
Yu Wang
Keyword(s):  
Stability Analysis ◽  
Dynamic Modeling ◽  
Local Stability ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Time Varying ◽  
Kinematic Constraints ◽  
Discrete Equations ◽  
Local Stability Analysis ◽  
Multiple Collisions

A model is developed for analyzing mechanical systems with a pair of bodies with topological changes in their kinematic constraints. It is built upon the concept of a Poincare´ map rather than following the traditional methods of differential equations. The model provides a set of well-defined and naturally-discrete equations of motion and is capable of giving physical insights of dynamic characteristics of deadbeat convergence of multiple collisions and periodic or chaotic responses. The development of a dynamic model and a local stability analysis are presented.

scholarly journals Is there a Connection between Local and Global (In-)Stability?

1986 ◽  
Vol 39 (3) ◽  
pp. 331 ◽  
Author(s):  
B Eckhardt ◽  
JA Louw ◽  
W-H Steeb
Keyword(s):  
Stability Analysis ◽  
Hamiltonian Systems ◽  
Local Stability ◽  
Large Scale ◽  
Equations Of Motion ◽  
Riemannian Curvature ◽  
Local Stability Analysis

We review two criteria which have been used to predict the onset of large scale stochasticity in Hamiltonian systems. We show that one of them, due to Toda and based on a local stability analysis of the equations of motion, is inconclusive. An approach based on the local Riemannian curvature K of trajectories correctly predicts chaos if K < 0 everywhere, but�no further conclusions can be drawn. New (counter-)examples are provided.

On the Properties of a Dynamic Model of Flexible Robot Manipulators

1998 ◽  
Vol 120 (1) ◽  
pp. 8-14 ◽  
Author(s):  
Marco A. Arteaga
Keyword(s):  
Dynamic Model ◽  
Structural Properties ◽  
Robot Manipulators ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Control Design ◽  
Flexible Manipulator ◽  
Robot Dynamics ◽  
Flexible Link ◽  
Flexible Robot

Control design of flexible robot manipulators can take advantage of the structural properties of the model used to describe the robot dynamics. Many of these properties are physical characteristics of mechanical systems whereas others arise from the method employed to model the flexible manipulator. In this paper, the modeling of flexible-link robot manipulators on the basis of the Lagrange’s equations of motion combined with the assumed modes method is briefly discussed. Several notable properties of the dynamic model are presented and their impact on control design is underlined.

A Probabilistic Tolerance Allocation Method for Dynamic Mechanical Systems With Periodic Response and Discontinuous Forcing Functions

1995 ◽  
Author(s):  
F. Zhang ◽  
B. J. Gilmore ◽  
A. Sinha
Keyword(s):  
Combustion Engine ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Optimization Procedure ◽  
Tolerance Allocation ◽  
Radial Clearance ◽  
Time Varying ◽  
Link Length ◽  
Design Variables ◽  
Forcing Functions

Abstract Tolerance allocation standards do not exist for mechanical systems whose response are time varying and are subjected to discontinuous forcing functions. Previous approaches based on optimization and numerical integration of the dynamic equations of motion encounter difficulty with determining sensitivities around the force discontinuity. The Alternating Frequency/Time approach is applied here to capture the effect of the discontinuity. The effective link length model is used to model the system and to account for the uncertainties in the link length, radial clearance and pin location. Since the effective link length model is applied, the equations of motion for the nominal system can be applied for the entire analysis. Optimization procedure is applied to the problem where the objective is to minimize the manufacturing costs and satisfy the constraints imposed on mechanical errors and design variables. Examples of tolerance allocation are presented for a single cylinder internal combustion engine.

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