scholarly journals Equivalent Electronic Circuit of a System of Oscillators Connected With Periodically Variable Stiffness

2022 ◽  
Author(s):  
Soumyajit Seth ◽  
Grzegorz Kudra ◽  
Krzysztof Witkowski ◽  
Jan Awrejcewicz
Keyword(s):  
Mechanical System ◽  
Electronic Circuit ◽  
Mechanical Design ◽  
Variable Stiffness ◽  
State Variables ◽  
Fixed Point Attractor ◽  
Point Attractor ◽  
Magnetic Resistance ◽  
Nonlinear Behaviors ◽  
Resistance Forces

In this paper, we have shown the electronic circuit equivalence of a mechanical system consists of two oscillators coupled with each other. The mechanical design has the effects of the magnetic, resistance forces and the spring constant of the system is periodically varying. We have shown that the system’s state variables, such as the displacements and the velocities, under the effects of different forces, lead to some nonlinear behaviors, like a transition from the fixed point attractor to the chaotic attractor through the periodic and quasi-periodic attractors. We have constructed the equivalent electronic circuit of this mechanical system and have verified the numerically obtained behaviors using the electronic circuit.

scholarly journals Fault Diagnosis of a High-Speed Cam-Driven Pin Assembly System

2016 ◽  
Vol 2016 ◽  
pp. 1-14 ◽  
Author(s):  
Chi-Cheng Cheng ◽  
Yih-Tun Tseng ◽  
Cheng-Da Wu ◽  
Der-Lin Wang
Keyword(s):  
Mechanical System ◽  
High Speed ◽  
Mechanical Design ◽  
Frequency Responses ◽  
Operation Speed ◽  
Future System ◽  
Electrical Devices ◽  
System Improvement ◽  
Fixture System ◽  
Physical Reasons

A cam-driven mechanical system applied for pin assembly of connectors of electrical devices is studied in this paper. Three cooperative cams are involved in the tasks of approaching, cutting, insertion, and restoring. In order to meet the demanded productivity growth, the operation speed tends to be elevated. However, high running speeds usually cause deficiencies of pin dropping and inaccurate positioning. Diagnosis is therefore conducted to explore their physical reasons so that modification of future mechanical design can be made. Frequency responses of experimental measurements show greater natural frequency and system stiffness caused by nonlinear dynamics for higher operation speed. It also appears that the clamping force is reduced and drift of the locked pin’s location is induced for higher running speed. In addition, separation of the fixture system induced by contact oscillation generates clearance larger than the thickness of the pin. Based on the mathematical models obtained from the technique of system identification, deeper insight of the mechanical system and future system improvement can be highly expected.

A Novel 4D Chaotic System Based on Two Degrees of Freedom Nonlinear Mechanical System

2018 ◽  
Vol 73 (7) ◽  
pp. 595-607 ◽  
Author(s):  
Sezgin Kacar ◽  
Zhouchao Wei ◽  
Akif Akgul ◽  
Burak Aricioglu
Keyword(s):  
Mechanical System ◽  
Chaotic System ◽  
Degrees Of Freedom ◽  
Electronic Circuit ◽  
Chaotic Behaviour ◽  
Two Degrees Of Freedom ◽  
Nonlinear Mechanical System ◽  
Linear Mechanical System ◽  
Low Amplitude ◽  
The Mathematical Model

AbstractIn this study, a non-linear mechanical system with two degrees of freedom is considered in terms of chaos phenomena and chaotic behaviour. The mathematical model of the system was moved to the state space and presented as a four dimensional (4D) chaotic system. The system’s chaotic behaviour was investigated by performing dynamic analyses of the system such as equilibria, Lyapunov exponents, bifurcation analyses, etc. Also, the electronic circuit realisation is implemented as a real-time application. This system exhibited vibration along with noise-like behaviour because of its very low amplitude values. Thus, the system is scaled to increase the amplitude values. As a result, the electronic circuit implementation of the 4D chaotic system derived from the model of a physical system is realised.

EFFECT OF DISSIPATION ON THE HAMILTONIAN CHAOS IN COUPLED OSCILLATOR SYSTEMS

2002 ◽  
Vol 12 (04) ◽  
pp. 859-867 ◽  
Author(s):  
V. SHEEJA ◽  
M. SABIR
Keyword(s):  
Degrees Of Freedom ◽  
Chaotic Behavior ◽  
Period Doubling ◽  
Dissipation Function ◽  
Hamiltonian Chaos ◽  
Fixed Point Attractor ◽  
Point Attractor ◽  
Route To Chaos ◽  
Period Doubling Bifurcations ◽  
External Driving

We study the effect of linear dissipative forces on the chaotic behavior of coupled quartic oscillators with two degrees of freedom. The effect of quadratic Rayleigh dissipation functions, one with diagonal coefficients only and the other with nondiagonal coefficients as well are studied. It is found that the effect of Rayleigh Dissipation function with diagonal coefficients is to suppress chaos in the system and to lead the system to its equilibrium state. However, with a dissipation function with nondiagonal elements, other types of behaviors — including fixed point attractor, periodic attractors and even chaotic attractors — are possible even when there is no external driving. In such a system the route to chaos is through period-doubling bifurcations. This result contradicts the view that linear dissipation always causes decay of oscillations in oscillator models.

The Optimum Design of Spatial Frames Using the Method of Constrained Steepest Descent With State Equations

1971 ◽  
Vol 93 (4) ◽  
pp. 1261-1267 ◽  
Author(s):  
D. L. Bartel ◽  
E. J. Haug ◽  
Kwan Rim
Keyword(s):  
Nonlinear Programming ◽  
Mechanical Design ◽  
The State ◽  
Steepest Descent ◽  
Mathematical Programming Problem ◽  
State Variables ◽  
State Equations ◽  
Design Problems ◽  
Out Of Plane ◽  
Plane Frames

This paper considers the design of a class of spatial frames which occur frequently in mechanical systems: plane frames with out-of-plane loads. The design objective is to minimize the weight subject to constraints on stress and geometry. The method of constrained steepest descent with state equations is introduced to solve the resulting mathematical programming problem. This method differs from the usual methods of nonlinear programming in that the state variables and the state equations are used explicitly in the formulation. This results in a natural matching of the essential features of the design problem and the method used to obtain its solution. The method is effective and general in that it can be readily applied to a wide variety of design problems which occur in mechanical design.

Structural Design and Model Establishment of Reducer Device

2012 ◽  
Vol 160 ◽  
pp. 381-385
Author(s):  
Hui Guo ◽  
Zhi Hua Gao ◽  
Xiao Jing Li ◽  
Pei Xin Qu
Keyword(s):  
Mechanical System ◽  
Dynamic Simulation ◽  
Structural Design ◽  
Mechanical Design ◽  
Three Dimensional ◽  
Technical Analysis ◽  
Modeling Processes ◽  
Component Model ◽  
Full Model ◽  
Movement Mechanism

The reducer device is a complicated mechanical system composed by several important components, which should establish model before manufacture and carry out dynamic simulation of movement mechanism. It could assemble component model into mechanical system by using the assembly module of Solidworks. Compared with three-dimensional assembly modeling processes that was created by the traditional CAD. This study has calculated and listed the key parameters of mechanical design and established a full model of assembly. The resulting model contribute to technical analysis for future manufacture.

scholarly journals Self-Stabilising Quadrupedal Running by Mechanical Design

2009 ◽  
Vol 6 (1) ◽  
pp. 73-85 ◽  
Author(s):  
Panagiotis Chatzakos ◽  
Evangelos Papadopoulos
Keyword(s):  
Mechanical System ◽  
Mechanical Design ◽  
Quadruped Robot ◽  
The Self ◽  
Rough Terrain ◽  
Stable Regime ◽  
Quadruped Robots ◽  
The Stability ◽  
Running Robots ◽  
Body Inertia

Dynamic stability allows running animals to maintain preferred speed during locomotion over rough terrain. It appears that rapid disturbance rejection is an emergent property of the mechanical system. In running robots, simple motor control seems to be effective in the negotiation of rough terrain when used in concert with a mechanical system that stabilises passively. Spring-like legs are a means for providing self-stabilising characteristics against external perturbations. In this paper, we show that a quadruped robot could be able to perform self-stable running behaviour in significantly broader ranges of forward speed and pitch rate with a suitable mechanical design, which is not limited to choosing legs spring stiffness only. The results presented here are derived by studying the stability of the passive dynamics of a quadruped robot running in the sagittal plane in a dimensionless context and might explain the success of simple, open loop running controllers on existing experimental quadruped robots. These can be summarised in (a) the self-stabilised behaviour of a quadruped robot for a particular gait is greatly related to the magnitude of its dimensionless body inertia, (b) the values of hip separation, normalised to rest leg length, and leg relative stiffness of a quadruped robot affect the stability of its motion and should be in inverse proportion to its dimensionless body inertia, and (c) the self-stable regime of quadruped running robots is enlarged at relatively high forward speeds. We anticipate the proposed guidelines to assist in the design of new, and modifications of existing, quadruped robots. As an example, specific design changes for the Scout II quadruped robot that might improve its performance are proposed.

Nonlinear Design-for-Control: Deploying Nonlinearity for Useful Purposes

2001 ◽  
Author(s):  
Douglas E. Adams
Keyword(s):  
Mechanical Design ◽  
Good Reason ◽  
Feedback Loops ◽  
Nonlinear Characteristics ◽  
Nonlinear Design ◽  
Nonlinear Mechanical ◽  
Design For Control ◽  
Potential Benefits ◽  
Nonlinear Behaviors ◽  
Destructive Behaviors

Abstract Nonlinearity can be beneficial. It can enhance/degrade system performance, strengthen/weaken linear systems, and give rise to extraordinarily constructive/destructive behaviors. In spite of these potential benefits, engineers have historically neglected and/or removed nonlinearity when designing, analyzing, and controlling mechanical systems for good reason. This paper examines the notion of nonlinear mechanical design-for-control in the context of common applications where nonlinearity enhances performance in some way. Examples of how general nonlinear characteristics and specific nonlinear behaviors have been used in engineering applications are given. A framework for carrying out design optimization with reconfigurable nonlinear mechanical feedback loops is also discussed.

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