Reconfiguration of a four-bar mechanism using phase space connections

Zhang, Jiaying; McInnes, Colin R.

doi:10.1016/j.ymssp.2016.03.024

Cited by 7 publications

(7 citation statements)

References 21 publications

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“…Such balancing is desirable because the ShF and ShM cause vibrations of the supporting frame which latter turn into noise, fatigue, wear, etc. The four-bar mechanism is often taken as example in dynamic balancing because its number of applications [1,2] Dynamic balancing can be performed in two stages. In the first one, the balancing conditions are commonly obtained using methods that involve Cartesian coordinates and the use of angles; this implies the use of trigonometric functions that derive into complex expressions [3][4][5][6].…”

Section: Introductionmentioning

confidence: 99%

Gradient Descent-Based Optimization Method of a Four-Bar Mechanism Using Fully Cartesian Coordinates

et al. 2019

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Machine vibrations often occur due to dynamic unbalance inducing wear, fatigue, and noise that limit the potential of many machines. Dynamic balancing is a main concern in mechanism and machine theory as it allows designers to limit the transmission of vibrations to the frames and base of machines. This work introduces a novel method for representing a four-bar mechanism with the use of Fully Cartesian coordinates and a simple definition of the shaking force (ShF) and the shaking moment (ShM) equations. A simplified version of Projected Gradient Descent is used to minimize the ShF and ShM functions with the aim of balancing the system. The multi-objective optimization problem was solved using a linear combination of the objectives. A comprehensive analysis of the partial derivatives, volumes, and relations between area and thickness of the counterweights is used to define whether the allowed optimization boundaries should be changed in case the mechanical conditions of the mechanism permit it. A comparison between Pareto fronts is used to determine the impact that each counterweight has on the mechanism’s balancing. In this way, it is possible to determine which counterweights can be eliminated according to the importance of the static balance (ShF), dynamic balance (ShM), or both. The results of this methodology when using three counterweights reduces the ShF and ShM by 99.70% and 28.69%, respectively when importance is given to the static balancing and by 83.99% and 8.47%, respectively, when importance is focused on dynamic balancing. Even when further reducing the number of counterweights, the ShF and ShM can be decreased satisfactorily.

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Section: Introductionmentioning

confidence: 99%

Gradient Descent-Based Optimization Method of a Four-Bar Mechanism Using Fully Cartesian Coordinates

et al. 2019

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“…Como es de esperarse, estas fuerzas y estos momentos pueden producir perturbaciones que deben eliminarse para mejorar el rendimiento dinámico del mecanismo. Varios métodos se presentan en la literatura para analizar estas fuerzas y los momentos debido a la inercia [1] [2].…”

Section: Introductionunclassified

Comparación del análisis cinemático y dinámico para un mecanismo de cuatro eslabones utilizando Matlab y MSC ADAMS

Hurel¹,

Rivas²,

Flores³

et al. 2018

Proceedings of the 16th LACCEI International Multi-Conference for Engineering, Education, and Technology: “Innovation in Educat

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The present article has as main objective to model a four-bars mechanism to the drive system of a gel and minerals encapsulating machine. This model includes a kinematic and dynamic analysis using the vector loop method; defining as main input variable the angular displacement of the crank, the same that is connected to the motor. The accelerations in the centers of gravity (kinematic variables) of each element were related to the forces acting on the element. This was done using Newton's second law. Through the dynamic analysis of the mechanism, the necessary torque was determined to move it to the initial kinematic conditions. The torque was calculated using the Matlab software in the force equations for the entire range of motion; this means the complete cycle of movement of the crank. The result of torque obtained in Matlab was contrasted with the simulation software MSC ADAMS, where clear similarities were obtained between both results.

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“…Strategies have also been considered to deal with energy dissipation using a range of control methods. The concept of heteroclinic connections between equal-energy unstable states has also been applied to reconfigure a linked bar mechanism [32].…”

Section: Introductionmentioning

confidence: 99%

Reconfiguration of a smart surface using heteroclinic connections

Zhang

McInnes

2017

Proc. R. Soc. A.

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A reconfigurable smart surface with multiple equilibria is presented, modelled using discrete point masses and linear springs with geometric nonlinearity. An energy-efficient reconfiguration scheme is then investigated to connect equal-energy unstable (but actively controlled) equilibria. In principle, zero net energy input is required to transition the surface between these unstable states, compared to transitions between stable equilibria across a potential barrier. These transitions between equal-energy unstable states, therefore, form heteroclinic connections in the phase space of the problem. Moreover, the smart surface model developed can be considered as a unit module for a range of applications, including modules which can aggregate together to form larger distributed smart surface systems.

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Reconfiguration of a four-bar mechanism using phase space connections

Cited by 7 publications

References 21 publications

Gradient Descent-Based Optimization Method of a Four-Bar Mechanism Using Fully Cartesian Coordinates

Gradient Descent-Based Optimization Method of a Four-Bar Mechanism Using Fully Cartesian Coordinates

Comparación del análisis cinemático y dinámico para un mecanismo de cuatro eslabones utilizando Matlab y MSC ADAMS

Reconfiguration of a smart surface using heteroclinic connections

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