Function generation by Galerkin's method

Akcali, Ibrahim Deniz; Dittrich, Günter

doi:10.1016/0094-114x(89)90081-5

Cited by 14 publications

(7 citation statements)

References 9 publications

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“…-0.00055926 Singh et al 2005 Four-bar mechanism y = sin(x) 0°≤ x ≤ 90° -0.012573 y = tan(x) 0°≤ x ≤ 45° -0.004634 y = e x 0 ≤ x ≤ 1 -0.000489 y = ln(x) 1 ≤ x ≤ 2 0.002359 Akçalı and Dittrich 1989 Four-bar mechanism y = sin(x) 0°≤ x ≤ 90° -0.0630 y = tan(x) 0°≤ x ≤ 45° -0.0015 Jaiswal and Jawale 2018…”

Section: Conflicts Of Interestmentioning

confidence: 99%

“…With the evolution of computers, many analytical methods have been developed, and they approximately express the desired function. Therefore, the structural error function which is the difference between the desired function and the function produced by a mechanism is taken into account and minimized using mathematical approaches depending on iteration such as the precision point method (Akçalı and Dittrich 1989), sub-domain method (Dhingra et al 2000a), galerkin method (Hartenberg and Denavit 1964) and the leastsquares method (Nolle 1997;Singh et al 2005). Here, the most important factor in minimizing the structural error is the excess number of unknown parameters of a mechanism.…”

Section: Introductionmentioning

confidence: 99%

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Optimal synthesis of function-generating slider-crank mechanism based on a closed-form solution using five design parameters

Mutlu¹,

Soliman²

2021

Turkish Journal of Engineering

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Kinematic dimensional synthesis is one of the essential steps during the process of design. It is classified into three tasks: function generation, path generation, and motion generation. In this paper, a design method is presented to solve the synthesis of the slider-crank mechanism for function generation based on a closed-form solution with five design parameters. The success criterion of a method used for function generation depends on the structural error function within an operational domain of the slider-crank mechanism. The structural error reduction is related to the number of design parameters utilized in mechanism synthesis, and the effective maximum number of design parameters for the slider-crank mechanism is five. In this study, the closed-form synthesis is found using three methods: precision point method, sub-domain method, and galerkin method. The system of equations is reduced to a twelfth-degree univariate polynomial equation, and thus all the available solutions are obtained. The effectiveness of this design method is tested with some examples of commonly used test functions, namely ex, sin(x), tan(x) and ln(x), using a developed computer program. This design method gives lower structural error than traditional methods in kinematics literature.

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Section: Conflicts Of Interestmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Optimal synthesis of function-generating slider-crank mechanism based on a closed-form solution using five design parameters

Mutlu¹,

Soliman²

2021

Turkish Journal of Engineering

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“…The methods have different names like galerkin, least square, accuracy points according to the mathematical approaches used when the error function is minimized. Bahmyari, Khedmati and Soares (2017) is example for galerkin method; Akcali and Dittrich (1989), Ramírez, Nogueir, Khelladi, Chassaing and Colominas (2014) can be given as example for the least squares method; for accuracy point method Diab and Smaili (2008), Jaiswal and Jawale (2017) can be shown.…”

Section: Introductionmentioning

confidence: 99%

Design of a New Bed Base Mechanism System

Mutlu¹,

Yapanmış²

2017

Uluslararası Muhendislik Arastirma Ve Gelistirme Dergisi

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In daily life, most of the devices, machines and furniture, which we use in our homes and make our life easier, have many different opening and closing systems. Some criteria may be required for the opening/closing shape of systems. For example, in some systems, it may be desirable that opened part uses minimum volume, facilitates daily life, or the system is balanced in each opening position. Those type of opening and closing systems are widely used sofa beds, seats and bed bases in the furniture sector. Many opening/closing systems have various locking mechanisms which are used to ensure opened final position or in some cases it is held in the final position by the force of the human arm. In this study, a kinematic analysis was carried out to design a base mechanism which could be stabilized at every position instead of the final position, and a virtual prototype was made.

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“…Several methods can already be seen in the citations above. In addition, Southerland and Roth [22] utilized an improved least-squares method, Chen and Chan [23] applied Marquardt's compromise technique, Sarganachari [24] a variable topology approach, Norouzi [25] used a gradientbased SQP method, and Akcali and Dittrick used Gelerkin's Method [26]. This paper presents a technique for reducing the structural error in function generating mechanisms via the addition of large numbers of four-bars.…”

Section: Introductionmentioning

confidence: 99%

Reducing Structural Error in Function Generating Mechanisms via the Addition of Large Numbers of Four-Bar Mechanisms

Hessein¹

2017

Preprint

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This paper presents a methodology for synthesizing planarlinkages to approximate any prescribed periodic function. Themechanisms selected for this task are the slider-crank and thegeared five-bar with connecting rod and sliding output (GFBS),where any number of drag-link (or double crank) four-bars areused as drivers. A slider-crank mechanism, when comparing theinput crank rotation to the output slider displacement, producesa sinusoid-like function. Instead of directly driving the inputcrank, a drag-link four-bar may be added that drives the crankfrom its output via a rigid connection between the two. Drivingthe input of the added four-bar results in a function that is lesssinusoid-like. This process can be continued through the additionof more drag-link mechanisms to the device, slowly alteringthe curve toward any periodic function with a single maximum.For periodic functions with multiple maxima, a GFBS is usedas the terminal linkage added to the chain of drag-link mechanisms.The synthesis process starts by analyzing one period ofthe function to design either the terminal slider-crank or terminalGFBS. A randomized local search is then conducted as thefour-bars are added to minimize the structural error between thedesired function and the input-output function of the mechanism.Mechanisms have been “grown” in this fashion to dozens of linksthat are capable of closely producing functions with a variety ofintriguing features.

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Function generation by Galerkin's method

Cited by 14 publications

References 9 publications

Optimal synthesis of function-generating slider-crank mechanism based on a closed-form solution using five design parameters

Optimal synthesis of function-generating slider-crank mechanism based on a closed-form solution using five design parameters

Design of a New Bed Base Mechanism System

Reducing Structural Error in Function Generating Mechanisms via the Addition of Large Numbers of Four-Bar Mechanisms

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