Reduced number of design parameters in optimum path synthesis with timing of four-bar linkage

Buśkiewicz, Jacek

doi:10.15632/jtam-pl.56.1.43

Cited by 12 publications

(10 citation statements)

References 46 publications

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“…The asteroid is the desired trajectory for this example when uniformly sampled by 40 discrete points [6]. The parametric equation for this curve is defined as x t ð Þ = 5cos 3 (2pt), y t ð Þ = 5sin 3 (2pt), t = 0, 1 ½ .…”

Section: Example 3 (Asteroid)mentioning

confidence: 99%

“…5 The solving methods for such problems in the literature can mainly vary based on the type of mechanism, the path geometry, the nature of the problem, etc. 6 The nature of the problem can be classified into two main categories: prescribed timing and non-prescribed timing problems. The term ''prescribed timing'' refers to a oneto-one correspondence between the input crank angle and each point of the desired trajectory.…”

Section: Introductionmentioning

confidence: 99%

“…That is why researchers have explored different optimization algorithms such as genetic algorithms, particle swarm optimization, hybrid optimization techniques, and so on. 6,[8][9][10] Structural error is one of the most common bases for the objective function of path optimization problems which is based on a point-to-point comparison between the desired and generated trajectories. 11,12 Finding the global optimum of such a highly nonlinear objective function is difficult and depends upon the initial guesses.…”

Section: Introductionmentioning

confidence: 99%

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Modified Shadow Robot Control method for optimal path synthesis of mechanisms: Application to five-link mechanism

Vali

Beigzadeh

Haghjoo

2023

Proceedings of the Institution of Mechanical Engineers, Part C:

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For optimal path synthesis of a mechanism with a single degree of freedom (DOF), a powerful method called Shadow Robot Control (SRC) has been recently proposed in the literature. However, this method is restricted to synthesis problems with prescribed timing (i.e. problems in which a particular input crank angle is associated with each point of the desired trajectory). In this paper, the SRC method was elaborated and modified to be capable of synthesizing both prescribed and nonprescribed timing problems. For this purpose, a new structure of contour error and objective function estimation was presented. As a result, there is no need to consider the input angles (crank angles) corresponding to desired path points as optimization parameters, even for non-prescribed timing problems. This prevents unnecessarily enlarging the search space, providing a more effective and robust optimization method (with respect to initial guess). The synthesis of a geared five-link mechanism was used to detail the proposed algorithm as a case study. Despite the five-link mechanism capability and simplicity of generating a complicated trajectory, this single DOF path generator seems less investigated in the literature. Few existing numerical problems of the five-link mechanism in the literature were solved. The comparison of the results shows the effective performance of the proposed algorithm in synthesizing the mechanism.

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Section: Example 3 (Asteroid)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Modified Shadow Robot Control method for optimal path synthesis of mechanisms: Application to five-link mechanism

Vali

Beigzadeh

Haghjoo

2023

Proceedings of the Institution of Mechanical Engineers, Part C:

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“…They applied the technique instead of traditional penalty functions and demonstrated that TLBO revealed the best performance. Bu skiewicz 41 introduced a one-step method for optimizing the open-path generation of the four-bar mechanism with timing. An objective function is defined to reduce the number of the design variables to six.…”

Section: Introductionmentioning

confidence: 99%

Geometrical Similarity Error Function-Innovative Adaptive Algorithm methodology in path generation synthesis of the four-bar mechanism using metaheuristic algorithms

Sardashti

Daniali

Varedi-Koulaei

2021

Proceedings of the Institution of Mechanical Engineers, Part C:

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This paper presents a novel methodology for path generation synthesis of the four-bar mechanism. A new objective function for the path generation synthesis problem, namely, the Geometrical Similarity Error Function (GSEF), is introduced. Indeed, GSEF assesses the similarity between generated and desired paths, and its number of design variables is less than those in the other synthesis methods. Then, using an Innovative Adaptive Algorithm (IAA), some operators are utilized for matching two similar paths. GSEF-IAA methodology has some significant advantages over the reported synthesis methods. The method is fast, takes much less CPU time, and saves a large amount of computer memory. Four path generation problems are solved using GSEF-IAA, and the results are compared with those of previous methods using some well-known optimization algorithms to demonstrate the efficiency of GSEF-IAA methodology.

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“…Bai et al (2020) studied a single-degree-of-freedom 10-bar mechanism to track 10 exact positions. Among the above three kinds of mechanism synthesis problems, the path generation of four-bar linkages is the most challenging problem (Wampler et al, 1992;Khan et al, 2015;Buskiewicz, 2018) because of the complexity of the path synthesis equation. To solve path synthesis equations, various methods were attempted, such as the homotopy method, the evolutionary algorithm, and the Fourier algorithm (Morgan and Wampler, 1990;Cabrera et al, 2011;Guigue and Hayes, 2016).…”

Section: Introductionmentioning

confidence: 99%

Mixed synthesis method of motion and path of planar four-bar linkages

Wu¹,

Li²,

Liang³

et al. 2021

Mech. Sci.

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Abstract. The mixed synthesis of motion and path generation, which is also known as the Alt–Burmester problem, is an attractive problem for study. However, such a problem for the four-bar linkages which possess more than M poses (M>5) and mixed N path points has not been well-solved. In this work, a mixed synthesis method is developed for planar four-bar linkages to cope with the above problem. The developed method can quickly select an optimal combination that contains five poses and N points by using the conic filtering algorithm, which is based on the similar characteristics of the value and direction between the conic and coupler curves in a certain neighborhood. Next, the selected five poses are substituted into a simplified equation system of motion synthesis which includes four equations and four variables to solve the parameters of the planar four-bar linkage. Finally, a case is provided to validate the effectiveness of the developed method in the mixed synthesis problem.

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Reduced number of design parameters in optimum path synthesis with timing of four-bar linkage

Cited by 12 publications

References 46 publications

Modified Shadow Robot Control method for optimal path synthesis of mechanisms: Application to five-link mechanism

Modified Shadow Robot Control method for optimal path synthesis of mechanisms: Application to five-link mechanism

Geometrical Similarity Error Function-Innovative Adaptive Algorithm methodology in path generation synthesis of the four-bar mechanism using metaheuristic algorithms

Mixed synthesis method of motion and path of planar four-bar linkages

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