Synthesis of adjustable spherical four-link mechanisms for approximate multi-path generation

Chanekar, Prasad Vilas; Fenelon, Michael A. A.; Ghosal, Ashitava

doi:10.1016/j.mechmachtheory.2013.08.009

Cited by 17 publications

(8 citation statements)

References 23 publications

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“…Lee et al [15] demonstrated a method to synthesize adjustable spherical four-bar mechanisms for two-phase motion generation. Chanekar and Ghosal [16,17] have dealt with optimization based method for synthesis for adjustable planar and spherical four-bar, crank-rocker mechanisms for multiple different and desired paths to be traced by a point on the coupler.…”

Section: Background and Literature Reviewmentioning

confidence: 99%

Analysis of Planar Reconfigurable Motion Generators

Venkataramanujam

Larochelle

2014

Volume 5A: 38th Mechanisms and Robotics Conference

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This article presents the kinematic analysis of a new class of mechanical devices called planar Reconfigurable Motion Generators (RMGs) for multi-phase motion generation tasks having only a slight change in the desired motion. The concepts of configuration matrices and state vectors are introduced as a novel way to represent planar RMGs. The kinematic analysis of a planar RMG in it’s initial configuration to determine the associated adjustable link lengths and angles is discussed. The adjustable link lengths are used to determine the link vector and state vector of a RMG. Future work will involve the application of configuration matrices and state vectors to aid in both systematic analysis and synthesis of RMGs.

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Section: Background and Literature Reviewmentioning

confidence: 99%

Analysis of Planar Reconfigurable Motion Generators

Venkataramanujam

Larochelle

2014

Volume 5A: 38th Mechanisms and Robotics Conference

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“…Although this method can increase the number of solutions, most of the increased linkage solutions still have motion defects, so it does not fundamentally eliminate the blindness of linkage synthesis process. Considering that modern computers can obtain massive solutions quickly and discriminate the defective linkage solutions in turn later (Myszka et al, 2009;Tipparthi and Larochelle, 2011;Bai, 2017), the method of type map (Han and Cao, 2019) is gradually applied in some linkage synthesis software, such as Synthetic (Su and McCarthy, 2005), Lincages (Erdman and Loftness, 2005), Sphinx (the latest version is SphinxPC) (Ruth and McCarthy, 1999;McCarthy, 2013) and the software developed by Han et al (2013). Among them, specially, Sphinx is the first software to solve the spherical G. Wang et al: Computer-aided synthesis of spherical and planar 4R linkages problems.…”

Section: Introductionmentioning

confidence: 99%

Computer-aided synthesis of spherical and planar 4R linkages for four specified orientations

Wang

Zhang

et al. 2019

Mech. Sci.

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Abstract. According to the burmester theory, an infinite number of spherical or planar 4R linkages for a specific four-orientation task can be synthesized, but most of the linkage solutions calculated by this method are invalid because of motion defect, poor performance and others. In order to improve the synthesis efficiency, a program package based on Matlab is developed to find a satisfied linkage solution automatically and quickly. Firstly, the calculation on circle points and the center points based on the burmester theory in spherical problems is introduced. Secondly, the calculation methods of linkage defect discrimination, linkage type classification, linkage performance evaluation and solutions visualization based on the theory of spherical trigonometry are presented respectively. Thirdly, the synthesis calculation of program package is extended to the planar 4R linkage based on the theory of planar analytic geometry. Finally, the examples of the spherical synthesis problem and the planar synthesis problem based on solutions map are introduced to test the program package, the result proves this program package is effective and flexible.

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“…A new algorithm is proposed by Peñuñuri et al for path generation problem of spherical 4R mechanism [32]. A novel optimization based methodology for synthesizing adjustable spherical four-link mechanisms is presented by Chanekar et al [33]. Motion generation synthesis is studied with least square approximation method for spherical linkages by Alizade et al [26].…”

Section: Introductionmentioning

confidence: 99%

Function generation synthesis of spherical 5R mechanism with regional spacing and Chebyshev approximation

Kiper

Bilgincan

2015

Mechanism and Machine Theory

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The Chebyshev approximation is well known to be applicable for the approximation of single input-single output functions by means of a function generator mechanism. The approximation method may be also applied to multi-input functions, although until recently, it was not used for function generation with multi-degrees-of-freedom mechanisms. In a recent study, the authors applied the approximation method to a two-degrees-of-freedom mechanism for the first time, however the selection and iteration of the design points at which the errors were minimized was not satisfactory. In this study, an alternative method of selection and iteration for these design points is introduced and the corresponding spacing is called the "regional spacing". As a case study for the application of the approximation of multi-input functions, a spherical 5R mechanism is used to generate a two input-single-output function. The input joints of the mechanism are selected as one of the fixed joints and the moving mid-joint, whereas the remaining fixed joint represents the output. The synthesis problem is analytically formulated and presented in polynomial form for five and six unknown parameters. The synthesis problem for five unknown parameters is illustrated as a numerical example. Regional spacing is used for the selection and iteration of design points for the synthesis. The Chebyshev approximation along with the Remez algorithm is utilized to find the unknown construction parameters and the error of the function. The design points and the coefficients of the approximation polynomial are determined by numerical iteration using six moving points. At each iteration step, the design points are relocated at the extremum error points in their respective regions. Iterations are repeated until the magnitudes of the extremum point errors are approximately equal. Finally, the construction parameters of the mechanism are determined and the variation of the percentage error between the desired and generated function values is obtained.

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Synthesis of adjustable spherical four-link mechanisms for approximate multi-path generation

Cited by 17 publications

References 23 publications

Analysis of Planar Reconfigurable Motion Generators

Analysis of Planar Reconfigurable Motion Generators

Computer-aided synthesis of spherical and planar 4R linkages for four specified orientations

Function generation synthesis of spherical 5R mechanism with regional spacing and Chebyshev approximation

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