Please use this identifier to cite or link to this item: https://hdl.handle.net/11147/4476
Title: Function generation synthesis of spherical 5R mechanism with regional spacing and Chebyshev approximation
Authors: Kiper, Gökhan
Bilgincan, Tunç
Kiper, Gökhan
Keywords: Function generation synthesis
Chebyshev approximation of bivariate functions
Spherical five bar mechanism
Remez algorithm
Regional spacing
Issue Date: Aug-2015
Publisher: Elsevier Ltd.
Source: Kiper, G., & Tunç, B. (2015). Function generation synthesis of spherical 5R mechanism with regional spacing and Chebyshev approximation. Mechanism and Machine Theory, 90, 37-46. doi:10.1016/j.mechmachtheory.2015.03.001
Abstract: 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 were 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.
URI: http://doi.org/10.1016/j.mechmachtheory.2015.03.001
http://hdl.handle.net/11147/4476
ISSN: 0094-114X
1873-3999
Appears in Collections:Mechanical Engineering / Makina Mühendisliği
Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection

Files in This Item:
File Description SizeFormat 
Function Generation Synthesis of Spherical 5R Mechanism.pdf546.81 kBAdobe PDFThumbnail
View/Open
Show full item record

CORE Recommender

Page view(s)

30
checked on Oct 20, 2021

Download(s)

22
checked on Oct 20, 2021

Google ScholarTM

Check

Altmetric


Items in GCRIS Repository are protected by copyright, with all rights reserved, unless otherwise indicated.