Function Synthesis of the Planar 5R Mechanism Using Least Squares Approximation

Kiper, Gökhan; Bağdadioğlu, Barış; Bilgincan, Tunç

doi:10.1007/978-3-319-06698-1_8

Cited by 3 publications

(4 citation statements)

References 9 publications

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“…If the three conditions given by the inequations ( 14), (15), and ( 16) are fulfilled, the dexterous workspace is singularity-free. To have an analytical solution of the synthesis, each inequation from the inequation system will be substituted through an equation, by imposing a coefficient k > 1.…”

Section: Synthesis Of Symmetrical Five-bar Linkage 5-rrrrr(a)mentioning

confidence: 99%

“…An interesting solution for motion between extreme points is demonstrated in the work done by Nafees et al [13] by using dyadic and triadic concepts. Kiper et al [14, 15] studied the synthesis of a planar five-bar mechanism by using the function generation synthesis with equal spacing and Chebyshev approximation, respectively, by using least squares approximation. In order to develop mechanisms with higher stiffness and low weight Kiper et al [16] proposed, starting from a five-bar linkage, to develop a calibration method for an overconstrained six-bar linkage with 2 DoF.…”

Section: Introductionmentioning

confidence: 99%

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Design of the five-bar linkage with singularity-free workspace

et al. 2023

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This paper shows the kinematic analysis and the synthesis of the five-bar linkage with symmetrical structure and singularity-free dexterous workspace. The type synthesis of the five-bar linkage shows that the number of symmetrical structures of five-bar linkage is limited to eight structures. This study deals with the forward and inverse kinematic analysis and synthesis of the five-bar structure 5-RRRRR. The synthesis equations allow the analytical computation of the link lengths of a symmetrical five-bar linkage using only revolute joints to avoid the singularities in an imposed dexterous workspace. A numerical example of the symmetrical five-bar linkage is analyzed and synthetized theoretically and characterized by computing the performance indices. The tests on an experimental model of the five-bar linkage 5-RRRRR confirm the singularity-free dexterous workspace.

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Section: Synthesis Of Symmetrical Five-bar Linkage 5-rrrrr(a)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Design of the five-bar linkage with singularity-free workspace

et al. 2023

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“…In the least squares approximation method, the aim is to minimize the sum of the squares of the errors at selected design points on the function domain. In [18][19], interpolation approximation is used for bi-variate function generation 2-dof linkages.…”

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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“…We have recently presented several studies on synthesis of 2-dof spherical and planar 5R mechanisms [7,8,9] as a case study of approximate analytical synthesis of multi-dof mechanisms. Specifically in [7] the function synthesis problem for a spherical 5R mechanism is addressed, where one of the fixed joints is an input, the mid-joint is the second input and the remaining fixed joint is the output.…”

Section: Introductionmentioning

confidence: 99%

Function Generation Synthesis with a 2-DoF Overconstrained Double-Spherical 7R Mechanism Using the Method of Decomposition and Least Squares Approximation

Kiper

Bağdadioğlu

2014

New Trends in Mechanism and Machine Science

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Abstract. This study addresses the approximate function generation synthesis with an overconstrained two degrees-of-freedom double spherical 7R mechanism using least squares approximation with equal spacing of the design points on the input domain. The 7R mechanism is a constructed by combining a spherical 5R mechanism with a spherical 4R mechanism with distant centers and a common moving link and then removing the common link. This construction allows the analysis and synthesis of the resulting single-loop mechanism by decomposing it into fictitious 5R and 4R loops. The two inputs to the mechanism are provided in the 5R loop and the output is in the 4R loop. The fictitious output of the 5R loop is an input to the 4R loop this intermediate variable is used to also decompose the function to be generated. This decomposition provides the designer extra freedom in synthesis and enables decreasing the error of approximation. A case study is presented at the end of the study where the 7R design is compared with an equivalent spherical 5R mechanism; hence the advantage of the 7R mechanism is demonstrated.

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Function Synthesis of the Planar 5R Mechanism Using Least Squares Approximation

Cited by 3 publications

References 9 publications

Design of the five-bar linkage with singularity-free workspace

Design of the five-bar linkage with singularity-free workspace

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

Function Generation Synthesis with a 2-DoF Overconstrained Double-Spherical 7R Mechanism Using the Method of Decomposition and Least Squares Approximation

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