Some improvements on the exact kinematic synthesis of spherical 4R function generators

Cervantes-Sánchez, J. Jesús; Medellín-Castillo, Hugo I.; Rico-Martínez, José M.; González-Galván, Emilio J.

doi:10.1016/j.mechmachtheory.2008.02.007

Cited by 18 publications

(12 citation statements)

References 16 publications

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“…The dimensions are given by the angle between adjacent joint axes, The relationship between the input and output angles can be easily derived. According to (Cervantes-Sánchez, et al, 2009a, 2009b …”

Section: Four-bar Function Generating Spherical Mechanismmentioning

confidence: 99%

“…The synthesis of such a function generating mechanism has been extensively studied, and many analytical (Rasim and Özgür, 2005, Zimmerman, 1967, Chiang, 1988, Cervantes-Sánchez, et al, 2009a, 2009b and optimization synthesis methods (Liu and Angeles, 1992, Gosselin and Angeles, 1989, Wang, et al, 2004 have been proposed. In general, the two types of synthesis methods can effectively reduce the motion error in a deterministic sense, in which the motion error is viewed as the difference between the actual motion output and the desired motion output without considering any uncertainty.…”

Section: Introductionmentioning

confidence: 99%

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Reliability analysis of spherical function generating mechanisms

Zhang

2014

JAMDSM

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Spherical mechanisms are widely used in engineering applications. Minimizing their motion error is critical for high performance of such mechanisms. The motion error is significantly affected by uncertainties in spherical mechanisms. The impact of the uncertainties on the motion error, however, is rarely considered in mechanism analysis and synthesis. In this work, we quantify the effects of randomness in the major mechanism dimension variables on the motion error through kinematic reliability with a probabilistic approach. Two types of reliability, the point kinematic reliability and the interval kinematic reliability, are discussed. For the former the First Order Second Moment (FOSM) method is employed while for the latter a multiple-extreme-value method is proposed to maintain high accuracy. The Monte Carlo simulation (MCS) is performed as a benchmark for the accuracy comparison. The effectiveness of the proposed method is demonstrated with two examples.

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Section: Four-bar Function Generating Spherical Mechanismmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Reliability analysis of spherical function generating mechanisms

Zhang

2014

JAMDSM

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“…Several methods were proposed to design spherical four-bar mechanisms through kinematic synthesis procedures for function generation [5,6,7]. Best design is considered to be the one that results in smaller amount of errors for the desired function.…”

Section: Introductionmentioning

confidence: 99%

Alternating Error Effects on Decomposition Method in Function Generation Synthesis

Maaroof

Dede

Kiper

2016

New Trends in Mechanism and Machine Science

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Abstract. In approximate function generation synthesis methods, error between the desired function's output and designed mechanism's output oscillate about zero error while crossing the zero error margin at precision points. The common goal of these methods is to minimize the error within the selected working region of the mechanism. For mechanisms like Bennett overconstrained six-revolute jointed linkages that have relatively large number of construction parameters, it is a difficult task to solve for them at once. Decomposition method enables to divide such linkages into two loops and independently solve for each loop with less construction parameters. Although some approximation methods are proven to produce smaller errors than others for a single-loop synthesis, in this work, it is shown that smaller errors are not guaranteed for a certain method when used along with decomposition method. Numerical examples indicate that in decomposition method, more attention should be given to the alternation of the error of each decomposed mechanism, rather than the approximation method used.

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“…Hartenberg and Denavit (1964) and Zimmerman (1967) have respectively presented the three-and four-precision-point function generation of the SFBM. Cervantes-Sánchez et al (2009a) have worked on formulation of the function synthesis problem of the SFBM for three and four precision points and further presented formulations for five and six precision points (Cervantes-Sánchez et al, 2009b). Rao et al (1973), Farhang et al (1988Farhang et al ( , 1999, Alizade et al (1994Alizade et al ( , 2005 and Murray and McCarthy (1995) used polynomial approximation method for three, four and five precision points for the function synthesis of the SFBM.…”

Section: Introductionmentioning

confidence: 99%

Function synthesis of Bennett 6R mechanisms using Chebyshev approximation

Alizade

Kiper

Bağdadioğlu

et al. 2014

Mechanism and Machine Theory

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This study focuses on approximate function synthesis of the three types of overconstrained Bennett 6R mechanisms using Chebyshev approximation. The three mechanisms are the double-planar, double-spherical and the plano-spherical 6R linkages. The single-loop 6R mechanisms are dissected into two imaginary loops and function synthesis is performed for both loops. First, the link lengths are employed as construction parameters of the mechanism. Then extra construction parameters for the input or output joint variables are introduced in order to increase the design points and hence enhance the accuracy of approximation. The synthesis formulations are applied computationally as case studies. The case studies illustrate how a designer can compare the three types of Bennett 6R mechanisms for the same function. Also we present a comparison of the spherical four-bar with the double-spherical 6R mechanism and show that the accuracy is improved when the 6R linkage is used.

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Some improvements on the exact kinematic synthesis of spherical 4R function generators

Cited by 18 publications

References 16 publications

Reliability analysis of spherical function generating mechanisms

Reliability analysis of spherical function generating mechanisms

Alternating Error Effects on Decomposition Method in Function Generation Synthesis

Function synthesis of Bennett 6R mechanisms using Chebyshev approximation

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