Inverted Slider-Crank Mechanism Driven by Hydraulic Cylinder: Transfer Functions and Approximations

Krasimir Ganchev

doi:doi:10.11648/j.engmath.20220601.11

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Inverted Slider-Crank Mechanism Driven by Hydraulic Cylinder: Transfer Functions and Approximations

Krasimir Ganchev

Published in Engineering Mathematics (Volume 6, Issue 1)

Received: 22 March 2022 Accepted: 15 April 2022 Published: 26 April 2022

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Abstract

Inverted slider-crank mechanisms driven by hydraulic cylinder have highly non-linear transfer functions, which in this form complicate kinematic and dynamic researches. A central slider-crank mechanism scheme is used with the specific small parameter equal to the ratio of the lengths of both links of the revolute pair of the mechanism (λ=R/L<1). The present study considers the two main transfer functions of the mechanism. In the first case the angle of the revolute pair as an independent parameter is accepted and in the second case the linear motion of the hydraulic cylinder as an independent parameter is accepted. The exact transfer functions of the mechanism are described and approximate representations of the transfer functions are found. In the first case we use a binomial order of the degrees of the small parameter calculated up to 4-th degree and very high accuracy of approximate function has been achieved (maximal error less than 1.6%). In the second case we use a trigonometric function, which corresponds to the exact transfer function up to second derivative, and the accuracy is also high (error less than 2%) in the main operating range. The power characteristics of the inverted slider-crank mechanism driven by hydraulic cylinder are determined using the transfer functions. All main conclusions are interpreted by geometrical representations.

Published in	Engineering Mathematics (Volume 6, Issue 1)
DOI	10.11648/j.engmath.20220601.11
Page(s)	1-5
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Inverted Slider-Crank Mechanism, Transfer Functions, Small Parameter, Approximation

References

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[3]	Hao W. (2011). Analysis report of 2010 excavator market in China,” Construction Machinery Technology & Management, vol. 2, article 23.
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[5]	Xu J. & Yoon H-S. (2016). A Review on Mechanical and Hydraulic System Modeling of Excavator Manipulator System. Journal of Construction Engineering. Volume 2016 \|Article ID 9409370 \| https://doi.org/10.1155/2016/9409370.
[6]	Gnasa U., Thielecke K., Modler K-H & Richter E-R. (1999). Design and development of a hydraulic manipulator with mechanism/Pro. International ADAMS users’ Conference, Berlin, 17-18 Nov 1999.
[7]	Mitrev R. (2015). Web Based Enviroment fod Design and Analysis of Hydraulic Escavator. Journal of Multidisciplinary Engineering Science and Technology (JMEST). Vol. 2 Issue 12, December – 2015. ISSN: 3159-0040.
[8]	Patel D., Patel B. & Patel M. (2015). A Critical Review on Kinematics of Hydraulic Excavator Backhoe Attachment. Int. J. Mech. Eng. & Rob. Res. Vol. 4, No. 2, April 2015. ISSN 2278 – 0149.
[9]	Silva R., Nunes M., Bento J. & Costa V. (2013). Modelling an Inverted Slider Crank Mechanism Considering Kinematic Analysis and Multibody Aspects. Proceedings of the XV International Symposium on Dynamic Problems of Mechanics (DINAME 2013), February 17-22, Buzios, RJ, Brazil.
[10]	Almestri S., Murrav A., Myzska D. & Wampler C. (2016). Singularity Traces of Single Degree-of-Freedom Planar Linkages that Include Prismatic and Revolute Joints. Journal of Mechanisms and Robotics 8 (5), Dec. 2016 DOI: 10.1115/1.4032410.
[11]	Williams R. Mechanism Kinematics and Dynamics (2021). on-line NotesBook Supplement. 119 p. Available at: https://www.ohio.edu/mechanical-faculty/williams/html/PDF/Supplement3011.pdf.
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[13]	Zhang Y. (2019). Design and synthesis of mechanical systems with coupled units. Mechanical engineering [physics.class-ph]. INSA de Rennes. English. NNT: 2019ISAR0004.
[14]	Janošević D., Mitrev R. & Marinkovic D. (2017). Dynamical modelling of hydraulic excavator considered as a multibody system. Tehnicki Vjesnik 24, Sept. 2017 (Suppl- 2): 327-338 DOI: 10.17559/TV-20151215150306.
[15]	Hu J. & Yoon H-S. (2016). A Review on Mechanical and Hydraulic System Modeling of Excavator Manipulator System. Journal of Construction Engineering. Jan. 2016 (3): 1-11. DOI: 10.1155/2016/9409370.
[16]	Batchvarov S., Kalenski P., Ganchev K. (1987). Dynamics of an antropomorphic robot with three degrees of freedom. Proceedings of the 7th World Congress of The theory of machines and mechanisms, 17-22 Sept 1987, Sevilla Spain, Proceedings p. 1071-74.
[17]	Ganchev K. (1989). Dynamical investigation of manipulation systems with inverted slider-crank mechanism driven by a hydraulic cylinder. Dissertation, Sofia (into Bulgarian).
[18]	Erdman A. (1992). Modern Kinematics: Development in the last forty years, John Wiley & Sons Inc., 608 p.

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APA Style

Krasimir Ganchev. (2022). Inverted Slider-Crank Mechanism Driven by Hydraulic Cylinder: Transfer Functions and Approximations. Engineering Mathematics, 6(1), 1-5. https://doi.org/10.11648/j.engmath.20220601.11

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ACS Style

Krasimir Ganchev. Inverted Slider-Crank Mechanism Driven by Hydraulic Cylinder: Transfer Functions and Approximations. Eng. Math. 2022, 6(1), 1-5. doi: 10.11648/j.engmath.20220601.11

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AMA Style

Krasimir Ganchev. Inverted Slider-Crank Mechanism Driven by Hydraulic Cylinder: Transfer Functions and Approximations. Eng Math. 2022;6(1):1-5. doi: 10.11648/j.engmath.20220601.11

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@article{10.11648/j.engmath.20220601.11,
  author = {Krasimir Ganchev},
  title = {Inverted Slider-Crank Mechanism Driven by Hydraulic Cylinder: Transfer Functions and Approximations},
  journal = {Engineering Mathematics},
  volume = {6},
  number = {1},
  pages = {1-5},
  doi = {10.11648/j.engmath.20220601.11},
  url = {https://doi.org/10.11648/j.engmath.20220601.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.engmath.20220601.11},
  abstract = {Inverted slider-crank mechanisms driven by hydraulic cylinder have highly non-linear transfer functions, which in this form complicate kinematic and dynamic researches. A central slider-crank mechanism scheme is used with the specific small parameter equal to the ratio of the lengths of both links of the revolute pair of the mechanism (λ=R/L). The present study considers the two main transfer functions of the mechanism. In the first case the angle of the revolute pair as an independent parameter is accepted and in the second case the linear motion of the hydraulic cylinder as an independent parameter is accepted. The exact transfer functions of the mechanism are described and approximate representations of the transfer functions are found. In the first case we use a binomial order of the degrees of the small parameter calculated up to 4-th degree and very high accuracy of approximate function has been achieved (maximal error less than 1.6%). In the second case we use a trigonometric function, which corresponds to the exact transfer function up to second derivative, and the accuracy is also high (error less than 2%) in the main operating range. The power characteristics of the inverted slider-crank mechanism driven by hydraulic cylinder are determined using the transfer functions. All main conclusions are interpreted by geometrical representations.},
 year = {2022}
}

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TY  - JOUR
T1  - Inverted Slider-Crank Mechanism Driven by Hydraulic Cylinder: Transfer Functions and Approximations
AU  - Krasimir Ganchev
Y1  - 2022/04/26
PY  - 2022
N1  - https://doi.org/10.11648/j.engmath.20220601.11
DO  - 10.11648/j.engmath.20220601.11
T2  - Engineering Mathematics
JF  - Engineering Mathematics
JO  - Engineering Mathematics
SP  - 1
EP  - 5
PB  - Science Publishing Group
SN  - 2640-088X
UR  - https://doi.org/10.11648/j.engmath.20220601.11
AB  - Inverted slider-crank mechanisms driven by hydraulic cylinder have highly non-linear transfer functions, which in this form complicate kinematic and dynamic researches. A central slider-crank mechanism scheme is used with the specific small parameter equal to the ratio of the lengths of both links of the revolute pair of the mechanism (λ=R/L). The present study considers the two main transfer functions of the mechanism. In the first case the angle of the revolute pair as an independent parameter is accepted and in the second case the linear motion of the hydraulic cylinder as an independent parameter is accepted. The exact transfer functions of the mechanism are described and approximate representations of the transfer functions are found. In the first case we use a binomial order of the degrees of the small parameter calculated up to 4-th degree and very high accuracy of approximate function has been achieved (maximal error less than 1.6%). In the second case we use a trigonometric function, which corresponds to the exact transfer function up to second derivative, and the accuracy is also high (error less than 2%) in the main operating range. The power characteristics of the inverted slider-crank mechanism driven by hydraulic cylinder are determined using the transfer functions. All main conclusions are interpreted by geometrical representations.
VL  - 6
IS  - 1
ER  -

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Author Information

Krasimir Ganchev

Central Laboratory of Mechatronics and Instrumentation, Bulgarian Academy of Sciences, Sofia, Bulgaria

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Krasimir Ganchev. (2022). Inverted Slider-Crank Mechanism Driven by Hydraulic Cylinder: Transfer Functions and Approximations. Engineering Mathematics, 6(1), 1-5. https://doi.org/10.11648/j.engmath.20220601.11

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ACS Style

Krasimir Ganchev. Inverted Slider-Crank Mechanism Driven by Hydraulic Cylinder: Transfer Functions and Approximations. Eng. Math. 2022, 6(1), 1-5. doi: 10.11648/j.engmath.20220601.11

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AMA Style

Krasimir Ganchev. Inverted Slider-Crank Mechanism Driven by Hydraulic Cylinder: Transfer Functions and Approximations. Eng Math. 2022;6(1):1-5. doi: 10.11648/j.engmath.20220601.11

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@article{10.11648/j.engmath.20220601.11,
  author = {Krasimir Ganchev},
  title = {Inverted Slider-Crank Mechanism Driven by Hydraulic Cylinder: Transfer Functions and Approximations},
  journal = {Engineering Mathematics},
  volume = {6},
  number = {1},
  pages = {1-5},
  doi = {10.11648/j.engmath.20220601.11},
  url = {https://doi.org/10.11648/j.engmath.20220601.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.engmath.20220601.11},
  abstract = {Inverted slider-crank mechanisms driven by hydraulic cylinder have highly non-linear transfer functions, which in this form complicate kinematic and dynamic researches. A central slider-crank mechanism scheme is used with the specific small parameter equal to the ratio of the lengths of both links of the revolute pair of the mechanism (λ=R/L). The present study considers the two main transfer functions of the mechanism. In the first case the angle of the revolute pair as an independent parameter is accepted and in the second case the linear motion of the hydraulic cylinder as an independent parameter is accepted. The exact transfer functions of the mechanism are described and approximate representations of the transfer functions are found. In the first case we use a binomial order of the degrees of the small parameter calculated up to 4-th degree and very high accuracy of approximate function has been achieved (maximal error less than 1.6%). In the second case we use a trigonometric function, which corresponds to the exact transfer function up to second derivative, and the accuracy is also high (error less than 2%) in the main operating range. The power characteristics of the inverted slider-crank mechanism driven by hydraulic cylinder are determined using the transfer functions. All main conclusions are interpreted by geometrical representations.},
 year = {2022}
}

Copy | Download

TY  - JOUR
T1  - Inverted Slider-Crank Mechanism Driven by Hydraulic Cylinder: Transfer Functions and Approximations
AU  - Krasimir Ganchev
Y1  - 2022/04/26
PY  - 2022
N1  - https://doi.org/10.11648/j.engmath.20220601.11
DO  - 10.11648/j.engmath.20220601.11
T2  - Engineering Mathematics
JF  - Engineering Mathematics
JO  - Engineering Mathematics
SP  - 1
EP  - 5
PB  - Science Publishing Group
SN  - 2640-088X
UR  - https://doi.org/10.11648/j.engmath.20220601.11
AB  - Inverted slider-crank mechanisms driven by hydraulic cylinder have highly non-linear transfer functions, which in this form complicate kinematic and dynamic researches. A central slider-crank mechanism scheme is used with the specific small parameter equal to the ratio of the lengths of both links of the revolute pair of the mechanism (λ=R/L). The present study considers the two main transfer functions of the mechanism. In the first case the angle of the revolute pair as an independent parameter is accepted and in the second case the linear motion of the hydraulic cylinder as an independent parameter is accepted. The exact transfer functions of the mechanism are described and approximate representations of the transfer functions are found. In the first case we use a binomial order of the degrees of the small parameter calculated up to 4-th degree and very high accuracy of approximate function has been achieved (maximal error less than 1.6%). In the second case we use a trigonometric function, which corresponds to the exact transfer function up to second derivative, and the accuracy is also high (error less than 2%) in the main operating range. The power characteristics of the inverted slider-crank mechanism driven by hydraulic cylinder are determined using the transfer functions. All main conclusions are interpreted by geometrical representations.
VL  - 6
IS  - 1
ER  -

Copy | Download