Skip to main content
SpringerLink
Log in

Function generation with planar four-bar mechanisms as a mixed problem of correlation of crank angles and dead center design

  • Published:
Sādhanā Aims and scope Submit manuscript

Abstract

Function generation synthesis of mechanisms can be considered as the design of correlation of crank angles and dead dead-center position design. These two problems have been clearly defined and solved separately. But some problems may require both correlation of crank angles and dead dead-center design at different configurations. Such problems are called mixed function generation problems. In this paper, an overview of these mixed function generation problems for the planar four-bar mechanism are given and the problems are solved analytically or semi-analytically. Except three of them, all presented mixed function generation problem formulations are novel. The solutions of all problems including three positions for the four-bar mechanism and the solution of a problem including four positions for a four-bar mechanism are addressed. All problems are first reduced to a univariate equation and a fast solution is found. Thus, link lengths can be found quickly by changing the problem definition problems, and several design iterations can be performed in a short time. Numerical solutions of all problems have been demonstrated using Excel.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6
Figure 7
Figure 8
Figure 9
Figure 10
Figure 11
Figure 12
Figure 13
Figure 14
Figure 15
Figure 16
Figure 17
Figure 18
Figure 19
Figure 20

Similar content being viewed by others

Abbreviations

CCA:

Correlation of crank angles

DCP:

Dead-center position

EDCP:

Extended dead-center position

FDCP:

Folded dead-center position

OPT:

Optimum transmission angle

DTA:

Deviation of transmission angle from 90°

a:

Input link length of a four-bar mechanism

b:

Coupler link length of a four-bar mechanism

d:

Output link length of a four-bar mechanism

c:

Cosine

s:

Sine

ϕ:

Input angle of a four-bar mechanism

ψ:

Output angle of a four-bar mechanism

E :

Extended dead-center position (Subscript)

F :

Folded dead-center position (Subscript)

D :

Dead-center position—folded or extended (Subscript)

I/O:

Input-Output

References

  1. Söylemez E 2018 Mechanisms (5th ed). METU Press

  2. Burmester L E H 1888 Atlas zu Lehrbuch der Kinematik: für Studirende der Maschinentechnik, Mathematik und Physik Geometrisch Dargestellt. Verlag von Arthur Felix

  3. Koetsier T 1989 The centenary of Ludwig Burmester’s ‘Lehrbuch der Kinematik.’ Mech. Mach. Theory 24(1): 37–38

    Article  Google Scholar 

  4. Hain K 1967 Applied Kinematics. McGraw-Hill

  5. Svoboda A 1948 Computing Mechanisms and Linkages. McGraw-Hill

  6. Beyer R 1953 Kinematische getriebesynthese: Grundlagen einer quantitativen getriebelehre ebener getriebe. Für den konstrukteur, für die vorlesung und das selbststudium. Springer

  7. Leviskii N I 1946 Synthesis of Mechanisms According to Chebyshev. Izdatelstvo Khar'kovskogo Universiteta

  8. Leviskii N I 1950 Design of Plane Mechanisms with Lower Pairs. Izdatelstvo Akademii Nauk USSR

  9. Freudenstein F 1954 An analytical approach to the design of four-link mechanisms. Trans. ASME 76(3): 48–492

    MathSciNet  Google Scholar 

  10. Alt H 1925 Ueber die totlagen des gelenkvierecks. Z. Angew. Math. Mech. 5(1): 347–354

    Google Scholar 

  11. Meyer zur Capellen W 1956 Die totlagen des ebenen gelenkvierecks in analytischer darstellung. Fors. Ing.-Wes., 22(2): 42–50

  12. Volmer J 1957 Die konstruktion von schubkurbeln mit hilfe von kurventafeln. Maschinenbau-Technik 6(6): 80–85

    Google Scholar 

  13. Freudenstein F and Primrose E J F 1973 The classical transmission-angle problem. In: Proceedings of Conference Mechanism Synthesis, I. Mech. E., C96/72, London

  14. Söylemez E 2002 Classical transmission-angle problem for slider–crank mechanisms. Mech. Mach. Theory 37(4): 419–425

    Article  Google Scholar 

  15. Sandor G N and Erdman A G 1984 Advanced Mechanism Sesign: Analysis and Synthesis (vol. 2). Prentice-Hall

  16. Hartenberg R S and Denavit J 1964 Kinematic Synthesis of Linkages. McGraw-Hill

  17. McCarthy J M and Soh G S 2010 Geometric Design of Linkages (2nd ed). Springer

  18. Hall A S 1961 Kinematics and Linkage Design. Prentice-Hall

  19. Norton R L 2004 Design of Machinery: An Introduction to the Synthesis and Analysis of Mechanisms and Machines (3rd ed.). McGraw-Hill

  20. Mallik A, Ghosh A and Dittrich G 1994 Kinematic Analysis and Synthesis of Mechanisms (vol. 1). CRC Press

  21. Pennestrì E and Valentini P P 2009 A review of simple analytical methods for the kinematic synthesis of four-bar and slider-crank function generators for two and three prescribed finite positions. In: Buletin Stiintific Seria Mecanica Aplicata, pp. 128-143. University of Pitesti

  22. Mutlu H 2021 Design of the crank–rocker mechanism for various design cases based on the closed-form solution. Sādhanā 46(1): 1–11

    Article  MathSciNet  Google Scholar 

  23. Kiper G and Erez M 2019 Function generation synthesis with planar 4-bar linkage as a mixed problem of correlation of crank angles and dead-center design. In: Recent Advances in Mechanisms, Transmissions and Applications: MeTrApp 2019, Springer, pp. 42–47

  24. Kiper G, Görgülü İ and Küçükoğlu S F 2020 Function generation synthesis of planar slider-crank linkages for given 3 positions and a dead-center position. In: New Trends in Mechanism and Machine Science: EuCoMeS 2020, Springer, pp. 41–47

  25. Kadak T and Kiper G 2021 Krank açıları verilen üç konum ve bir ölü konum için dört-çubuk mekanizmasının işlev sentezi. In: UMTS-2021: Ulusal Makine Teorisi Sempozyumu Bildiriler Kitabı, Makina Teorisi Derneği, pp 24–29

  26. Söylemez E 2023 Kinematic Synthesis of Mechanisms Using Excel® and Geogebra. Springer

  27. Söylemez E 2009 Using computer spreadsheets in teaching mechanisms. In: Proceedings of EUCOMES 08, Springer, pp. 45–53

  28. Söylemez E and Kiper G 2023 Four-bar function generation using Excel solver. In: Advances in Mechanism and Machine Science: IFToMM WC 2023, Springer, 3: 208–218

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, İzmir Institute of Technology, İzmir, Turkey

    Tarik Kadak & Gökhan Kİper

Authors
  1. Tarik Kadak
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Gökhan Kİper
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Gökhan Kİper.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kadak, T., Kİper, G. Function generation with planar four-bar mechanisms as a mixed problem of correlation of crank angles and dead center design. Sādhanā 49, 143 (2024). https://doi.org/10.1007/s12046-024-02483-2

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s12046-024-02483-2

Keywords

Search

Navigation