Research Papers

A Function Generation Synthesis Methodology for All Defect-Free Slider-Crank Solutions for Four Precision Points

[+] Author and Article Information
Ali Almandeel

Department of Mechanical
and Aerospace Engineering,
University of Dayton,
Dayton, OH 45469
e-mail: mandeel@gmail.com

Andrew P. Murray, David H. Myszka

Department of Mechanical
and Aerospace Engineering,
University of Dayton,
Dayton, OH 45469

Herbert E. Stumph, III

Stress Engineering Services, Inc.,
7030 Stress Engineering Way,
Mason, OH 45040

Manuscript received December 30, 2013; final manuscript received March 19, 2015; published online June 10, 2015. Assoc. Editor: Qiaode Jeffrey Ge.

J. Mechanisms Robotics 7(3), 031020 (Aug 01, 2015) (10 pages) Paper No: JMR-13-1261; doi: 10.1115/1.4030182 History: Received December 30, 2013; Revised March 19, 2015; Online June 10, 2015

The well-established methodology for slider-crank function generation states that five precision points can be achieved without structural error. The resulting designs, however, do not necessarily satisfy all of the kinematic requirements for designing a slider-crank linkage used in common machine applications such as driving the ram of a mechanical press. First, linkage solutions to the five precision point synthesis problem may need to change circuits to reach the precision points. Second, there is no guarantee that the input crank is fully rotatable. This paper presents a modification to the function generation synthesis methodology that reveals a continuum of defect-free, slider-crank solutions for four precision points. Additionally, the methodology allows the specification of velocity or acceleration at the precision points. Although smaller accelerations at a point of zero slide velocity are associated with longer dwell, a point having zero velocity and acceleration is shown not to be possible. Examples are included to illustrate this kinematic synthesis methodology.

Copyright © 2015 by ASME
Topics: Linkages , Circuits
Your Session has timed out. Please sign back in to continue.


Erdman, A., Sandor, G., and Kota, S., 2001, Mechanism Design: Analysis and Synthesis, Vol. 1, Prentice Hall, Upper Saddle River, NJ.
Erdman, A., and Sandor, G., 1984, Advanced Mechanism Design: Analysis and Synthesis, Vol. 2, Prentice-Hall, Upper Saddle River, NJ.
McCarthy, J., and Soh, G., 2010, Geometric Design of Linkages (Interdisciplinary Applied Mathematics), Springer, New York.
Waldron, K., and Kinzel, G., 2004, Kinematics, Dynamics, and Design of Machinery, Wiley, New York.
Freudenstein, F., 1954, “An Analytical Approach to the Design of Four-Link Mechanisms,” Trans. ASME, 76(3), pp. 483–492.
Freudenstein, F., 1959, “Structural Error Analysis in Plane Kinematic Synthesis,” J. Eng. Ind., 81(1), pp. 15–22.
Akcali, I., and Dittrich, G., 1989, “Function Generation by Galerkin's Method,” Mech. Mach. Theory, 24(1), pp. 39–43. [CrossRef]
Liu, Z., and Angeles, J., 1994, “Optimization of Planar, Spherical and Spatial Function Generators Using Input-Output Curve Planning,” ASME J. Mech. Des., 116(3), pp. 915–919. [CrossRef]
Plecnik, M., and McCarthy, J. M., 2011, “Five Position Synthesis of a Slider-Crank Function Generator,” ASME Paper No. DETC2011-47581. [CrossRef]
Myszka, D. H., and Murray, A. P., 2010, “Pole Arrangements That Introduce Prismatic Joints Into the Design Space of Four- and Five-Position Rigid-Body Synthesis,” Mech. Mach. Theory, 45(9), pp. 1314–1325. [CrossRef]
Tari, H., and Su, H.-J., 2010, “Complete Solution to the Eight-Point Path Generation of Slider-Crank Four-Bar Linkages,” ASME J. Mech. Des., 132(8), p. 081003. [CrossRef]
Russell, K., and Sodhi, R. S., 2005, “On the Design of Slider-Crank Mechanisms. Part II: Multi-Phase Path and Function Generation,” Mech. Mach. Theory, 40(3), pp. 301–317. [CrossRef]
Figliolini, G., Conte, M., and Rea, P., 2012, “Algebraic Algorithm for the Kinematic Analysis of Slider-Crank/Rocker Mechanisms,” ASME J. Mech. Rob., 4(1), p. 011003. [CrossRef]
McLarnan, C., 1963, “Synthesis of Six-Link Plane Mechanisms by Numerical Analysis,” ASME J. Manuf. Sci. Eng., 85(1), pp. 5–10. [CrossRef]
Dhingra, A., Cheng, J., and Kohli, D., 1994, “Synthesis of Six-Link, Slider-Crank and Four-Link Mechanisms for Function, Path and Motion Generation Using Homotopy With m-Homogenization,” ASME J. Mech. Des., 116(4), pp. 1122–1131. [CrossRef]
Zanganeh, K. E., and Angeles, J., 1993, “Symbolic Approach to the Input-Output Analysis of the Stephenson Six-Bar Linkage,” 19th Annual ASME Design Automation Conference, Part 2, Albuquerque, NM, Sept. 19–22, pp. 67–72.
Dhingra, A., and Mani, N., 1993, “Finitely and Multiply Separated Synthesis of Link and Geared Mechanisms Using Symbolic Computing,” ASME J. Mech. Des., 115(3), pp. 560–567. [CrossRef]
Gonzalez-Palacios, M. A., and Angeles, J., 1991, “SIXPAQ: A Comprehensive Software Package for Analysis and Synthesis of Six-Bar Dwell-Linkages,” ASME International Computers in Engineering Conference, Santa Clara, CA, Aug. 18–22, Vol. 1, pp. 309–314.
Chase, T. R., and Mirth, J. A., 1993, “Circuits and Branches of Single-Degree-of-Freedom Planar Linkages,” ASME J. Mech. Des., 115(2), pp. 223–230. [CrossRef]
Balli, S. S., and Chand, S., 2002, “Defects in Link Mechanisms and Solution Rectification,” Mech. Mach. Theory, 37(9), pp. 851–876. [CrossRef]
Barker, C., and Jeng, Y.-R., 1985, “Range of the Six Fundamental Position Angles of a Planar Four-Bar Mechanism,” Mech. Mach. Theory, 20(4), pp. 329–344. [CrossRef]
Mirth, J. A., and Chase, T. R., 1993, “Circuit Analysis of Watt Chain Six-Bar Mechanisms,” ASME J. Mech. Des., 115(2), pp. 214–222. [CrossRef]
Davis, H., Chase, T., and Mirth, J., 1994, “Circuit Analysis of Stephenson Chain Six-Bar Mechanisms,” Trans. ASME, 70, pp. 349–358.
Gosselin, C., and Angeles, J., 1990, “Singularity Analysis of Closed-Loop Kinematic Chains,” IEEE Trans. Rob. Autom., 6(3), pp. 281–290. [CrossRef]
Grashof, F., 1883, Theoretische Maschinenlehre: Bd. Theorie der Getriebe und der Mechanischen Messinstrumente, L. Voss, Leipzig, Germany.
Xue, C., Ting, K.-L., and Wang, J., 2011, “Mobility Criteria of Planar Single-Loop N-Bar Chains With Prismatic Joints,” ASME J. Mech. Rob., 3(1), p. 011011. [CrossRef]
Stumph, H. E., and Murray, A. P., 2000, “Defect-Free Slider-Crank Function Generation for 4.5 Precision Points,” ASME Paper No. DETC200/MECH-14070. [CrossRef]
Wampler, C. W., and Sommese, A. J., 2011, “Numerical Algebraic Geometry and Algebraic Kinematics,” Acta Numer., 20, pp. 469–567. [CrossRef]
Neumaier, A., 1990, Interval Methods for Systems of Equations, Vol. 37, Cambridge University Press, New York.
Roth, B., 1993, “Computations in Kinematics,” Computational Kinematics, Springer, New York, pp. 3–14.


Grahic Jump Location
Fig. 1

A slider-crank mechanism with vector loop

Grahic Jump Location
Fig. 2

Linkage solution for five precision points where the points reside on separate circuits

Grahic Jump Location
Fig. 3

Five precision points lie on the same circuit branch, but the input link is unable to make a complete revolution

Grahic Jump Location
Fig. 4

The motion curve and corresponding linkage for precision points of Table 1 and Δp5=-0.10

Grahic Jump Location
Fig. 5

Motion curve and corresponding slider-crank linkage where BDC and TDC where specified in Table 2 and Δp3=2.50 is selected

Grahic Jump Location
Fig. 6

Motion curve for slider-crank linkage from example where acceleration was specified at BDC

Grahic Jump Location
Fig. 7

Motion curve for slider-crank linkage where acceleration was specified at BDC and range of viable TDC positions is determined




Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In