Skip to main content
Top
Published in: Meccanica 11-12/2019

10-09-2019

A loop-by-loop defect rectification procedure for optimal synthesis of Stephenson III path generators

Authors: Ramanpreet Singh, Himanshu Chaudhary, Amit K. Singh

Published in: Meccanica | Issue 11-12/2019

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

This paper presents a formulation of constraints for the synthesis of Stephenson III mechanism and a loop-by-loop defect-rectification procedure. The procedure divides the Stephenson III mechanism into two loops, namely, Loop I, i.e., four-bar, and Loop II, i.e., five-bar mechanisms. Then, the defects are identified using the established methodology to formulate the defect-specific constraints in the simplified form. Based on the constraints, an optimization problem is formulated to synthesize a Stephenson III mechanism for path generation. A well-established meta-heuristic algorithm is used to solve the constrained optimization problem. For demonstrating the effectiveness of the formulated constraints, two numerical examples are considered, in which Stephenson III path generator mechanisms are synthesized. It is found that the mechanisms synthesized using the proposed procedure are defect-free when constraints are imposed, which is verified using the stick-diagram.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Appendix
Available only for authorised users
Footnotes
1
Branch term is used in place of circuit in the original research.
 
2
Not applicable for rocker-crank and double-rocker mechanism.
 
Literature
1.
go back to reference Sandor G, Erdman A (1984) Advanced mechanical design: analysis and synthesis, vol 2. Prentice Hall, New Jersey Sandor G, Erdman A (1984) Advanced mechanical design: analysis and synthesis, vol 2. Prentice Hall, New Jersey
2.
go back to reference Chase TR, Mirth JA (1993) Circuits and branches of single-degree-of-freedom planar linkages. J Mech Des 115(2):223–230CrossRef Chase TR, Mirth JA (1993) Circuits and branches of single-degree-of-freedom planar linkages. J Mech Des 115(2):223–230CrossRef
3.
go back to reference Chase TR, Fang WE (1991) Order rectification for complex number based Burmester curves. J Mech Des 113(3):239–247CrossRef Chase TR, Fang WE (1991) Order rectification for complex number based Burmester curves. J Mech Des 113(3):239–247CrossRef
4.
go back to reference Acharyya SK, Mandal M (2009) Performance of EAs for four-bar linkage synthesis. Mech Mach Theory 44(9):1784–1794CrossRef Acharyya SK, Mandal M (2009) Performance of EAs for four-bar linkage synthesis. Mech Mach Theory 44(9):1784–1794CrossRef
5.
go back to reference Mirth JA, Chase TR (1995) Circuit rectification for four precision position synthesis of Stephenson six-bar linkages. Trans Am Soc Mech Eng J Mech Des 117:644–645 Mirth JA, Chase TR (1995) Circuit rectification for four precision position synthesis of Stephenson six-bar linkages. Trans Am Soc Mech Eng J Mech Des 117:644–645
6.
go back to reference McCarthy JM (2006) Geometric design of linkages, vol 11. Springer, BerlinMATH McCarthy JM (2006) Geometric design of linkages, vol 11. Springer, BerlinMATH
7.
go back to reference Guo XN, Chu JK (2004) Mobility of stephenson six-bar chains: part I—circuit and circuit defect. In: ASME 2004 international design engineering technical conferences and computers and information in engineering conference. American Society of Mechanical Engineers, pp 789–797 Guo XN, Chu JK (2004) Mobility of stephenson six-bar chains: part I—circuit and circuit defect. In: ASME 2004 international design engineering technical conferences and computers and information in engineering conference. American Society of Mechanical Engineers, pp 789–797
8.
go back to reference Waldron KJ (1977) Graphical solution of the branch and order problems of linkage synthesis for multiply separated positions. ASME J Eng Ind 99(3):591–597CrossRef Waldron KJ (1977) Graphical solution of the branch and order problems of linkage synthesis for multiply separated positions. ASME J Eng Ind 99(3):591–597CrossRef
9.
go back to reference Stevensen EN Jr (1979) Elimination of branch, Grashof, and order defects in path-angle generation and function generation synthesis. ASME J Mech Des 101:428–437 Stevensen EN Jr (1979) Elimination of branch, Grashof, and order defects in path-angle generation and function generation synthesis. ASME J Mech Des 101:428–437
10.
go back to reference Filemon E (1972) Useful ranges of centerpoint curves for design of crank-and-rocker linkages. Mech Mach Theory 7(1):47–53CrossRef Filemon E (1972) Useful ranges of centerpoint curves for design of crank-and-rocker linkages. Mech Mach Theory 7(1):47–53CrossRef
11.
go back to reference Waldron KJ (1994) Solution rectification in three position motion generation synthesis. J Mech Des 116(1):88–91CrossRef Waldron KJ (1994) Solution rectification in three position motion generation synthesis. J Mech Des 116(1):88–91CrossRef
12.
go back to reference Tinubu S, Gupta KC (1984) Optimal synthesis of function generation without the branch defect. ASME J Mech Trans Autom Des 106(3):348–354CrossRef Tinubu S, Gupta KC (1984) Optimal synthesis of function generation without the branch defect. ASME J Mech Trans Autom Des 106(3):348–354CrossRef
13.
go back to reference Yan HS, Chiou ST (1987) An algorithm for the optimal synthesis of complex function generators. Eng Optim + A35 12(1):75–88CrossRef Yan HS, Chiou ST (1987) An algorithm for the optimal synthesis of complex function generators. Eng Optim + A35 12(1):75–88CrossRef
14.
go back to reference Watanabe K, Funabashi H (1984) Kinematic analysis of Stephenson six-link mechanisms: 1st report, discrimination of composition loops. Bull JSME 27(234):2863–2870CrossRef Watanabe K, Funabashi H (1984) Kinematic analysis of Stephenson six-link mechanisms: 1st report, discrimination of composition loops. Bull JSME 27(234):2863–2870CrossRef
15.
go back to reference Angeles J, Bernier A (1987) The global least-square optimization of function-generating linkages. ASME J Mech Trans Autom Des 109:204–209CrossRef Angeles J, Bernier A (1987) The global least-square optimization of function-generating linkages. ASME J Mech Trans Autom Des 109:204–209CrossRef
16.
17.
go back to reference Mirth JA, Chase TR (1993) Circuit analysis of Watt chain six-bar mechanisms. J Mech Des 115(2):214–222CrossRef Mirth JA, Chase TR (1993) Circuit analysis of Watt chain six-bar mechanisms. J Mech Des 115(2):214–222CrossRef
18.
go back to reference Chase TR (1995) Circuit rectification for four precision position synthesis of four-bar and watt six-bar linkages. J Mech Des 117:613 Chase TR (1995) Circuit rectification for four precision position synthesis of four-bar and watt six-bar linkages. J Mech Des 117:613
19.
go back to reference Krishnamurty S, Turcic DA (1988) A general method of determining and eliminating branching in planar multiloop mechanisms. ASME J Mech Des 110(4):414–422 Krishnamurty S, Turcic DA (1988) A general method of determining and eliminating branching in planar multiloop mechanisms. ASME J Mech Des 110(4):414–422
20.
go back to reference Sardashti A, Daniali HM, Varedi SM (2013) Optimal free-defect synthesis of four-bar linkage with joint clearance using PSO algorithm. Meccanica 48(7):1681–1693CrossRef Sardashti A, Daniali HM, Varedi SM (2013) Optimal free-defect synthesis of four-bar linkage with joint clearance using PSO algorithm. Meccanica 48(7):1681–1693CrossRef
21.
go back to reference Wilhelm SR, Sullivan T, Van de Ven JD (2017) Solution rectification of slider-crank mechanisms with transmission angle control. Mech Mach Theory 107:37–45CrossRef Wilhelm SR, Sullivan T, Van de Ven JD (2017) Solution rectification of slider-crank mechanisms with transmission angle control. Mech Mach Theory 107:37–45CrossRef
22.
go back to reference Shen Q, Lee WT, Russell K (2015) On adjustable planar four-bar motion generation with order, branch and circuit defect rectification. J Mech Robot 7(3):034501CrossRef Shen Q, Lee WT, Russell K (2015) On adjustable planar four-bar motion generation with order, branch and circuit defect rectification. J Mech Robot 7(3):034501CrossRef
23.
go back to reference Singh R, Chaudhary H, Singh AK (2017) Defect-free optimal synthesis of crank-rocker linkage using nature-inspired optimization algorithms. Mech Mach Theory 116:105–122CrossRef Singh R, Chaudhary H, Singh AK (2017) Defect-free optimal synthesis of crank-rocker linkage using nature-inspired optimization algorithms. Mech Mach Theory 116:105–122CrossRef
24.
go back to reference Watanabe K, Katoh H (2004) Identification of motion domains of planar six-link mechanisms of the Stephenson-type. Mech Mach Theory 39(10):1081–1099CrossRef Watanabe K, Katoh H (2004) Identification of motion domains of planar six-link mechanisms of the Stephenson-type. Mech Mach Theory 39(10):1081–1099CrossRef
25.
go back to reference Guo XN, Chu JK (2004) Mobility of Stephenson six-bar chains: part II—the motion order. In: ASME 2004 international design engineering technical conferences and computers and information in engineering conference. American Society of Mechanical Engineers, pp 909–914 Guo XN, Chu JK (2004) Mobility of Stephenson six-bar chains: part II—the motion order. In: ASME 2004 international design engineering technical conferences and computers and information in engineering conference. American Society of Mechanical Engineers, pp 909–914
26.
go back to reference Parrish B, McCarthy JM (2013) Identification of a usable six-bar linkage for dimensional synthesis. In: New trends in mechanism and machine science. Springer, Netherlands, pp 255–262 Parrish B, McCarthy JM (2013) Identification of a usable six-bar linkage for dimensional synthesis. In: New trends in mechanism and machine science. Springer, Netherlands, pp 255–262
27.
go back to reference Mirth JA (2012). The application of geometric constraint programming to the design of motion generating six-bar linkages. In: ASME 2012 international design engineering technical conferences and computers and information in engineering conference. American Society of Mechanical Engineers, pp 1503–1511 Mirth JA (2012). The application of geometric constraint programming to the design of motion generating six-bar linkages. In: ASME 2012 international design engineering technical conferences and computers and information in engineering conference. American Society of Mechanical Engineers, pp 1503–1511
28.
go back to reference Hwang WM, Chen YJ (2008) Defect-free synthesis of Stephenson-III motion generators. Proc Inst Mech Eng Part C J Mech Eng Sci 222(12):2485–2494CrossRef Hwang WM, Chen YJ (2008) Defect-free synthesis of Stephenson-III motion generators. Proc Inst Mech Eng Part C J Mech Eng Sci 222(12):2485–2494CrossRef
29.
go back to reference Plecnik MM, McCarthy JM (2016) Kinematic synthesis of Stephenson III six-bar function generators. Mech Mach Theory 97:112–126CrossRef Plecnik MM, McCarthy JM (2016) Kinematic synthesis of Stephenson III six-bar function generators. Mech Mach Theory 97:112–126CrossRef
30.
go back to reference Plecnik MM, McCarthy JM (2016) Computational design of Stephenson II six-bar function generators for 11 accuracy points. J Mech Robot 8(1):011017CrossRef Plecnik MM, McCarthy JM (2016) Computational design of Stephenson II six-bar function generators for 11 accuracy points. J Mech Robot 8(1):011017CrossRef
31.
go back to reference Plecnik MM, McCarthy JM (2014) Numerical synthesis of six-bar linkages for mechanical computation. J Mech Robot 6(3):031012CrossRef Plecnik MM, McCarthy JM (2014) Numerical synthesis of six-bar linkages for mechanical computation. J Mech Robot 6(3):031012CrossRef
32.
go back to reference Hwang WM, Chen YJ (2010) Defect-free synthesis of Stephenson-II function generators. J Mech Robot 2(4):041012CrossRef Hwang WM, Chen YJ (2010) Defect-free synthesis of Stephenson-II function generators. J Mech Robot 2(4):041012CrossRef
33.
go back to reference Sonawale KH, Arredondo A, McCarthy JM (2013) Computer aided design of useful spherical watt I six-bar linkages. ASME Paper No. DETC2013-13454 Sonawale KH, Arredondo A, McCarthy JM (2013) Computer aided design of useful spherical watt I six-bar linkages. ASME Paper No. DETC2013-13454
34.
go back to reference Waldron KJ, Kinzel GL, Agrawal SK (2016) Kinematics, dynamics, and design of machinery. Wiley, Hoboken Waldron KJ, Kinzel GL, Agrawal SK (2016) Kinematics, dynamics, and design of machinery. Wiley, Hoboken
35.
go back to reference Waldron KJ (1976) Elimination of the branch problem in graphical Burmester mechanism synthesis for four finitely separated positions. J Eng Ind 98(1):176–182CrossRef Waldron KJ (1976) Elimination of the branch problem in graphical Burmester mechanism synthesis for four finitely separated positions. J Eng Ind 98(1):176–182CrossRef
36.
go back to reference Ting KL (1986) Five-bar Grashof criteria. ASME J Mech Trans Autom Des 108(4):533–537CrossRef Ting KL (1986) Five-bar Grashof criteria. ASME J Mech Trans Autom Des 108(4):533–537CrossRef
37.
go back to reference Mundo D, Liu JY, Yan HS (2006) Optimal synthesis of cam-linkage mechanisms for precise path generation. J Mech Des 128(6):1253–1260CrossRef Mundo D, Liu JY, Yan HS (2006) Optimal synthesis of cam-linkage mechanisms for precise path generation. J Mech Des 128(6):1253–1260CrossRef
38.
go back to reference Mundo D, Gatti G, Dooner DB (2009) Optimized five-bar linkages with non-circular gears for exact path generation. Mech Mach Theory 44(4):751–760CrossRef Mundo D, Gatti G, Dooner DB (2009) Optimized five-bar linkages with non-circular gears for exact path generation. Mech Mach Theory 44(4):751–760CrossRef
39.
go back to reference Rao RV (2016) Teaching-learning-based optimization algorithm. In: Teaching learning based optimization algorithm. Springer, New York, pp 9–39 Rao RV (2016) Teaching-learning-based optimization algorithm. In: Teaching learning based optimization algorithm. Springer, New York, pp 9–39
40.
go back to reference Kunjur A, Krishnamurty S (1997) Genetic algorithms in mechanism synthesis. J Appl Mech Robot 4(2):18–24 Kunjur A, Krishnamurty S (1997) Genetic algorithms in mechanism synthesis. J Appl Mech Robot 4(2):18–24
41.
go back to reference Mirjalili S, Lewis A (2016) The whale optimization algorithm. Adv Eng Softw 1(95):51–67CrossRef Mirjalili S, Lewis A (2016) The whale optimization algorithm. Adv Eng Softw 1(95):51–67CrossRef
42.
go back to reference Sancibrian R, Sarabia EG, Sedano A, Blanco JM (2016) A general method for the optimal synthesis of mechanisms using prescribed instant center positions. Appl Math Model 40(3):2206–2222MathSciNetCrossRef Sancibrian R, Sarabia EG, Sedano A, Blanco JM (2016) A general method for the optimal synthesis of mechanisms using prescribed instant center positions. Appl Math Model 40(3):2206–2222MathSciNetCrossRef
Metadata
Title
A loop-by-loop defect rectification procedure for optimal synthesis of Stephenson III path generators
Authors
Ramanpreet Singh
Himanshu Chaudhary
Amit K. Singh
Publication date
10-09-2019
Publisher
Springer Netherlands
Published in
Meccanica / Issue 11-12/2019
Print ISSN: 0025-6455
Electronic ISSN: 1572-9648
DOI
https://doi.org/10.1007/s11012-019-01039-7

Other articles of this Issue 11-12/2019

Meccanica 11-12/2019 Go to the issue

Premium Partners