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Optimum design of a knuckle lever linkage

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Sommario

Viene studiato un sistema articolato a ginocchiera, sul tipo di quelli impiegati in alcune presse meccaniche. Vengono dapprima riportati brevemente i risultati dell'analisi geometrica, cinematica e statica del meccanismo; si considerano successivamente diversi criteri di ottimizzazione e per ciascun criterio si scrive la relativa funzione obiettivo; viene poi presa in considerazione la funzione obiettivo complessiva, combinazione lineare delle precedenti.

L'ottimizzazione è conseguita con metodi numerici. Vengono alla fine riportati anche alcuni risultati numerici.

Summary

The paper deals with a knuckle lever linkage, like that employed in some mechanical presses. The results of the geometric, kinematic and statical analysis of the mechanism are firstly reported; several objective functions are then considered, each function corresponding to a different criterion of optimization. A comprehensive objective function is also considered.

The optimization is obtained by numerical approach. Some numerical results are finally reported.

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Abbreviations

a :

acceleration of slider 5

D :

nondimensional length of 0103 (fig. 1)

f 1...f 9 :

objective functions

f 10...f 90 :

minimum values off 1...f9

F 2...F 5 :

forces applied to links 2 ... 5

L 1...L 4 :

nondimensional lengths of links 1 ... 4

m 5 :

mass of slider 5

Q :

external force applied to slider 5

s :

displacement of slider 5

s 1 ...s 4 :

particular values ofs

T :

torque applied to link 1

T 0 ...T 3 :

particular values ofT

v :

velocity of slider 5

w 1 ...w 8 :

weight off 1 ...f 8 inf 9

α :

angle defined in figure 1a)

β :

angular position of link 2

γ :

angular position of link 3

γ 0 :

γ value at end of stroke

γ a :

γ value whenφ=π−α

γ b :

γ value whenφ=2π−α

Δ :

angle described by link 4

ɛ :

L 1/L2

ϑ :

angle between the dead center positions of link 2

η :

angle between links 2 and 4

η min :

minimum value ofη

λ :

L 3/L 4

μ :

angle between links 2 and 3

μ 0 :

μ value at the external dead center position

μ min :

minimum value ofμ

ω :

angle described by link 3

σ :

angular position of link 4

σ 0 :

σ value at end of stroke

φ :

angular position of link 1

References

  1. R. Fletcher andM. J. D. Powell,A rapidly convergent descent method for minimization, Computer Journal, Vol. VI, 1963, pp. 163–168.

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  2. A. T. Gasarow,Kurbelantriebe für Umformmaschinen, Moscow, 1958.

  3. S. Muller, Berechnung des Kniehebelantriebes in Kniehelelpressen, Maschinenbautechnik, Vol. XV, 1966, pp. 411–414.

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  4. U. Meneghetti,Introduzione allo studio della pressa a ginocchiera, Pubblicazioni dell'Ist. di Meccanica applicata alle macchine dell'Università di Bologna, n. 56, 1971.

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Authors and Affiliations

  1. Instituto di Meccanica applicata alle macchine, Università di Bologna, Italy

    Umberto Meneghetti

Authors
  1. Alberto Maggiore
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  2. Umberto Meneghetti
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Maggiore, A., Meneghetti, U. Optimum design of a knuckle lever linkage. Meccanica 11, 120–124 (1976). https://doi.org/10.1007/BF02138005

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  • DOI: https://doi.org/10.1007/BF02138005

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