CalcGrashofType

CalcGrashofType[linkage]
Calculates the type of the four-bar linkage based on Grashof's classification. The function returns the type and the range of the input angles
  • CalcGrashofType function is used in the four-bar mechanism synthesis package. The classification is based on the range of movement of the input and output links.
  • Given the 3 Grashof constant T1, T2, T3 if the product of the three constant is positive then the fou-bar linkage is called Grashof linkage otherwise it is a non-Grashof linkage
  • T1=l0-l1+l2-l3
  • T2=l0-l1-l2+l3
  • T3=-l0-l1+l2+l3
  • The fourbar1 and fourbar2 linkages have one additional linkage record called "$GrashofConstants". This record contains the definition of the Grashof constraints in a list.
  • 4 Grashof linkage classes are defined as follows:
NameT1T2T3
$CrankRocker+++
$RockerCrank+--
$DoubleCrank--+
$GrashofDoubleRocker-+-
  • 4 Non-Grashof linkage classes are defined as follows:
NameT1T2T3
$00DoubleRocker---
$0PiDoubleRocker++-
$Pi0DoubleRocker+-+
$PiPiDoubleRocker-++
  • 4 fold-able linkage classes are defined as follows:
NameCondition
$FoldabeCrankT1*T2=0T3>0
$Foldabe0RockerT1*T2 ==0 T3<0
$FoldabePiRockerT1*T2 <0 T3==0
$FoldabeRhombusT1*T2 ==0 T3==0
Load the LinkageDesigner package
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Click for copyable input
Calculate the Grashof type of fourbar1
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Since the linkage is a crank-rocker therfore the input linkage can be fully rotated
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If the geometric dimension is changed the Grashof type is changed
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The resulted four-bar linkage is a rocker-crank that can be rotated between the given range
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  • McCarthy, J. Michael, Soh, Gim Song. Geometric Design of Linkages Series: Interdisciplinary Applied Mathematics, Vol. 11 2nd Edition., 2011, XXVIII, 448 p., Hardcover ISBN: 978-1-4419-7891-2