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Theory of Machine
Theory of Machine
Theory of Machine
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1 HP= 2 LP
❖ Permanent contact
❖ Ex- TP, SP & Rolling pair
If DOF = 0, the assembly of links is a structure and no motion is possible.
If DOF < 0,then the assembly is a preloaded structure, no motion is possible, and in general stresses are present.
If DOF > 0, the assembly of links is a mechanism and will exhibit relative motion
Grubler’s Equation
Grubler’s Equation
❖ Grubler criterion does not include geometry, so it can give wrong prediction
❖ We must use inspection.
The Grashof’s law states that for a four-bar linkage system, the sum of the shortest and longest link of a planar quadrilateral linkage is less than or equal to the sum of the remaining two links, then the shortest link can rotate fully with respect to a neighboring link
S+L ≤ P+Q
S+L < P+Q
Shortest Fixed
S+L < P+Q
Adjacent to shortest fixed
S+L < P+Q
Shortest = coupler
S+L = P+Q
If all lengths are different(2,3,4,5)
Same as S+L < P+Q
S+L = P+Q
If lengths are same(2,2,5,7)
S+L = P+Q
If lengths are same(2,2,5,5)
Parallelogram linkage
Parallelogram linkage
S Fixed
l Fixed
Deltoid linkage
S Fixed
Deltoid linkage
S+L > P+Q
