Grashof's law says that a link can rotate fully when:

Sum of shortest and longest links <= sum of the other two links

Sum of shortest and longest links >= sum of the other two links

Shortest link is longer than half the frame

Sum of the two shortest links equals the longest link

For links 30, 70, 80 and 60 mm, which result is correct?

s + l = 110 < p + q = 130, Grashof

s + l = 110 > p + q = 130, not Grashof

s + l = 100 < p + q = 140, Grashof

s + l = 90 < p + q = 150, Grashof

Practice · 6 marks

Grashof's law and four-bar classification

Short answer

Grashof's law: s + l ≤ p + q for a four-bar linkage, where s=shortest, l=longest. Given AB=30, BC=70, CD=80, DA=60 mm: s+l=110 < p+q=130, so Grashof condition satisfied. Inversions: AB fixed (shortest) - double crank; BC fixed (adjacent) - crank rocker; DA fixed (adjacent) - crank rocker; CD fixed (opposite) - double rocker.

State Grashof's law for a four-bar linkage. A four-bar linkage ABCD has link lengths AB = 30 mm, BC = 70 mm, CD = 80 mm and DA = 60 mm. Check whether it satisfies Grashof's law and name the type of mechanism obtained when each of the four links in turn is fixed.

Grashof's law

In a planar four-bar linkage, if the sum of the shortest and longest links is less than or equal to the sum of the other two links, then the shortest link can make a full rotation relative to the other links. If the sum is greater, no link can rotate fully (all inversions are double-rockers).

s + l \le p + q

where $s$ = shortest, $l$ = longest, $p, q$ = the other two links.

Check

$s = 30$ mm (AB), $l = 80$ mm (CD), $p = 60$ mm, $q = 70$ mm.

s + l = 30 + 80 = 110\ \text{mm} \quad < \quad p + q = 60 + 70 = 130\ \text{mm}

The linkage satisfies Grashof's law, so it is a Grashof chain and the shortest link AB can rotate fully.

Inversions

Fixed link	Relation to shortest link	Mechanism
AB (30 mm)	Shortest link fixed	Double-crank (drag link)
BC (70 mm)	Adjacent to shortest	Crank-rocker (AB is crank, CD rocker)
DA (60 mm)	Adjacent to shortest	Crank-rocker (AB is crank, CD rocker)
CD (80 mm)	Opposite to shortest	Double-rocker (coupler AB rotates fully)

Shortest link fixed: both links adjacent to it rotate completely.
A link adjacent to the shortest link fixed: the shortest link is the crank and the link opposite the shortest link is the rocker.
Link opposite the shortest link fixed (shortest link is the coupler): both side links only oscillate, while the coupler makes full turns.

Answer: $s + l = 110$ mm $< p + q = 130$ mm, so Grashof; double-crank (AB fixed), crank-rocker (BC or DA fixed), double-rocker (CD fixed).

✓ Answer checked by Claude Opus 5.5 (high effort)

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