Project ForgeA double-parallelogram mechanism is shown in the figure: a single rigid link PQ is connected via three parallel, equal-length links to three fixed pivots on the ground. Note that PQ is a single link. The mobility of the mechanism is
- A-1
- B0
- 1
- D2
Explanation
Naive Grubler/Kutzbach counting on 5 links (ground + the single rigid link PQ + 3 coupler links) and 6 revolute joints gives DOF=3(5-1)-2(6)=12-12=0. But this is a classic 'Grubler paradox' mechanism: the special geometry (all three coupler links parallel and equal length) introduces a redundant/passive constraint that the simple count double-penalizes, so the true mobility is 1 — the coupler link PQ is free to translate along a straight-line path while remaining parallel to itself, exactly like a pantograph or parallel-link flexure.
Source: GATE ME 2011 (2011)
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