Project ForgeA planar four-bar linkage mechanism with 3 revolute kinematic pairs and 1 prismatic kinematic pair is shown in the figure, where AB⊥CE and FD⊥CE. The T-shaped link CDEF is constructed such that the slider B can cross the point D, and CE is sufficiently long. Given lengths: GF=3cm (ground link), AG=5cm (crank, pivoted to ground at G), AB=3cm (coupler, ending in slider B), FD=1.5cm (T-link CDEF pivoted to ground at F). For the given lengths as shown, the mechanism is
- a Grashof chain with links AG, AB, and CDEF completely rotatable about the ground link FG
- Ba non-Grashof chain with all oscillating links
- Ca Grashof chain with AB completely rotatable about the ground link FG, and oscillatory links AG and CDEF
- Don the border of Grashof and non-Grashof chains with uncertain configuration(s)
Explanation
Since crank AG (5cm) exceeds the fixed-pivot distance GF (3cm), the fixed point F lies inside the circle traced by crank pin A, so crank AG can rotate a full 360° (the classic crank-and-slotted-lever condition). Because CE is stated to be 'sufficiently long' and slider B can cross D without obstruction, the coupler AB and the T-shaped link CDEF driven through the prismatic pair are also able to complete full rotations as AG sweeps through 360° — confirmed against the published GATE 2022 solution for this specific mechanism, which verifies all three moving links (AG, AB, CDEF) are completely rotatable about ground link FG.
Source: GATE ME 2022 Session 1 (ME-1) (2022)
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