Project ForgeA four bar mechanism is shown in the figure. The link numbers are mentioned near the links. Input link 2 is rotating anticlockwise with a constant angular speed ω2. Length of different links are: O2O4=O2A=L, AB=O4B=√2L. The magnitude of the angular speed of the output link 4 is ω4 at the instant when link 2 makes an angle of 90° with O2O4 as shown. The ratio ω4/ω2 is ___ (round off to two decimal places).
Explanation
Set O2=(0,0), O4=(L,0), A=(0,L) (link 2 vertical). Solving the constraints |AB|=|O4B|=√2L gives B=(L(1+√3)/2, L(1+√3)/2)≈(1.366L,1.366L). V_A=ω2ẑ×(0,L,0)=(−Lω2,0). Writing V_B=V_A+ω3ẑ×(B−A)=ω4ẑ×(B−O4) and matching x,y components gives two equations in ω3,ω4; solving yields ω4≈0.789ω2.
Source: GATE ME 2019 Session 2 (Set 3) (2019)
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