Question

In the configuration of the planar four-bar mechanism at a certain instant as shown in the figure, the angular velocity of the 2 cm long link is ω2=5 rad/s. Given the dimensions as shown (crank 2 cm, coupler 5 cm, rocker 4 cm, ground link 10 cm, with the crank lying exactly along the ground link at this instant), the magnitude of the angular velocity ω4 of the 4 cm long link is given by _____ rad/s (round off to 2 decimal places).

Accepted Answer

The correct answer is 1.25 rad/s (± 0.03). Placing the crank pivot at (0,0) and the rocker pivot at (10,0), the crank pin is at A=(2,0), and solving the two circle equations (5 cm from A, 4 cm from the rocker pivot) gives the coupler point B≈(6.5625, 2.0454). Velocity of A: V_A=ω2×(2,0)=(0,10) cm/s. Writing V_B two ways (via the coupler from A, and via the rocker from the fixed pivot) and equating components: since A and the rocker pivot both lie on y=0, the x-component equation gives ω3=ω4 exactly (an exact consequence of the crank lying along the ground link at this instant, not an approximation). The y-component equation then gives 10+4.5625ω4=−3.4375ω4, so ω4=−10/8=−1.25 rad/s; magnitude 1.25 rad/s.

Explanation