Question

Center of Zero Velocity Hydraulic cylinder D extends upward with a velocity of v, = 4 ft/s. Find the angular velocity o of bar ABC and the velocity of sliding block A. U =4 ft/s (find the instantaneous center of zero velocity)

Answer 1

From the figure,

DB = 1); AB = 2costi + 2sinoj DA= ri + bi

$\small Vector\;Loop: DB = DA+AB$

Separate i and j components.

$\small x+2cos\theta = 0\\b+2sin\theta = l$

Take derivatives.

- 2sind * w = 0 0 + 2costw = 1

Substituting given velocity of the hydraulic cylinder.

$\small \dot x-2sin\theta * w = 0\\2cos(180-30)w = \dot l = v_b = 4ft/s \Rightarrow w = -2.309 rad/s$

$\small \dot x = 2sin(180-30)* (-2.309) = -2.309ft/s$

So,

Angular velocity fo bar ABC = -2.309 rad/s

Velocity of slider A = -2.309 ft/s