Once again, the relative velocity equation is used to determine the velocity of a point on a rotating and translating bar.
vC = vB
+ vC/B = vB + ωBC × rC/B
The velocity of point B is known from previous analysis and the velocity of point C is constrained in the vertical direction. The angular velocity ωBC is not known.
vCj = -
314.2 cosθi - 314.2 sinθj +
ωBCk × (
3"sinαi + 3"cosαj )
Completing the cross product and equating the i and j components gives,
i: 0 = -314.2 cosθ - 3ωBC cosα
j: vC = -314.2 sinθ + 3ωBC sinα
The two angles θ and α are actually related (see diagram). The horizontal distance of both arms must equal each other since points A and C always aligned in the vertical direction.
(3 in) sinα = (1 in) sinθ
Substituting α = sin-1 (sinθ /3)
into the i terms and solving for ωBC gives, gives
This can now be used with the j terms to solve for the velocity of C in terms of the angle θ,