The link $AB$ can rotate around a fixed pivot point A and is connected to the link $BD.$ The position of the pivot A allows link $AB$ to lie horizontally on the base, so that link $BD$ can be connected and hang vertically right at the edge of the base. A moment, $M_A,$ is applied to link $AB$ to maintain a constant angular velocity, ${}_{AB},$ and drag link $BD$ up the edge of the base as shown below.

Determine the angular acceleration of link BD$,{}_{BD},$ as a function of $$ at any instant.

The length of link $AB,L_{AB},$ from pivot point $A$ to the pin connection at $B$ is known.

Hint: Point C on the corner of the base is not moving.

B

Solve without instantaneous center of zero velocity

Use this for parts with fixed points

$v_D={}_{\frac{A}{D}}{r}_{\frac{D}{A}}$

$a_D={}_{AD}{r}_{\frac{D}{A}}-{}_{AD}^2(r_{\frac{D}{A}})$

Use this for parts moving away from

$v_C=v_A+r_{\frac{C}{A}}+(v_{\frac{C}{A}}{)}_{xyz}$

$a_C=a_A+{}^{}{r}_{\frac{C}{A}}+(r_{\frac{C}{A}})+2(v_{\frac{C}{A}}{)}_{xyz}+(a_{\frac{C}{A}}{)}_{xyz}$