Problem 3: (35 points)
Figure 3 illustrates two links. The angular position of link B
OA is a known function of time and rotates in the clockwise
direction (measured from dotted vertical reference line).
Link OA is connected to link CB through the sliding collar
A, and CB is connected to ground by a hinge at C.
Tasks:
(a) Redraw the mechanism in a general configuration,
select coordinates, and obtain the kinematic constraint
expressions. Also, obtain the general equations defining the
orientation of link CB and the distance from C to A in terms
of $\theta$. [6']
(b) State the general equation defining the angular velocity
of link CB and the length changing rate of CA, and put them
into matrix format, and solve the angular velocity of link CB and the length changing rate of CA
in terms of $\theta$, your defined variables and their derivatives. (11')
(c) State the general equation defining the angular acceleration of link CB and the length of CA,
and put them into matrix format, and solve the acceleration of link CB and the acceleration of CA
in terms of $\theta$, your defined variables and their derivatives. (13')
(d) State the general equations defining the velocity and acceleration of point B. (5')