Source: Physics Competition - Mechanics
Problem Sets:
Problem
A pushrod AB slides in a vertical guide K, driven by a cam M rotating about axis O with constant angular velocity $\omega$. At the instant shown, the contact point A is at a distance $r$ from O (OA=r). The angle between the normal $n$ to the cam surface at A and the line OA is $\alpha$.
P0728-problem-1
Let $\vec{v}_{A,cam}$ be the velocity of the contact point A on the cam and $\vec{v}_{AB}$ be the velocity of the pushrod (follower). The rod is constrained to move vertically, so $\vec{v}_{AB}$ is vertical. The follower has a flat horizontal face, so the relative sliding velocity between the cam and the follower must be tangential to the cam surface.
The velocity of point A on the cam is related to the velocity of the rod by:
$$\vec{v}_{A,cam} = \vec{v}_{AB} + \vec{v}_{slide}$$Since $\vec{v}_{AB}$ is vertical and $\vec{v}_{slide}$ is tangential to the surface, the norm component of $\vec{v}_{A,cam}$ and $v_{AB}$ must be equal.
$$(v_{AB})_{norm} = (\vec{v}_{A,cam})_{norm}$$Therefore,
$$v_{AB} \sin\alpha = v_{A,cam} \cos\alpha$$ $$v_{AB} = \omega r \cot\alpha$$