The mechanism below has a crank that revolves clockwise at O $.$

Using vector diagrams, determine:

a$)$ The linear velocity of the piston and the angular velocity of the link $AB$ about $A.$

b$)$ The angular acceleration of the link $AB$ about A and the inertial resistance produced by the piston.

c$)$ Using trigonometry, confirm your results for the velocity and acceleration in parts $($a$)$ and $($b$).$