For the four - bar linkage shown in the figure, the angular velocity of link AB is $$1$$ rad/s. The length of link CD is $$1.5$$ times the length of link $$AB$$. In the configuration shown, the angular velocity of link CD in rad/s is

For the configuration shown, the angular velocity of link AB is $$10$$ rad/s counterclockwise. The magnitude of the relative sliding velocity (in ms^-1) of slider B with respect to rigid link CD is

Match the approaches given below to perform stated kinematics/dynamics analysis of machine

Analysis
$$P.$$ Continuous relative rotation
$$Q.$$ Velocity and acceleration
$$R.$$ Mobility
$$S.$$ Dynamic - static analysis

Approach
$$1.$$ D' Alembert's principal
$$2.$$ Grubler's criterion
$$3.$$ Grashoff's law
$$4.$$ Kennedy's theorem

A quick return mechanism is shown in below. The crank OS is drive at $$2$$ rev/s in counter clockwise direction

If the quick return ratio is $$1:2$$, then the length of the crank in mm is