A 4-bar mechanism with all revolute pairs has link lengths $${l_f} = 20\,\,mm,\,\,{l_{in}} = 40\,\,mm,\,\,{l_{co}} = 50mm$$ and $${l_{out}} = 60\,mm.$$ The suffixes $$'f', 'in', 'co'$$ and $$'out'$$ denote the fixed link, the input link, the coupler and output link respectively. Which one of the following statements is true about the input and output links?

A circular object of radius r rolls without $$V$$ slipping on a horizontal level floor with the center having velocity $$V.$$ The velocity at the point of contact between the object and the floor is

A link OB is rotating with a constant angular velocity of 2 rad/s in counter clockwise direction and a block is sliding radially outward on it with an uniform velocity of 0.75 m/s with respect to the rod, as shown in the figure below. If OA = 1 m, the magnitude of the absolute acceleration of the block at location A in m/s² is

A planar closed kinematic chain is formed with rigid links $$PQ = 2.0 m, QR = 3.0 m, RS = 2.5 m$$ and $$SP = 2.7 m$$ with all revolute joints. The link to be fixed to obtain a double rocker (rocker-rocker) mechanism is