The mechanism of a machine is constructed so that for a short time the roller at A follows the surface of the cam described by the equation r = a + b cosθ. If θ' and θ'' are given, determine the magnitudes of the roller’s velocity and acceleration at the instant θ = θ₁. Neglect the size of the roller. Also determine the velocity components v_Ax and v_Ay of the roller at this instant. The rod to which the roller is attached remains vertical and can slide up or down along the guides while the guides move horizontally to the left. Given:

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8 = 0.5 8' = 0 rad S rad 2 S 0₁ = 30 deg a = 0.3 m b = 0.2 m