A Scotch-yoke mechanism is used to convert rotary motion into reciprocating motion. As the disk rotates at the constant angular rate ω, a pin A slides in a vertical slot causing the slotted member to displace horizontally according to x = r sin(ωt) relative to the fixed disk center O. Determine the expressions for the velocity and acceleration of a point P on the output shaft of the mechanism as functions of time, and determine the maximum velocity and acceleration of point P during one cycle. Use the values r = 75 mm and ω = π rad /s.
