For the mechanism in the posture shown in Fig. P3.51, the first- and second-order kinematic coefficients are θ

3 = −8.333 rad/rad,r

2 =

−100 mm/rad, θ

3 = −8.642 rad/rad2, and r

2 =

−237.033 mm/rad2 (where θ2 is the input and r2 is the vector from ground pin O2 to pin A). Wheel 3 is rolling without slipping on the ground link at point C and sliding in the slot that is cut in link 2.

The radius of the ground link is ρ1 = 60 mm, and the radius of the wheel is ρ3 = 15 mm. Determine:

(a) the unit normal vector to the path of point D;

(b) the radius of curvature of the path of this point;

and

(c) the x and y coordinates of the center of curvature of this path. If the angular velocity of link 2 is a constant ω2 = 30 rad/s ccw, then determine the acceleration of point D.