For the rack-and-pinion mechanism in the posture shown, the first- and second-order kinematic coefficients are R

2 = −400 mm/rad, R

4 =

−346.41 mm/rad, R

2 = 1 385.6 mm/rad 2, and R

4 = 1 400 mm/rad2 (where R2 is the vector from ground pin O2 to the point of contact, C, of link 3). Determine:

(a) the first- and second-order kinematic coefficients of point B;

(b) the unit tangent vector and the unit normal vector to the path traced by point B;

(c) the radius of curvature of this path; and

(d) the x and y coordinates of the center of curvature of this path. If the constant angular velocity of the input link is ω2 =

−12kˆ rad/s, determine the acceleration of point B.