For the linkage of Prob. 3.61 in the posture shown, the first- and second-order kinematic coefficients are θ

3 = θ

4 = 1 rad/rad, R

34 = −12 in/rad, θ

3 =

θ

4 = +2.309 rad/rad2, and R

34 = −20.785 in/rad2 (where R34 is the vector from O4 to point B fixed in link 3). Determine the firstand second-order kinematic coefficients of coupler point C. Then, determine:

(a) the unit tangent vector and the unit normal vector to the path traced by point C;

(b) the radius of curvature of this path;

and

(c) the x and y coordinates of the center of curvature of this path. If the angular velocity of input link 2 is a constant ω2 = 15kˆ rad/s, determine the acceleration of point C.