The cam rotation angle, the rise and fall, and the output motion of a disk cam with a reciprocating roller follower are as given in Table P6.35. The diameter of the base circle of the cam is 2.80 in, the diameter of the roller follower is 1.20 in, and the follower eccentricity is 0.40 in.

Sketch the displacement diagram and its first two derivatives. At the cam rotation angle Θ =

230◦, Table P6.35 Displacement information for disk cam and the reciprocating roller follower.

Cam Angle

Θ (degrees)

Lift L

(in) Output motion y 0◦−30◦ 0 Dwell 30◦−90◦ 1.20 Full-rise simple harmonic motion 90◦−120◦ 0 Dwell 120◦−180◦ 0.80 Full-rise cycloidal motion 180◦−210◦ 0 Dwell 210◦−270◦ 0.80 Full-return cycloidal motion 270◦−300◦ 0 Dwell 300◦−360◦ 1.20 Full-return simple harmonic motion determine:

(a) the first-, second-, and third-order kinematic coefficients of the displacement diagram;

(b) the radius of the curvature of the cam surface;

(c) the unit tangent and normal vectors to the cam at the point of contact with the follower; and

(d) the coordinates of the point of contact between the cam and the follower. Express your answers in the moving Cartesian coordinate system attached to the cam; and

(e) the pressure angle of the cam.