The cam angle, the rise and fall, and the output motion of a disk cam with a reciprocating roller follower are as given in Table P6.31. The diameter of the base circle of the cam is 9.60 in, the diameter of the roller follower is 2.40 in, and the eccentricity

(offset) of the roller follower is 2.80 in.

Table P6.31 Displacement information for plate cam with reciprocating roller follower.

Cam angle

Θ (degrees)

Lift L

(in) Output y 0◦−5◦ 0 Dwell 5◦−115◦ 2.00 Full-rise cycloidal motion 115◦−120◦ 0 Dwell 120◦−180◦ 3.40 Full-rise simple harmonic motion 180◦−210◦ 0 Dwell 210◦−310◦ 4.80 Full-return eighth-order polynomial motion 310◦−325◦ 0 Dwell 325◦−360◦ 0.60 Full-return simple harmonic motion Sketch the displacement diagram and its first two derivatives. At the cam rotation angle Θ = 235◦, determine:

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

(b) the coordinates of the point of contact between the cam and the roller follower, expressed in the rotating Cartesian coordinate system attached to the cam;

(c) the radius of the curvature of the cam profile;

and

(d) the pressure angle of the cam.