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 P6.32. The diameter of the base circle of the cam is 180 mm, the diameter of the roller follower is 80 mm, and the eccentricity of the roller follower is 40 mm.

Table P6.32 Displacement information for disk cam and reciprocating roller follower.

Cam angle

Θ (degrees)

Lift L

(mm) Output y 0◦−40◦ 0 Dwell 40◦−100◦ 60 Half-rise simple harmonic motion 100◦−180◦ 20π Half-rise cycloidal motion 180◦−260◦ 0 Dwell 260◦−360◦ 60+20π Full-return cycloidal motion Part I: Sketch the displacement diagram and its first two derivatives. At the cam rotation angle

Θ = 85◦, determine:

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

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

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

(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. Part II: Repeat the problem for the cam angle Θ = 120◦.