Machinery's Handbook, 31st Edition
2364 CAMS AND CAM DESIGN closed-track cams but, in general, springs are necessary to keep the roller in contact with the cam at all times. Closed-track cams do not require a spring and have the advantage of positive drive throughout the rise and return cycle. The positive drive is sometimes required as in the case where a broken spring would cause serious damage to a machine. Displacement Diagrams.— Design of a cam begins with the displacement diagram. A sim- ple displacement diagram is shown in Fig. 3. One cycle means one whole revolution of the cam; i.e., one cycle represents 360 ° . The horizontal distances T 1 , T 2 , T 3 , T 4 are expressed in units of time (seconds); or radians or degrees. The vertical distance, h , represents the maximum “rise” or stroke of the follower.
T 1 Rise Interval
T 3 Dwell Interval
T 2 Return Interval
T 4 Dwell Interval
h = Follower Stroke
One Cycle = 360°
Fig. 3. A Simple Displacement Diagram The displacement diagram of Fig. 3 is not a very favorable one because the motion from rest (the horizontal lines) to constant velocity takes place instantaneously and this means that accelerations become infinitely large at these transition points. Types of Cam Displacement Curves: A variety of cam curves are available for moving the follower. In the following sections only the rise portions of the total time-displacement diagram are studied. The return portions can be analyzed in a similar manner. Complex cams are frequently employed which may involve a number of rise-dwell-return intervals in which the rise and return aspects are quite different. To analyze the action of a cam it is necessary to study its time-displacement and associated velocity and acceleration curves. The latter are based on the first and second time-derivatives of the equation describing the time-displacement curve: y f t y f v dt dy d dy a dt d y d d y displacement velocity acceleration 2 2 2 2 2 φ ω φ ω φ = = = = = = = = = ^ ^ h h or Meaning of Symbols and Equivalent Relations y = displacement of follower, inch (m) h = maximum displacement of follower, inch (m) t = time for cam to rotate through angle φ , sec, = φ / ω , sec T = time for cam to rotate through angle β , sec, = β / ω , or β /6 N , sec φ = cam angle rotation for follower displacement y , degrees β = cam angle rotation for total rise h , degrees
v = velocity of follower, in/sec (m/s) a = follower acceleration, in/sec 2 (m/s 2 ) t/T = φ / β N = cam speed, rpm ω = angular velocity of cam, degrees/sec = β/ T = φ/ t = d φ / dt = 6 N ω R = angular velocity of cam, radians/sec = πω /180
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