Machinery's Handbook, 31st Edition
CAMS AND CAM DESIGN 2375 Fig. 16 shows the shape of the cam when O 1 from Fig. 15 is chosen as the cam shaft cen ter, and it is seen that the pressure angle at a point on the cam profile corresponding to point P 1 is α 1 and at a point corresponding to point P 2 is α 2 . In the foregoing, a cam mechanism has been so proportioned that the pressure angles α 1 and α 2 at points on the cam corresponding to points P 1 and P 2 were obtained. Even though P 1 and P 2 are the points of greatest slope on the displacement diagram, the pressure angles produced at some other points on the actual cam may be slightly greater. However, if the pressure angles α 1 and α 2 are not to be exceeded at any point—i.e., they are to be maximum pressure angles—then P 1 and P 2 must be selected to be at the locations where these maximum pressure angles occur. If these locations are not known, then the graphical procedure described must be repeated, letting P 1 take various positions on the curve for rise ( AB ) and P 2 various positions on the return curve ( CD ) and then setting R min equal to the largest of the values determined from the various positions.
β 1
β 2
B C
P ” 1
P 2
h
τ 1
y 2 y 1 0 2 4 6 8 1012141618202224262830323436 360° = L = 2 π k A P 1 D E τ 2
Fig. 17. Displacement Diagram Determination of Cam Size for Swinging Roller Follower.— The proportioning of a cam with swinging roller follower having specific pressure angles at selected points follows the same procedure as that for a translating follower. Example: Given the diagram for the roller displacement along its circular arc, Fig. 17 with h = 1.95 in., the periods of rise and fall, respectively, β 1 = 160 ° and β 2 = 120 ° , the length of the swinging follower arm L f = 3.52 in., rotation of the cam away from pivot point M , and pressure angles α 1 = α 2 = 45 ° (corresponding to the points P 1 and P 2 in the displacement diagram). Find the cam proportions. Solution: Distances k tan τ 1 and k tan τ 2 are determined as in the previous example, Fig. 14. In Fig. 18, R y 1 is determined by making the distance R u R y 1 = y 1 along the arc R u R o and R y 2 by making R u R y 2 = y 2 . The arc R u R o = h and R u indicates the lowest position of the center of the swinging roller follower and R o the highest position. Because the cam (i.e., the surface of the cam as it passes under the follower roller) rotates away from pivot point M , k tan τ 1 is laid out away from M , that is, from R y 1 to E 1 and k tan τ 2 is laid out toward M from R y 2 to E 2 . Angle α 1 at E 1 determines one ray and α 2 at E 2 another ray, which together subtend an area A having the property that if the cam shaft center is chosen inside this area, the pressure angles at the points of the cam corresponding to P 1 and P 2 in the displacement diagram will not exceed the given values α 1 and α 2 , respec tively. If the cam shaft center is chosen on the ray drawn from E 1 at an angle α 1 = 45 ° , the pressure angle α 1 on the cam profile corresponding to point P 1 will be exactly 45 ° , and if chosen on the ray from E 2 , the pressure angle α 2 corresponding to P 2 will be exactly 45 ° . If another point, O 2 for example, is chosen as the cam shaft center, the pressure angle corre sponding to P 1 will be α ′ 1 and that corresponding to P 2 will be α 2 .
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