Machinery's Handbook, 31st Edition
CAMS AND CAM DESIGN
2365
W = effective weight, lbs (kg) g = gravitational constant = 386 in/sec 2 (9.81 m/s 2 )
f(t) = means a function of t f( φ ) = means a function of φ
R min = minimum radius to the cam pitch curve, inch (m) R max = maximum radius to the cam pitch curve, inch (m) r f = radius of cam follower roller, inch (m) ρ = radius of curvature of cam pitch curve (path of center of roller follower), inch (m) R c = radius of curvature of actual cam surface, in., (m) = ρ − r f for convex surface; = ρ + r f for concave surface.
B
Acceleration = ∞ Velocity
h
y
A
t
T
Acceleration = ∞
Fig. 4. Cam Displacement, Velocity, and Acceleration Curves for Constant Velocity Motion Four displacement curves are of the greatest utility in cam design. 1. Constant-Velocity Motion: (Fig. 4 ) (1a) } (1b) 0 < t < T (1c) * Except at t = 0 and t = T where the acceleration is theoretically infinite. This motion and its disadvantages were mentioned previously. While in the unaltered form shown it is rarely used except in very crude devices, nevertheless, the advantage of uniform velocity is an important one and by modifying the start and finish of the follower stroke this form of cam motion can be utilized. Such modification is explained in the sec tion Displacement Diagram Synthesis on page 2367 . (2d) (2e) (2f) Examination of the above formulas shows that the velocity is zero when t = 0 and y = 0; and when t = T and y = h . 2. Parabolic Motion: (Fig. 5 ) For 0 ≤ t ≤ T /2 and 0 ≤ φ ≤ β/ 2 For T /2 ≤ t ≤ T and β/ 2 ≤ φ ≤ β y = 2 h ( t / T ) 2 = 2 h ( φ / β ) 2 v = 4 ht / T 2 = 4 h ωφ / β 2 a = 4 h / T 2 = 4 h ( ω / β ) 2 (2a) (2b) (2c) y = h [1 − 2(1 − t / T ) 2 ] = h [1 − 2(1 − φ / β ) 2 ] v = 4 h / T (1 − t / T ) = (4 h ω / β )(1 − φ / β ) a = − 4 h / T 2 = − 4 h ( ω / β ) 2 y h T t = v dt dy y h or β φ = T h v h or β ω = = = a dt d y 0 * 2 2 = =
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