Machinery's Handbook, 31st Edition
178
Simple Mechanisms Differential Pulley
r R
In the differential pulley a chain must be used, engaging sprockets, so as to prevent the chain from slipping over the pulley faces. PR W R r P R W R r W R r PR 2 1 2 2 = − = − = − ^ ^ h h The Chinese windlass employs the differential motion principle in that the resultant motion is the difference between two original motions. The hoisting rope is arranged to unwind from one part of a drum or pulley onto another part differing somewhat in diameter. The distance that the load or hook moves for one revolution of the compound hoisting drum is equal to half the difference between the circumferences of the two drum sections. Screw
P
W
Chinese Windlass
R
F = force at end of handle or wrench; R = lever-arm of F ; r = pitch radius of screw; p = lead of thread; Q = load. Then, neglecting friction: . . F Q R p Q F p R 62832 62832 # # = = If μ is the coefficient of friction, then: For motion in direction of load Q which assists it:
Q
p
. . 62832 62832
r p r p µ + −
R r
F Q =
#
# µ
r
F
For motion opposite load Q which resists it: . . F Q r p p r R r 62832 62832 # # µ µ = − + Geneva Wheel
R
Geneva wheels are frequently used on machine tools for indexing or rotating some part of the machine through a fractional part of a revolution. The driven wheel shown in the illustration has four radial slots located 90 degrees apart, and the driver carries a roller k which engages one of these slots each time it makes a revolution, thus turning the driven wheel one-quarter revolution. The concentric surface b engages the concave surface c between each pair of slots before the driving roller is disengaged from the driven wheel, which prevents the latter from rotating while the roller is moving around to engage the next successive slot. The circular boss b on the driver is cut away at d to provide a clearance space for the projecting arms of the driven wheel. In designing gearing of the general type illustrated, it is advisable to so proportion the driving and driven members that the angle a will be approximately 90 degrees. The radial slots in the driven part will then be tangent to the circular path of the driving roller at the time the roller enters and leaves the slot. When the gearing is designed in this way, the driven wheel is started gradually from a state of rest and the motion is also gradually checked.
d
c
b
k
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