| L = 2 √ {c2 − (r1 + r2)2} + (r1 + r2) ( π − 2 sin−1 | r1 + r2 | ); |
| c |
(32 A)
and for an uncrossed belt:—
| L = 2 √ {c2 − (r1 − r2)2 } + π (r1 + r2 + 2 (r1 − r2) sin−1 | r1 − r2 | ; |
| c |
(32 B)
in which r1 is the greater radius, and r2 the less.
When the axes of a pair of pulleys are not parallel, the pulleys should be so placed that the part of the belt which is approaching each pulley shall be in the plane of the pulley.
§ 60. Speed-Cones.—A pair of speed-cones (fig. 109) is a contrivance for varying and adjusting the velocity ratio communicated between a pair of parallel shafts by means of a belt. The speed-cones are either continuous cones or conoids, as A, B, whose velocity ratio can be varied gradually while they are in motion by shifting the belt, or sets of pulleys whose radii vary by steps, as C, D, in which case the velocity ratio can be changed by shifting the belt from one pair of pulleys to another.
| Fig. 109. |
In order that the belt may fit accurately in every possible position on a pair of speed-cones, the quantity L must be constant, in equations (32 A) or (32 B), according as the belt is crossed or uncrossed.