Chains require pulleys or drums, grooved, notched and toothed, so as to fit the links of the chain.
Wrapping connectors for communicating continuous motion are endless.
Wrapping connectors for communicating reciprocating motion have usually their ends made fast to the pulleys or drums which they connect, and which in this case may be sectors.
| Fig. 108. |
The line of connexion of two pieces connected by a wrapping connector is the centre line of the belt, cord or chain; and the comparative motions of the pieces are determined by the principles of § 36 if both pieces turn, and of § 37 if one turns and the other shifts, in which latter case the motion must be reciprocating.
The pitch-line of a pulley or drum is a curve to which the line of connexion is always a tangent—that is to say, it is a curve parallel to the acting surface of the pulley or drum, and distant from it by half the thickness of the wrapping connector.
Pulleys and drums for communicating a constant velocity ratio are circular. The effective radius, or radius of the pitch-circle of a circular pulley or drum, is equal to the real radius added to half the thickness of the connector. The angular velocities of a pair of connected circular pulleys or drums are inversely as the effective radii.
A crossed belt, as in fig. 108, A, reverses the direction of the rotation communicated; an uncrossed belt, as in fig. 108, B, preserves that direction.
The length L of an endless belt connecting a pair of pulleys whose effective radii are r1, r2, with parallel axes whose distance apart is c, is given by the following formulae, in each of which the first term, containing the radical, expresses the length of the straight parts of the belt, and the remainder of the formula the length of the curved parts.
For a crossed belt:—