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# Kinematics of Machinery a Brief Treatise On Constrained Motions of Machine Elem

Kinematics of Machinery a Brief Treatise On Constrained Motions of Machine Elem
John Henry Barr
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Since this sliding causes friction it is desirable to reduce it to a minimum. Decreasing the length of teeth lessens the angle of action and the length of the path of contact, and therefore reduces the sliding. For con- tinuous action, one pair of teeth must come into contact before the preceding pair quits contact ; therefore, the angle of action cannot be less than the angle subtended by the pitch arc; or the arc of action aPa' (or bPb') must at least equal the dis- tance between similar poin...ts (on the pitch line) of two adjacent teeth of either wheel. This condition fixes the minimum length of the teeth. If the given pitch of the two wheels (Fig. Ill) is aa r W, this determines the minimum arc of action. This arc may be distributed in any way between the approach and recess arcs, though these are commonly nearly equal. Lay off Pa = Pb = Pg, and Pa' = Pb' = Pg r equal to the desired arcs of approach and recess, respectively; then g and g' are the extreme points in the faces of B and A, respectively ; or circles drawn with the radii O'g and Og' are the boundaries of the teeth of the two wheels.

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