Page:The Kinematics of Machinery.djvu/92

 proportion to the angular velocities of the bodies. The pitch circles of spur-wheels are thus simply the centroids of their normal sections. We

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touch here, consequently, upon a case in which the centroids are of peculiar simplicity, and which moreover has the most extended practical application in the construction of machines.

§ 9. Reduction of Centroids.

The pair of centroids which we found in the first example of § 8 completely determines the relative motion between the links d—e and a—h of the given kinematic chain, and must therefore equally express that motion, whichever link of the chain be fixed or in whatever way it be set in motion. Let us suppose the chain to be arranged in the first of the four methods given on page 41, that is by making b—c the fixed link; we can obtain in this way another important mechanism, one in which the links, a—h and d—e both describe circles, connected