Velocity diagrams. Their construction and their uses. Intended for all who are interested in mechanical movements by MacCord Charles William 1836-1915

Author:MacCord, Charles William, 1836-1915
Language: eng
Format: epub
Tags: Links and link-motion, Machinery, Kinematics of
Publisher: New York, J. Wiley; London, Chapman & Hall
Published: 1901-03-25T05:00:00+00:00

Fig. 42.

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we have already shown that the angular velocities of the driver and follower are inversely proportional to the radii of contact, at any given instant.

Assuming then, in Fig. 42, CA, which is equal to DF, as the unit distance, and assigning to F any linear velocity at pleasure; from what precedes we shall have, when for instance J and K meet upon the line of centres,

KF:KD:: lin. vel. Fi lin. veL A.

The required velocity of A may then be easily determined graphically as in Fig. 43. Upon either of two lines intersecting in K at any convenient angle, set off from K the distances KF, KDy\tzkcn from Fig. 42; on the other line set off KV, the assigned linear velocity of F\ draw FF, and through D a parallel to it, cutting the prolongation of KV in V\ then KV^ is the required linear velocity of A^ since by similar triangles we have

KF:KD'.:KV:KV\

68. We repeat in Fig. 44 the construction for determining the velocity of B when that of A is known; AC representing the position of the crank, AB that of the link, and ^B the line of travel. Let AM, perpendicular to ACy represent the velocity of A ; this has a component Am in the line of the link, to which BN mwst be equal. Then drawing at N a perpendicular to AB^ cutting CB in 7?, we have BR as the resultant velocity of B. This work may be abbreviated by drawing AR^ parallel to CB^ and limited by the prolongation of Mm perpendicular to AB, since the triangle AmR' thus formed, is similar and equal to BNR.

Now, in constructing a velocity diagram such as is required, it is clearly advisable not to select random points

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VELOCITY DIAGRAMS,

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oi contact between the driver and follower, like K and / in the preceding illustrations, but to proceed in an orderly and

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