Valves and valve gear mechanisms by Dalby William Ernest 1874-1918

Author:Dalby, William Ernest, 1874-1918
Language: eng
Format: epub
Tags: Steam-engines
Publisher: London, E. Arnold
Published: 1906-03-25T05:00:00+00:00

Pig. 100. EqDlVALENT EOCBNTRIC CORBSSPOHDINO WITH THE SiKPLIFIKD OSAB, FiG. 99.

Again, the point a divides the line OA in the same proportion that the point P divides the link Ee. Also b divides the line BO in the same proportion that P divides the link Ee. Therefore

Aa:aC = Gb: 65, and the angles AaC and CbB are equal. Therefore the triangles AaC and CbB are similar. Since, therefore, aC is parallel to 65, AC is parallel to CB, but C being a common point, the lines AC &nd CB are in the same straight line, and this line is divided by the point C in the same ratio that a divides OA, that is in the same ratio that P divides the link Ee. Hence to find the equivalent eccentric for a given position of P: —

Set out the two eccentrics from a common point 0, making the

Digitized byGoOgIC

constant angle x with each other. Join the ends with a straight line and take the point C so that it divides AB in the same ratio that the assigned position of P divides the link Ee. Join OC. Then 00 is the equivalent eccentric for the motion of P.

The equivalent eccentric ia shown dotted in Fig. 99. It wilt now be undeiBtood that, if the equivalent eccentric be made a real eccentric, and if the point P is connected to it by a real eccentric rod, and both the actual eccentrics and the link be taken away, P, being constrained to move in a straight line, will receive the same motion from the single eccentric that it actually received from the combined action of the two actual eccentrics and the link.

The link in Fig. 99 will receive the same motion if it is driven by the equivalent eccentric and either of the actual eccentrics, the other being suppressed.

For instance, suppose OA to be connected to the link as before, the dotted equivalent eccentric gear to be made into a real gear and the eccentric QB and its gear to be suppressed altogether. Every point in the link will move in exactly the same way as it did under the joint action of the cranks OA and QB.

Examining the motion of the point E, it will be found that it may be considered due to an imaginary eccentric QB found by joining the points A and C and taking B so that

AC:CB~eP:PE.

97. Approzlniate theory of the Stephenion link motion. EqnlTalent eccentrio. Passing from the simplified form. Fig. 99, to the actual form, Fig. 101, the main differences in the conditions of motion of the link are:—

(1) The point P is compelled to move in an exact, or in some cases an approximately horizontal line, so that when its position is changed relatively to the link, the link itself must be raised or lowered.

(2) The point e moves nearly in a line, passing through the central position fig and the centre of the axle; and E moves nearly in a line, passing through its central position E, and the centre of the axle.

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