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out by careful plotting, or, if convenient, it is preferably determined by a model, as irregularities due to incorrect locus of this point cannot be corrected by the other parts of the gear without more or less distortion of same. When this point is so fixed that a change of same is impracticable it may be better, however, to modify other elements if thereby the motion in general can be improved.

HELMHOLTZ MODIFICATION.

Among the various modifications of the Walschaert gear the one made by Helmholtz is probably of some advantage. This modification consists in making the link straight, and the radius rod is connected to the lifting link instead of to the link-block. The curving of the link is compensated for by the reversing shaft, or lifting-arm fulcrum, being located in a given position above the link, so that the locus of the suspension point of the lifting link forms an arc of a circle with its chord perpendicular to the centre line of the radius rod in its centre position. The radius of this arc bears the same relation to the length of the radius rod as the distance of the radius-rod connection above the link-block bears to the length of the lifting link, which results in that this connection is moving in

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an arc with a radius of the length of the radius rod, and the same motion of the valve is obtained as in the direct Walschaert gear.

Two advantages may be claimed for this modification, of which one is the straight link being simpler to make than the curved one, and the other is that on large piston-valve engines with inside admission the link fulcrum can be lowered by the amount the radius-rod connection falls over the link-block, whereby the eccentric-rod connection can be brought closer to the centre line of the axle with less length of link and eccentric throw. It has, however, the disadvantage that there is little choice in the location of the reversing shaft, or lifting-arm fulcrum, a proper position for which is hardly obtainable on all types of engines, and admits of no other method of lifting the radius rod in linking-up, or reversing, the engine.

Fig. 33 shows a combination of two diagrams: namely, those of Reauleaux and Zeuner, which coincide exactly as to the different valve events, which may be found as follows:

The distance AB represents the travel of the valve as well as the stroke of the engine, though in different scales, which makes no difference when the cut-off is always expressed in fractions or per cent of AB. The maximum cut-off is determined upon to be AR. Draw a perpendicular line RC from AB until it cuts the arc ACB. Next decide on a desired lead, and, with that as a radius, draw an arc with A as a centre. Draw a line from C tangent to the lead circle around A, when the lap of the valve is found to be equal to

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Fig. 33.—Combination of the Reauleaux and Zeuner Diagrams.

the perpendicular distance from the line CS to the centre o of the diagram. The crank will then be in position OS when the valve commences to open, or the angle AOS in advance of the dead-centre, and on OC at cut-off. Continuing, we find the valve in its middle position when the crank is on OG which is drawn parallel to SC through the centre 0. Extend this line to F, and with the exhaust lap as a radius draw the exhaust lap circle on the opposite side of the line GF and draw DE tangent to this circle, when OD is the position of the crank at the release point. From this point the exhaust remains open until the crank reaches the position OE, when it closes and compression takes place until it agairı reaches OS for admission and one revolution is completed.

By placing the Zeuner diagram upon this, draw HJ perpendicular to FG, and with the radius OH of the eccentric circle as a diameter, draw the admission valve circle OVHNO, and the lap circle with the steam lap as a radius and find the intersection occurs at V, both with the circles and the previously laiddown admission line OS and the cut-off point at the intersections at n. On the line OH set off the width of the steam port from L toward H equal to Lm, and with Omn as radius draw the arc KmK. The shaded figure enclosed by the letters VKK'nL represents the steam port opening during the admission period, and the width of the port opening at any desired position of the crank is found by measuring the distance radially from O between the lap and valve circles on the port line, as the case may be, on the desired crank position.

The exhaust openings are determined in the same manner, and are shown on opposite side of FG, where the crank passes through the arc DJE during the exhaust period with a positive exhaust lap of the size EF. When the exhaust edge of the valve is line and

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line this arc becomes GIF, or 180 degrees, and when a negative lap (clearance) occurs, the duration of the exhaust period exceeds the half revolution of the crank. The various events are indicated around the

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