linkage applied to the "Grasshopper" type of side lever engine. A B is a link pivoted at A, and connected at B to the centre of the link P C, so that A B = B P = B C. Hence, B is the centre

Fig. 44.

of a circle passing through PA C, having PC for a diameter, therefore if the point C move in the line A C, the point P will move in the line P A perpendicular to A C, since the angle PA C must always be a right angle (Euclid iii., 31).

In actual practice it is more convenient to attach C to the end of a radius bar, CD, pivoted at D, as with a small movement the paths of C and P are sufficiently in straight lines for all practical purposes. The dotted lines show the travel of the radius bar.

=

45°,

EX. 14.-Draw the linkwork of Scott-Russell's parallel motion (Fig. 44) as follows:-A B = 11⁄2", CD = 2′′, angle A B P and trace out the path of P, while P moves in a line equal in length to twice P A.

Peaucellier's Straight Line Motion (Fig. 45).—This was invented by a French military officer in 1801, and consists of eight links, so arranged that a certain point moves in a perfect

*

straight line for all possible positions of the link work. The links A B and A C are equal, and are pivoted together at A, their other ends are attached to two corners of an equal four-link frame, BDCP, of which the corner, D, is attached to one end

* In counting the number of links in any linkage, the fixed link, as A E in Fig. 45, is counted.

=

of a short link, DE, having its end, E, pivoted in the line AP, and such that A E ED. Under these conditions the point P moves in a straight line, but if the distance A E is made greater or less than the length of the link ED, then the point P draws the arc of a circle having its centre to the right or the left of P respectively, the radius of which depends upon the ratio of A E to ED.

=

=

=

EX. 15.-Draw the linkwork of Peaucellier's straight line motion (Fig. 45) as follows:-AB = A C 41", A E ED 1ğ", DB CP = PB = 13", and trace out the path of the point P for all possible positions of the links.

=

DC

=

(Notice that the limiting positions are reached when the links ED, DB and ED, DC become a straight line.)

=

EX. 16.-Draw the linkwork of Peaucellier's straight line motion as in Fig. 45, but making A E 1" in the first case, and 21" in the second case, and trace the path of P for each case. Parallel Motions for Engine Indicators.-These comprise sóme important applications of straight line linkages, and afford very useful examples in drawing.

Thompson's Indicator (Fig. 46).—The end, A, of the link A B is attached to the piston of the indicator by a ball and socket joint, so that A moves in the vertical straight line shown dotted. CD and FE are swinging links pivoted to the indicator at D and F respectively. The pencil is fixed at P, and moves four times the distance of the piston travel, which is usually ". The pencil link PBC is horizontal, and the link CD vertical, when the piston

E

Fig. 46.

B

is at mid-stroke; and the points P AD are in one straight line for all positions of the movement.

EX. 17.-Draw the linkwork of Thompson's indicator in position at bottom-stroke as follows:-PE = 1.81′′, PC

=

1.34", CD

=

1.77", EF

=

=

3.15" = 4 times B C, BA 0.98", pivot D is 0.78" to right of dotted line of piston travel, and pivot F is 1.45′′ to left of same line; the pencil point P is 2.24" to the left of the line and a distance equal to half the travel of the pencil below the pivot F. Find at least 6 points in the path of P for a travel of the point A of ". Scale twice full size.

Crosby Indicator (Fig. 47).-The piston-rod is shown by

A B, and moves in a vertical straight line. A short link, BE, connects the piston-rod to the pencil link, PEF, and is connected at the point C to one end of a short swinging link, D C, pivoted at D to the indicator. The end, F, of the pencil link is attached to one end of a swinging link, F G, pivoted at G to the instrument, and the pencil is fixed at P. The piston-stroke is ", and is multiplied six times.

Fig. 47.

DQ

E

GB

པ་--

=

EX. 18. Draw the link work of Crosby's indicator (Fig. 47) in position at half

=

stroke. Pencil link horizontal, fixed point G is ğ" from pistonrod centre, fixed point D7" from piston-rod centre and 13" above G. BE = 3" 2", BC 1", G F 14", DC7", FP GF = 33′′ six times FE. Then draw path of P for a travel of the piston rod A B of 3". Scale twice full size. Tabor Indicator (Fig.

=

48).-In this instrument the short

link C D or E F of the Thompson or Crosby Indicator (Figs. 46

G

The

and 47) is dispensed with and replaced by a small pin, which is made to move in a curved slot cut in a small plate fixed to the instrument, the shape of which causes the pencil to move in a straight line. piston-rod is shown by A B and is connected at B by a short link B C to a point C in the pencil-rod P E, the end E of the pencil-rod is attached to the end of a swinging link E F, pivoted at F. The slotted plate is shown at G, the pin D moving in the slot. The stroke of the piston is ", and is multiplied five times. The points FBP are in the same straight line at all parts of the stroke.

Fig. 48.

=

EX. 19.-Draw the link work of the Tabor indicator as in Fig. 48, when at bottom of stroke; the line FBP being horizontal. Length of E P = 31′′ = five times E C, C D EC, EF 11′′ and F is fixed" from centre of piston-rod. Links BC and E F are parallel. Trace out shape of curve in plate G, while P moves in a vertical straight line for 3". Scale twice full size.

=

Link Work for Atkinsons' Differential Gas Engine (Fig. 49). The object of this very ingenious arrangement of links to give two forward and two backward strokes of different lengths to the piston of the gas engine while the crank makes one complete revolution, thus giving one explosion per revolution. The crank shaft is shown at A, A B being the crank, the end B is connected by a link, BCE, at the point C to the end C of a swinging arm, CD, longer than the crank, and which, therefore, swings twice through a certain arc while the crank makes one revolution. The piston-rod, PE, is connected by a working joint to the piston at P, the opposite end being attached to a point E in the link B CE. As a result of this arrangement

the piston moves in a horizontal line as follows, supposing it to start from the back stroke the crank A B being at about the position B':

(1) Outwards for a short stroke while the crank moves through 59°, the link D C moving downwards, the charging stroke;

Inwards for a shorter stroke, while the crank moves through 76°, the link DC moving upwards, the compression stroke;

(3) Outwards for a much longer stroke, while the crank moves through 92°, the link D C moving upwards, the explosion stroke; (4) Inwards for a stroke of the same length as (3), while the crank moves through 133°, the link DC moving downwards, the exhaust stroke; the crank having thus made one complete revolution. The connecting-rod, P E, is inclined at 21° to the centre line of the movement of the piston, when at the limiting top and

bottom positions. These limiting positions are when the link BC and the crank A B are in the same straight line.

=

=

EX. 20.-Show the travel of the piston in an Atkinson's differential gas engine for an arrangement of links, as in Fig. 49. Take at least twelve different positions of the crank. Connecting-rod, PE = 3', radius link, D C = 1′ 6′′, crank 127′′ long, C B 2' 28", CE 4", angle BCE 95°. Scale, 3" Ï'. = = Joy's Valve Gear (Fig. 50).-This arrangement affords a very useful example of the paths of points in linkwork, and is besides of great service in leading up to the drawing of valve diagrams. The slide valve is worked through a system of rods, which derive motion from a point in the connecting-rod, thus dispensing with the usual eccentrics and link motion. In Fig. 50 is shown the arrangement for a large vertical marine engine.

NI

5.17

M

PC is the piston-rod, CB the connecting-rod, and BA the crank. A link, DE, is attached at one end to a point D in the connectingrod, and at the other end to the end E of a swinging link or radius-rod, EF, pivoted at the top end, F. From a point G in the link D E, a long link, G L, is carried to the front of the engine, and is connected at its end, L, through the link LM to the slide-rod M N, which moves in a parallel vertical line to the piston. A point, H, in this link is connected to one end of a radius rod, H K, the upper end of which is pivoted at K. Reversing is effected by attaching the link HK to a moving frame, which can swing about a pivot below K, so that H K can be moved through a sufficient arc to move the linkwork for reversing. The locus of the points E and H are, of course, circular arcs, and in drawing the linkwork it is usual to trace the complete paths of the points D, G,

and L.

B

Fig. 50.

EX. 21.-Draw the linkwork of Joy's valve gear, as in Fig. 50. Connecting-rod, CB = 7′ 2′′, C D = 3′ 1′′; crank, AB 1'8"; link FE 4' 8"; link DE 2′ 6′′; DG = 8"; link

=

=

=