angular velocities of the wheels are inversely as the perpendiculars let fall upon the common tangent from the centres of motion.

73. The form of wheels represented in fig. 52 is used in silk-mills and in the Cometarium. The curves may be indefinitely varied, but they must always be constructed to answer the conditions explained in Art. 72.

74. Roëmer's Wheels.-E F and C D are the axes of two conical wheels or bevel wheels K and G, having their vertices turned in opposite directions; the teeth of K are formed like those of the ordinary bevel wheel; but the teeth on a are formed by a series of pins, e k, fixed on the surface of the frustum G. By varying the relative position of these pins any given velocity ratio may be obtained.

75. Various combinations have been invented for producing a varying angular velocity; such as the eccentric crown wheel and broad pinion, the eccentric spur wheel with a shifting intermediate wheel, and so on.

INTERMITTENT AND RECIPROCATING MOTIONS PRODUCED BY WHEELWORK HAVING ROLLING CONTACT.

76. The following is an example of an intermittent motion produced by the continuous motion of a toothed wheel:

A driving wheel a, having sunk teeth on a portion of its edge,

communicates an intermittent motion to the wheel B, which has a corresponding number of teeth on a portion of its edge. The

Fig. 54.

G

portion D C of the wheel B, being a plain arc of a circle described from A as centre, allows the plain portion of the wheel a to revolve without any interruption. The wheels are brought into gear by a pin p fixed to the wheel A, and a GUIDEPLATE G e fixed to the wheel B.

Now, when a revolves in the direction of the arrow, the plain portion of its edge runs past D C without moving the wheel B, and at the same time keeps it from shifting; but when the pin p comes into contact with the guide-plate, the wheel B is moved round, and the teeth D E engage themselves with the

B

Fig. 55.

A

D

E

teeth on B, and thus the wheel B is constrained to make a revolution; it then remains at rest until the pin p again comes round to meet the guide- plate.

one.

77. The Rack and Pinion.-By this combination a circular reciprocating motion is changed into a reciprocating rectilinear Teeth are cut upon the edge of the straight bars, B C and D E, so as to work with the teeth upon the pinion A. These toothed bars are called racks, and they are constrained to move in rectilinear paths by guides or rollers. The racks in this combination move in opposite directions.

78. Fig. 55 represents an application of the double rack, for

Fig. 56.

B

converting a continuous circular motion of a wheel, A, into a reciprocating rectilinear motion, given to the frame

B E.

The teeth on a are formed by pins or staves placed about one quarter round the face of the wheel; these staves act alternately

upon the racks formed on the upper and under sides of the frame. The tooth on each rack which comes first into contact with the stave of the pinion is made longer than the others, in order that the first stave should act obliquely upon it, thereby tending to lessen the shock. In this figure the lower stave is represented as leaving the last rack on the under side, and the upper stave as commencing its action on the elongated tooth of the upper rack.

V. ON SLIDING-PIECES, PRODUCING MOTION BY SLIDING CONTACT.

The Wedge or Movable Inclined Plane.

G

E

Fig. 57.

79. Let A B C be a movable inclined plane or wedge, sliding along the smooth surface D E, by a pressure P applied to the end в C, and producing a vertical motion in a heavy rod G P1 resting on the plane A C, and constrained to move in a straight path by means of guide rollers. The velocity ratio of P and P1 will be constant, being expressed by the following equality :— velocity P A B length of the wedge

velocity P1 BC

or

D

thickness of the wedge

P

B

E

To transmit motion from an axis A D to another axis B C, parallel to it.

B C.

Fig. 58.

G

80. The axis a D carries an arm A E, and a pin E F, which enters and slips freely in a slit made in the arm G B, attached to the axis When the axis A D revolves it communicates a rotation in the same direction to the other axis B C, but with a varying velocity ratio, for the pin F continually changes its distance BF from the axis B C.

When the distance between the parallel axes is small, and the axis

D

B

A D revolves uniformly, the angular velocity of the axis B C

varies, very nearly, inversely as the distance, B F, of the pin from this axis.

The Eccentric Wheel.

81. This mechanism is usually employed to give motion to the

E

R

K

Fig. 59.

L

slide valve of the steam engine. In fig. 59, в represents the axis of the eccentric wheel; c G the centre of the circle; E R F K a hoop which embraces the eccentric wheel so that the one may revolve freely within the other; E F D a frame connecting

this loop with the extremity D of the bent lever D L G, turning on the fixed centre L. Now, when the eccentric wheel revolveş in the direction of the arrow shown in the figure, the frame with the pin D is pushed to the right, and when the lob side of the eccentric has passed the line of centres, B and D, the frame with the pin D is drawn to the left, and so on. Thus the continuous rotation of the axis в produces a reciprocating circular motion in the pin D. The stroke of the pin D will be equal to twice c B, or double the eccentricity of the wheel.

Cambs, Wipers, and Tappets.

82. Cambs are those irregular pieces of mechanism to which a rotatory motion is given for the purpose of producing, by sliding contact, reciprocating motions in rods and levers.

F

E

The

83. In fig. 60, B C D represents the camb, turning on its axis Fig. 60. A, and giving a reciprocating rectilinear motion to the heavy rod E F, which is restrained to move in its rectilinear path by the guide rollers. rotation of the axis ▲ being in the direction of the arrow, the rod E F has an upward motion until the extreme point в of the camb comes in a line with the rod, then the portion B G of the camb allows the rod to fall, by its own weight or by the action of a spring, until the point G comes in a line with the rod, and so on; thus one revolution of the camb here presented will cause the rod

B

to make three upward and three downward strokes. By varying the curve of the camb any law of motion may be given to the rod.

Fig. 61.

84. In fig. 61, the pin E of the rod is made to traverse a groove E G D, cut in the camb plate, so that the pressure of the camb upon the pin produces the downward stroke of the rod as well as its upward stroke. In this case the rod will only make one upward and one downward stroke in every revolution of the camb plate. The length of the stroke of the rod will be equal to the difference between A D and a G, where D is the point in the groove furthest from the centre A, and G is the point nearest to it.

E

85. To find the curve forming the groove of a camb, so that the velocity ratio of the rod and the axis of the camb may be

constant.

Let A be the centre of the camb, and C A B Q the direction of the rod. From A as a centre, with

any convenient distance A c, describe the circle C E D B N.

Fig. 62.

O

D

d

b

E

On B A take в a, equal to the length of the stroke of the rod : divide it into any convenient number of equal parts, say five, in the points b, c, d, e; and divide the semicircle B D E F G into the same number of equal parts by the radial lines, a D, a E, A F. From A as a centre, with a b, A c, a d, a e, as radii, describe circles cutting A D, A E, &c., respectively, in the points g, k, l, m; then through these points draw the curve ajklm c; and similarly in the semicircle B N c draw the other curve a n p c.

m

n

N

All lines drawn through the centre a of this curve are equal; thus a cln = g p = &c. Hence, if the rod had two pins. placed at a and c, the camb would revolve between them, and