_Wall Boxes._--In pa.s.sing from one part of a building to another a shaft may have to pa.s.s through a wall. In that case a neat appearance is given to the opening and a suitable support obtained for a pillow block by building into the wall a _wall box_, one form of which is shown in fig.

30.

EXERCISE 30: _Wall Box._--Draw the views of the wall box shown in fig. 30, and also a sectional plan; the plane of section to pa.s.s through the box a little above the joggles for the pillow block.

Scale 3 inches to a foot.

[Ill.u.s.tration: FIG. 29.]

[Ill.u.s.tration: FIG. 30.]

VIII. PULLEYS.

_Velocity Ratio in Belt Gearing._--Let two pulleys A and B be connected by a belt, and let their diameters be D_{1} and D_{2}; and let their speeds, in revolutions per minute, be N_{1} and N_{2} respectively. If there is no slipping, the speeds of the rims of the pulleys will be the same as that of the belt, and will therefore be equal. Now the speed of the rim of A is evidently = D_{1} 3.1416 N_{1}; while the speed of the rim of B is = D_{2} 3.1416 N_{2}. Hence D_{1} 3.1416 N_{1} = D_{2} 3.1416 N_{2}, and therefore

N_{1} D_{2} ----- = -----.

N_{2} D_{1}

_Pulleys for Flat Bands._--In cross section the rim of a pulley for carrying a flat band is generally curved as shown in figs. 31 and 32, but very often the cross section is straight. The curved cross section of the rim tends to keep the band from coming off as long as the pulley is rotating. Sometimes the rim of the pulley is provided with f.l.a.n.g.es which keep the band from falling off.

Pulleys are generally made entirely of cast iron, but a great many pulleys are now made in which the centre or nave only is of cast iron, the arms being of wrought iron cast into the nave, while the rim is of wrought sheet iron.

The arms of pulleys when made of wrought iron are invariably straight, but when made of cast iron they are very often curved. In fig. 31, which shows an arrangement of two cast-iron pulleys, the arms are straight; while in fig. 32, which shows another cast-iron pulley, the arms are curved. Through unequal cooling, and therefore unequal contraction of a cast-iron, pulley in the mould, the arms are generally in a state of tension or compression; and if the arms are straight they are very unyielding, so that the result of this initial stress is often the breaking of an arm, or of the rim where it joins an arm. With the curved arm, however, its shape permits it to yield, and thus cause a diminution of the stress due to unequal contraction.

The cross section of the arms of cast-iron pulleys is generally elliptical.

[Ill.u.s.tration: Fig. 31.]

EXERCISE 31: _Fast and Loose Pulleys_.--Fig. 31 shows an arrangement of fast and loose pulleys. A is the fast pulley, secured to the shaft C by a sunk key; B is the loose pulley, which turns freely upon the shaft. The loose pulley is prevented from coming off by a collar D, which is secured to the shaft by a tapered pin as shown. The nave or boss of the loose pulley is here fitted with a bra.s.s liner, which may be renewed when it becomes too much worn. Draw the elevations shown, completing the left-hand one. Scale 6 inches to a foot.

By the above arrangement of pulleys a machine may be stopped or set in motion at pleasure. When the driving band is on the loose pulley the machine is at rest, and when it is on the fast pulley the machine is in motion. The driving band is shifted from the one pulley to the other by pressing on that side of the band which is advancing towards the pulleys.

[Ill.u.s.tration: FIG. 32.]

EXERCISE 32: _Cast-iron Pulley with Curved Arms and Cone Keys_.--Draw a complete side elevation and a complete cross section of the pulley represented in fig. 32 to a scale of 3 inches to a foot. In drawing the side elevation of the arms first draw the centre lines as shown; next draw three circles for each arm, one at each end and one in the middle; the centres of these circles being on the centre line of the arm, and their diameters equal to the widths of the arm at the ends and at the middle respectively. Arcs of circles are then drawn to touch these three circles. The centres and radii of these arcs may be found by trial. The cone keys for securing the pulley to the shaft were described on p. 23.

_Pulleys for Ropes_.--Ropes made of hemp are now extensively used for transmitting power. These ropes vary in diameter from 1 inch to 2 inches, and are run at a speed of about 4,500 feet per minute. The pulleys for these ropes are made of cast iron, and have their rims grooved as shown in fig. 33, which is a cross section of the rim of a pulley carrying three ropes. The angle of the V is usually 45, and the rope rests on the sides of the groove, and not on the bottom, so that it is wedged in, and has therefore a good hold of the pulley. The diameter of the pulley should not be less than 30 times the diameter of the rope. Two pulleys connected by ropes should not be less than thirty feet apart from centre to centre, but this distance may be as much as 100 feet.

[Ill.u.s.tration: FIG. 33.]

EXERCISE 33: _Section of Rim of Rope Pulley._--Draw, half size, the section of the rim of a rope pulley shown in fig. 33.

IX. TOOTHED WHEELS.

_Pitch Surfaces of Spur Wheels._--Let two smooth rollers be placed in contact with their axes parallel, and let one of them rotate about its axis; then if there is no slipping the other roller will rotate in the opposite direction with the same surface velocity; and if D_{1}, D_{2} be the diameters of the rollers, and N_{1}, N_{2} their speeds in revolutions per minute, it follows as in belt gearing that--

N_{1} D_{2} ----- = -----.

N_{2} D_{1}

If there be considerable resistance to the motion of the follower slipping may take place, and it may stop. To prevent this the rollers may be provided with teeth; then they become _spur wheels_; and if the teeth be so shaped that the ratio of the speeds of the toothed rollers at any instant is the same as that of the smooth rollers, the surfaces of the latter are called the _pitch surfaces_ of the former.

_Pitch Circle._--A section of the pitch surface of a toothed wheel by a plane perpendicular to its axis is a circle, and is called a _pitch circle_. We may also say that the pitch circle is the edge of the pitch surface. The pitch circle is generally traced on the side of a toothed wheel, and is rather nearer the points of the teeth than the roots.

_Pitch of Teeth._--The distance from the centre of one tooth to the centre of the next, or from the front of one to the front of the next, _measured at the pitch circle_, is called the _pitch of the teeth_. If D be the diameter of the pitch circle of a wheel, _n_ the number of teeth, and _p_ the pitch of the teeth, then D 3.1416 = _n_ _p_.

[Ill.u.s.tration: FIG. 34.]

By the diameter of a wheel is meant the diameter of its pitch circle.

_Form and Proportions of Teeth._--The ordinary form of wheel teeth is shown in fig. 34. The curves of the teeth should be cycloidal curves, although they are generally drawn in as arcs of circles. It does not fall within the scope of this work to discuss the correct forms of wheel teeth. The student will find the theory of the teeth of wheels clearly and fully explained in Goodeve's 'Elements of Mechanism,' and in Unwin's 'Machine Design.'

The following proportions for the teeth of ordinary toothed wheels may be taken as representing average practice:--

Pitch of teeth = _p_ = arc _a b c_ (fig. 34).

Thickness of tooth = _b c_ = .48_p_.

Width of s.p.a.ce = _a b_ = .52_p_.

Total height of tooth = _h_ = .7_p_.

Height of tooth above pitch line = _k_ = .3_p_.

Depth of tooth below pitch line = _l_ = .4_p_.

Width of tooth = 2_p_ to 3_p_.

EXERCISE 34: _Spur Wheel._--Fig. 35 shows the elevation and sectional plan of a portion of a cast-iron spur wheel. The diameter of the pitch circle is 23-7/8 inches, and the pitch of the teeth is 1-1/2 inches, so that there will be 50 teeth in the wheel. The wheel has six arms. Draw a complete elevation of the wheel and a half sectional plan, also a half-plan without any section. Draw also a cross section of one arm. Scale 4 inches to a foot.

[Ill.u.s.tration: FIG. 35.]

_Mortise Wheels._--When two wheels gearing together run at a high speed the teeth of one are made of wood. These teeth, or cogs, as they are generally called, have tenons formed on them, which fit into mortises in the rim of the wheel. This wheel with the wooden teeth is called a _mortise wheel_. An example of a mortise wheel is shown in fig. 36.

[Ill.u.s.tration: FIG. 36.]

_Bevil Wheels._--In bevil wheels the pitch surfaces are parts of cones.

Bevil wheels are used to connect shafts which are inclined to one another, whereas spur wheels are used to connect parallel shafts. In fig. 36 is shown a pair of bevil wheels in gear, one of them being a mortise wheel. At (_a_) is a separate drawing, to a smaller scale, of the pitch cones. The pitch cones are shown on the drawing of the complete wheels by dotted lines.

The diameters of bevil wheels are the diameters of the bases of their pitch cones.

EXERCISE 35: _Pair of Bevil Wheels._--Draw the sectional elevation of the bevil wheels shown in gear in fig. 36. Commence by drawing the centre lines of the shafts, which in this example are at right angles to one another; then draw the pitch cones shown by dotted lines. Next put in the teeth which come into the plane of the section, then complete the sections of the wheels. The pinion or smaller wheel has 25 teeth, and the wheel has 50 teeth, which makes the pitch a little over 3 inches. Each tooth of the mortise wheel is secured as shown by an iron pin 5/16 inch diameter. Scale 3 inches to a foot.

X. CRANKS AND CRANKED SHAFTS.