The Project Gutenberg eBook of Precision locating and dividing methods
    
This ebook is for the use of anyone anywhere in the United States and
most other parts of the world at no cost and with almost no restrictions
whatsoever. You may copy it, give it away or re-use it under the terms
of the Project Gutenberg License included with this ebook or online
at www.gutenberg.org. If you are not located in the United States,
you will have to check the laws of the country where you are located
before using this eBook.

Title: Precision locating and dividing methods

Author: Anonymous

Release date: September 28, 2022 [eBook #69061]

Language: English

Original publication: United States: The Industrial Press

Credits: deaurider and the Online Distributed Proofreading Team at https://www.pgdp.net (This file was produced from images generously made available by The Internet Archive)


*** START OF THE PROJECT GUTENBERG EBOOK PRECISION LOCATING AND DIVIDING METHODS ***





Transcriber’s Notes:

  Underscores “_” before and after a word or phrase indicate _italics_
    in the original text.
  Equal signs “=” before and after a word or phrase indicate =bold=
    in the original text.
  Small capitals have been converted to SOLID capitals.
  Illustrations have been moved so they do not break up paragraphs.
  Typographical and punctuation errors have been silently corrected.




             =MACHINERY’S REFERENCE SERIES=

    EACH NUMBER IS ONE UNIT IN A COMPLETE LIBRARY OF
      MACHINE DESIGN AND SHOP PRACTICE REVISED AND
               REPUBLISHED FROM MACHINERY

                       NUMBER 135
                 PRECISION LOCATING AND
                    DIVIDING METHODS

                        CONTENTS
      Precision Locating Methods                        3
      Accurate Dividing and Spacing Methods            21
      Locating Work for Boring on Milling Machine      32

         Copyright, 1914, The Industrial Press,
                Publishers of MACHINERY,
         140-148 Lafayette Street, New York City

      Other books in this series dealing with
      the subjects of Toolmaking and kindred
      topics are as follows:

      No.  31—THREAD TOOLS AND GAGES
      No.  64—GAGE MAKING AND LAPPING
      No. 107—DROP FORGING DIE SINKING
      No. 130—GAGING TOOLS AND METHODS

[Illustration: MACHINERY]

             MACHINERY

            The Leading
        Mechanical Journal

       MACHINE DESIGN
           CONSTRUCTION
              SHOP PRACTICE

       THE INDUSTRIAL PRESS
       140-148 Lafayette St.
           New York City
    51-52 Chancery Lane, London




CHAPTER I

PRECISION LOCATING METHODS


The degree of accuracy that is necessary in the construction of
certain classes of machinery and tools, has made it necessary for
toolmakers and machinists to employ various methods and appliances
for locating holes or finished surfaces to given dimensions and
within the prescribed limits of accuracy. In this treatise, various
approved methods of locating work, such as are used more particularly
in tool-rooms, are described and illustrated. These are not given, in
every case, as being the best possible method under all conditions,
because, as every mechanical man knows, the best way may be dependent
upon the element of accuracy with little regard for the time required
to do the work, or this order may be reversed; therefore, one method is
seldom, if ever, the best under all circumstances, and it is necessary
for the workman to consider the conditions in each case and then be
guided by his judgment and experience in determining just how the work
should be done.


Button Method of Accurately Locating Work

Among the different methods employed by toolmakers for accurately
locating work such as jigs, etc., on the faceplate of a lathe, one of
the most commonly used is known as the “button method.” This method is
so named because cylindrical bushings or buttons are attached to the
work in positions corresponding to the holes to be bored, after which
they are used in locating the work. These buttons which are ordinarily
about ½ or ⅝ inch in diameter, are ground and lapped to the same size,
and the ends are finished perfectly square. The outside diameter
should preferably be such that the radius can easily be determined,
and the hole through the center should be about ⅛ inch larger than the
retaining screw so that the button can be adjusted laterally.

As a simple example of the practical application of the button method,
suppose three holes are to be bored in a jig-plate according to the
dimensions given in Fig. 1. A common method of procedure would be as
follows: First lay out the centers of all holes to be bored, by the
usual method. Mark these centers with a prick-punch and then drill
holes for the machine screws which are used to clamp the buttons. After
the buttons are clamped lightly in place, set them in correct relation
with each other and with the jig-plate. The proper location of the
buttons is very important, as their positions largely determine the
accuracy of the work. The best method of locating a number of buttons
depends, to some extent, upon their relative positions, the instruments
available, and the accuracy required. When buttons must be located at
given distances from the finished sides of a jig, a surface plate and
vernier height gage are often used. The method is to place that side
from which the button is to be set, upon an accurate surface plate and
then set the button by means of the height gage, allowance being made,
of course, for the radius of the button. The center-to-center distance
between the different buttons can afterwards be verified by taking
direct measurements with a micrometer.

[Illustration: Fig. 1. Simple Example of Work Illustrating Application
of Button Method]

Figs. 2 and 3 illustrate a method which requires only a micrometer. Two
of the buttons are set at the correct distance from one edge of the
plate by measuring from a parallel strip. Obviously, the micrometer
reading will exceed the distance from the center of a button to the
edge of the plate, by the amount equal to the thickness of the parallel
strip plus the radius of the button. The center-to-center distance
between each pair of buttons is also tested as indicated in Fig. 3, by
measuring the overall distance and deducting the diameter of one button.

After the buttons have been set and the screws are tightened, all
measurements should be carefully checked. The work is then mounted
on the faceplate of the lathe and one of the buttons is set true by
the use of a test indicator as shown in Fig. 4. When the dial of the
indicator ceases to vibrate, thus showing that the button runs true,
the latter should be removed so that the hole can be drilled and bored
to the required size. In a similar manner other buttons are indicated
and the holes bored, one at a time. It is evident that if each button
is correctly located and set perfectly true in the lathe, the various
holes will be located the required distance apart within very close
limits.

[Illustration: Fig. 2. Determining Distance from Button to Edge of
Plate]

Another example of work illustrating the application of the button
method is shown in Fig. 5. The disk-shaped part illustrated is a flange
templet which formed a part of a fixture for drilling holes in flanged
plates, the holes being located on a circle 6 inches in diameter.
It was necessary to space the six holes equi-distantly so that the
holes in the flanges would match in any position, thus making them
interchangeable. First a plug was turned so that it fitted snugly in
the 1¼-inch central hole of the plate and projected above the top
surface about ¾ inch. A center was located in this plug and from it
a circle of three inches radius was drawn. This circle was divided
into six equal parts and then small circles ⅝ inch in diameter were
drawn to indicate the outside circumference of the bushings to be
placed in the holes. These circles served as a guide when setting the
button and enabled the work to be done much more quickly. The centers
of the holes were next carefully prick-punched and small holes were
drilled and tapped for No. 10 machine screws. After this the six
buttons were attached in approximately the correct positions and the
screws tightened enough to hold the buttons firmly, but allow them to
be moved by tapping lightly. As the radius of the circle is 3 inches,
the radius of the central plug, ⅝ inch, and that of each button, ⁵/₁₆
inch, the distance from the outside of the central plug to the outside
of any button, when correctly set, must be 3 ¹⁵/₁₆ inches. Since there
are six buttons around the circle, the center-to-center distance is
equal to the radius, and the distance between the outside or any two
buttons should be 3⅝ inches. Having determined these dimensions, each
button is set equi-distant from the central plug and the required
distance apart, by using a micrometer. As each button is brought into
its correct position, it should be tightened down a little so that it
will be located firmly when finally set. The work is then strapped to
the faceplate of a lathe and each button is indicated for boring the
different holes by means of an indicator, as previously described. When
the buttons are removed it will be found that in nearly all cases the
small screw holes will not run exactly true; therefore, it is advisable
to form a true starting point for the drill by using a lathe tool.

[Illustration: Fig. 3. Testing Location of Buttons]

Fig. 7 shows a method of locating buttons from the finished sides of a
plate, and this same plate with the five buttons attached is shown in
Fig. 6. As the dimensions in Fig. 7 indicate, the holes must not only
be accurate with relation to each other, but also with reference to
the edges of the templet; therefore, it is necessary to work from the
sides as well as the center. The width of the plate was first measured
carefully and found to be 5 inches. As the center-to-center distance
between buttons _B_ and _C_ and also buttons _D_ and _E_, is 2½ inches,
the distance from the center of each outside button to the edge of the
plate is 1¼ inch. A ¼-inch parallel was clamped against the side, as
shown in the illustration, and then the distance from the outside of
each button to the outside of the parallel (1 ¹³/₁₆ inch) was measured
in conjunction with the distance _L_ from the central button. The
distance _L_ was obtained by first determining the center-to-center
distance _M_ which represents the hypotenuse of a right-angled triangle.

      _M_² = 1.25² + 1.625²
              ______________    _____
    or _M_ = √1.25² + 1.625² = √4.024 = 2.050 inches.

Therefore, _L_ = 2.050 + 0.625 = 2.675 inches.

In this case, the center button was first located correctly from the
sides and end and then the other buttons were set. When doing precision
work of this kind, the degree of accuracy obtained will depend upon
the instruments used, the judgment and skill of the workman, and the
care exercised. A good general rule to follow when locating bushings
or buttons is to use the method which is the most direct and which
requires the least number of measurements, in order to prevent an
accumulation of errors.


Locating Work by the Disk Method

Comparatively small precision work is sometimes located by the disk
method, which is the same in principle as the button method, the chief
difference being that disks are used instead of buttons. These disks
are made to such diameters that when their peripheries are in contact,
each disk center will coincide with the position of the hole to be
bored; the centers are then used for locating the work. To illustrate
this method, suppose that the master-plate shown at the left in Fig. 8
is to have three holes _a_, _b_, and _c_ bored into it, to the center
distances given.

[Illustration: Fig. 4. Testing Concentricity of Button Preparatory to
Boring Hole in Lathe]

It is first necessary to determine the diameters of the disks. If
the center distances between all the holes were equal, the diameters
would, of course, equal this dimension. When, however, the distances
between the centers are unequal, the diameters may be found as follows:
Subtract, say, dimension _y_ from _x_, thus obtaining the difference
between the radii of disks _C_ and _A_ (see right-hand sketch); add
this difference to dimension _z_, and the result will be the diameter
of disk _A_. Dividing this diameter by 2 gives the radius, which,
subtracted from center distance _x_ equals the radius of _B_; similarly
the radius of _B_ subtracted from dimension _y_ equals the radius of
_C_.

For example, 0.930-0.720 = 0.210 or the difference between the radii
of disks _C_ and _A_. Then the diameter of _A_ = 0.210 + 0.860 = 1.070
inch, and the radius equals 1.070 ÷ 2 = 0.535 inch. The radius of _B_ =
0.930-0.535 = 0.395 inch and 0.395 × 2 = 0.790, or the diameter of _B_.
The center distance 0.720-0.395 = 0.325, which is the radius of _C_;
0.325 × 2 = 0.650 or the diameter of _C_.

[Illustration: Fig. 5. Flange Templet with Buttons Attached]

[Illustration: Fig. 6. Hinge Jig Templet with Buttons Attached]

After determining the diameters, the disks should be turned nearly to
size and finished, preferably in a bench lathe. First insert a solder
chuck in the spindle, face it perfectly true, and attach the disk by a
few drops of solder, being careful to hold the work firmly against the
chuck while soldering. Face the outer side and cut a sharp V-center
in it; then grind the periphery to the required diameter. Next fasten
the finished disks onto the work in their correct locations with their
peripheries in contact, and then set one of the disks exactly central
with the lathe spindle by applying a test indicator to the center in
the disk. After removing the disk and boring the hole, the work is
located for boring the other holes in the same manner.

[Illustration: Fig. 7. Hinge Jig Templet Illustrated in Fig. 6]

Small disks may be secured to the work by means of jeweler’s wax.
This is composed of common rosin and plaster of paris and is made as
follows: Heat the rosin in a vessel until it flows freely, and then add
plaster of paris and keep stirring the mixture. Care should be taken
not to make the mixture too stiff. When it appears to have the proper
consistency, pour some of it onto a slate or marble slab and allow it
to cool; then insert the point of a knife under the flattened cake thus
formed and try to pry it off. If it springs off with a slight metallic
ring, the proportions are right, but if it is gummy and ductile,
there is too much rosin. On the other hand, if it is too brittle and
crumbles, this indicates that there is too much plaster of paris. The
wax should be warmed before using. A mixture of beeswax and shellac, or
beeswax and rosin in about equal proportions, is also used for holding
disks in place. When the latter are fairly large, it may be advisable
to secure them with small screws, provided the screw holes are not
objectionable.


Disk-and-Button Method of Locating Holes

The accuracy of work done by the button method previously described
is limited only by the skill and painstaking care of the workman,
but setting the buttons requires a great deal of time. By a little
modification, using what is sometimes called the “disk-and-button
method,” a large part of this time can be saved without any sacrifice
of accuracy. The disk-and-button method is extensively used in many
shops. Buttons are used, but they are located in the centers of disks
of whatever diameters are necessary to give the required locations.
As three disks are used in each step of the process, it is sometimes
called the “three-disk method.”

To illustrate the practical application of this method, suppose six
equally-spaced holes are to be located in the circumference of a
circle six inches in diameter. To locate these, one needs, besides the
buttons, three disks three inches in diameter, each having a central
hole exactly fitting the buttons. It is best to have, also, a bushing
of the same diameter as the buttons, which has a center-punch fitted
to slide in it. First the center button is screwed to the templet, and
one of the disks _A_, Fig. 9, is slipped over it; then a second disk
_B_ carrying a bushing and center-punch is placed in contact with disk
_A_ and a light blow on the punch marks the place to drill and tap for
No. 2 button, which is kept in its proper place while tightening the
screw by holding the two disks _A_ and _B_ in contact. Next the third
disk _C_ is placed in contact with disks _A_ and _B_ and locates No. 3
button, and so on until the seven buttons are secured in position. The
templet is then ready to be strapped to the lathe faceplate for boring.

[Illustration: Fig. 8. An Example of Precision Work, and Method of
Locating Holes by Use of Disks in Contact]

Of course, it is not possible to use disks of “standard” sizes for
many operations, but making a special disk is easy, and its cost
is insignificant as compared with the time saved by its use. One
who employs this method, especially if he also uses disks to lay
out angles, soon accumulates a stock of various sizes. While it is
desirable to have disks of tool steel, hardened and ground, or, in the
larger sizes, of machine steel, case-hardened and ground, a disk for
occasional use will be entirely satisfactory if left soft.

Another example of work is shown in Fig. 10. This is a jig templet
similar to the one illustrated in Figs. 6 and 7. Sketch _A_ gives its
dimensions and sketch _B_ shows the disk-and-button way of locating the
holes. A steel square is clamped with its stock against the right-hand
edge of the templet and its blade extending across the top. The lower
edge of the blade should be located 0.250 inch from the upper edge of
the templet by the use of size blocks. A 2½-inch disk, touching both
blade and stock, locates hole _C_. Another 2½-inch disk, touching the
first disk and the square blade, locates hole _B_. Next a disk 1.600
inch diameter is placed in contact with the two upper disks and
locates the center hole _A_; and, finally, the disks for holes _B_ and
_C_ are used to locate holes _D_ and _E_.

[Illustration: Fig. 9. Locating Holes on a Circle and Equi-distant by
using Disks and Buttons in Combination]

Two other jobs that illustrate this method may be of interest.
The first one, shown in Fig. 11, required the locating of nine
equally-spaced holes on a circumference of 7⅜ inches diameter. In any
such case, the size of the smaller disks is found by multiplying the
diameter of the circle upon which the centers of the disks are located
by the sine of half the angle between two adjacent disks. The angle
between the centers of adjacent disks equals 360 ÷ number of disks. 360
÷ 9 = 40; hence, in this case, the diameter of the smaller disks equals
7⅜ multiplied by the sine of 20 degrees, or 7⅜ × 0.34202 = 2.5224
inches. 7⅜-2.5224 = 4.8526 inches, which is the diameter of the central
disk.

The templet shown in Fig. 12 required two holes on a circumference 6½
inches diameter, with their centers 37 degrees 20 minutes apart. To
find the diameter of the smaller disks, multiply the diameter of the
large circle by the sine of one-half the required angle, as in the
preceding example; thus 6½ × sin 18 degrees 40 minutes = 2.0804 inches,
which is the diameter of the two smaller disks. The diameter of the
larger disk equals 6½-2.0804 = 4.4196 inches.

Very accurate results can be obtained by the disk-and-button method.
Of course, absolute exactness is equally unattainable with buttons and
a micrometer, or any other method; the micrometer does not show the
slight inaccuracy in any one chordal measurement, while in using the
disks the error is accumulative and the insertion of the last disk in
the series shows the sum of the errors in all the disks. It is only in
cases like the one illustrated in Fig. 9 that we note this, and then,
though in correcting the error, we may change the diameter of the
circle a very slight amount, an exceedingly accurate division of the
circumference is secured.


Use of Two- and Three-Diameter Disks

Fig. 13 illustrates, on an enlarged scale, a piece of work requiring
great accuracy, which was successfully handled by an extension of the
three-disk method. Fourteen holes were required in a space hardly
larger than a silver half-dollar, and, although the drawing gave
dimensions from the center of the circle, the actual center could not
be used in doing the work, as there was to be no hole there; moreover,
a boss slightly off center prevented the use of a central disk, unless
the bottom of the disk were bored out to receive this boss, which was
not thought expedient. Hence, the method adopted was to make the plate
thicker than the dimension given on the drawing, and then bore it out
to leave a rim of definite diameter, this rim to be removed after it
had served its purpose as a locating limit for the disks.

[Illustration: Fig. 10. (A) Layout of Jig-Plate. (B) Disk-and-Button
Method of Locating Holes]

As the holes _A_ and _B_, which were finished first, were 0.600 inch
apart and 0.625 inch from the center, the rim was bored to 1.850 inch
and two 0.600-inch disks, in contact with the rim and with each other,
located these holes. As hole _C_ was to be equi-distant from holes
_A_ and _B_, and its distance from the center was given, the size of
the disk for this hole was readily determined. The disks for holes
_A_, _B_ and _C_ have two diameters; the upper diameters are made to
whatever size is required for locating the disks of adjacent holes, and
they also form a hub which can be used when setting the disks with an
indicator. Hole _D_ was 0.4219 inch from _B_, and calculations based
on this dimension and its distance from the center showed that it was
0.4375 inch from hole _C_.

A “three-story” disk or button was made for hole _D_. The diameter of
the large part was 0.46875 inch and it overlapped disks _C_ and _B_
(the upper sections of which were made 0.375 inch and 0.4062 inch,
respectively), thus locating _D_. Then hole _F_ and all the remaining
holes were located in a similar manner. The upper diameters of disks
_E_ and _D_ were used in locating disks for other adjacent holes,
as well as a hub for the indicator; for instance, to locate a hole
with reference to holes _C_ and _D_, the diameter of the new disk and
the diameter of the upper part of disk _D_, were varied to give the
required location. The relation between the disks _B_, _D_ and _F_ is
shown by the side view.

[Illustration: Fig. 11. Example of Circular Spacing requiring a Large
Central Disk]

It had been decided that no screws should be used in attaching the
buttons or disks to the work, as it was feared that the tapped holes
would introduce inaccuracy by deflecting the boring-tools; therefore
the following method was employed. After all the disks were fastened
in place by clamps, a soft solder of low melting point was flowed
about them, filling the work to the top of the rim. When the solder
had cooled, the clamps were removed, the work transferred to the lathe
faceplate, indicated in the usual way, and the holes bored by a “_D_”
or “hog-nose” drill, guided by an axial hole in each disk, which had
been provided for that purpose when the disks were made. It was thought
that the unequal contraction of the solder and the plate in cooling
might throw the holes “out of square;” however, careful measurements
failed to show any appreciable lack of parallelism in test-bars
inserted in the holes.

[Illustration: Fig. 12. Locating Holes at an Angle by use of Disks and
Buttons]

[Illustration: Fig. 13. Locating Holes by Means of Two- and
Three-Diameter Disks in Contact]


Accurate Angular Measurements with Disks

For setting up a piece of work on which a surface is to be planed or
milled at an exact angle to a surface already finished, disks provide
an accurate means of adjustment. One method of using disks for angular
work is illustrated at _A_ in Fig. 14. Let us assume that the lower
edge of plate shown is finished and that the upper edge is to be
milled at an angle _a_ of 32 degrees with the lower edge. If the two
disks _x_ and _y_ are to be used for locating the work, how far apart
must they be set in order to locate it at the required angle? The
center-to-center distance can be determined as follows: Subtract the
radius of the larger disk from the radius of the smaller disk, and
divide the difference by the sine of one-half the required angle.

[Illustration: Fig. 14. Obtaining Accurate Angular Measurements with
Disks]

      _Example_: If the required angle _a_ is 32 degrees,
    the radius of the large disk, 2 inches, and the radius of the
    small disk, 1 inch, what is the center-to-center distance?

      The sine of one-half the required angle, or 16 degrees, is
    0.27564. The difference between the radii of the disks equals
    2 - 1 = 1, and 1 ÷ 0.27564 = 3.624 inches. Therefore, for an
    angle of 32 degrees, disks of the sizes given should be set so
    that the distance between their centers is 3.624 inches.

Another method of accurately locating angular work is illustrated at
_B_ in Fig. 14. In this case, two disks are also used, but they are
placed in contact with each other and changes for different angles
are obtained by varying the diameter of the larger disk. The smaller
disk is a standard 1-inch size, such as is used for setting a 2-inch
micrometer. By this method any angle up to about 40 degrees can be
obtained within a very close limit of accuracy. The following rule may
be used for determining the diameter of the larger disk, when both
disks are in contact and the diameter of the small disk is known:

Multiply twice the diameter of the small disk by the sine of one-half
the required angle; divide this product by 1 minus the sine of one-half
the required angle; add the quotient to the diameter of the small disk
to obtain the diameter of the large disk.

      _Example_: The required angle a is 15 degrees.
    Find the diameter of the large disk to be in contact
    with the standard 1-inch reference disk.

      The sine of 7 degrees 30 minutes is 0.13053.
    Multiplying twice the diameter of the small disk
    by the sine of 7 degrees 30 minutes, we have
    2 × 1 × 0.13053 = 0.26106. This product divided by
    1 minus the sine of 7 degrees 30 minutes

                             0.26106
                          = ——————————— = 3.002.
                            1 - 0.13053

    This quotient added to the diameter of the small
    disk equals 1 + 0.3002 = 1.3002 inch, which is the
    diameter of the large disk.

[Illustration: Fig. 15. Disk-and-Square Method of Accurately Setting
Angular Work]

The accompanying table gives the sizes of the larger disks to the
nearest 0.0001 inch for whole degrees ranging from 5 to 40 degrees
inclusive. Incidentally, the usefulness of these disks can be increased
by stamping on each one its diameter and also the angle which it
subtends when placed in contact with the standard 1-inch disk.

DISK DIAMETERS FOR ANGULAR MEASUREMENT

    +------+---------++------+---------++------+---------++
    | Deg. |  Inch   || Deg. |  Inch   || Deg. |  Inch   ||
    +------+---------++------+---------++------+---------++
    |   5  | 1.0912  ||  17  | 1.3468  ||  29  | 1.6680  ||
    |   6  | 1.1104  ||  18  | 1.3708  ||  30  | 1.6983  ||
    |   7  | 1.1300  ||  19  | 1.3953  ||  31  | 1.7294  ||
    |   8  | 1.1499  ||  20  | 1.4203  ||  32  | 1.7610  ||
    |   9  | 1.1702  ||  21  | 1.4457  ||  33  | 1.7934  ||
    |  10  | 1.1909  ||  22  | 1.4716  ||  34  | 1.8262  ||
    |  11  | 1.2120  ||  23  | 1.4980  ||  35  | 1.8600  ||
    |  12  | 1.2334  ||  24  | 1.5249  ||  36  | 1.8944  ||
    |  13  | 1.2553  ||  25  | 1.5524  ||  37  | 1.9295  ||
    |  14  | 1.2775  ||  26  | 1.5805  ||  38  | 1.9654  ||
    |  15  | 1.3002  ||  27  | 1.6090  ||  39  | 2.0021  ||
    |  16  | 1.3234  ||  28  | 1.6382  ||  40  | 2.0396  ||
    +------+---------++------+---------++------+---------++
    |                                  _Machinery_  ||
    +----------------------------------------------------++


Disk-and-Square Method of Determining Angles

The method shown in Fig. 15 for determining angles for setting up
work on a milling machine or planer, possesses several advantages. No
expensive tools are required, the method can be applied quickly, and
the results obtained are quite accurate enough for any but the most
exacting requirements. As will be seen, an ordinary combination square
is used in connection with a disk, the head of the square being set at
different points on the blade according to the angle that is desired.
Theoretically, a one-inch disk could be used for all angles from about
6 degrees up to a right angle, but in practice it is more convenient
and accurate to employ larger disks for the larger angles.

The only inaccuracy resulting from this method is due to setting the
square at the nearest “scale fraction” instead of at the exact point
determined by calculation. This error is very small, however, and is
negligible in practically all cases. The dimension _x_ required for any
desired angle _a_ can be found by multiplying the radius of the disk,
by the cotangent of one-half the desired angle, and adding to this
product the radius of the disk.

    _Example_: The square blade is to be set to an
      angle of 15 degrees 10 minutes, using a 2-inch disk.
      At what distance _x_ (see Fig. 15) should the
      head of the square be set?

      Cot 7 degrees 35 minutes = 7.5113,
      and 7.5113 × 1 + 1 = 8.5113 inches.

      By setting the square to 8½ inches “full,” the
      blade would be set very close to the required angle
      of 15 degrees 10 minutes.

Locating Work by means of Size Blocks

The size-block method of locating a jig-plate or other part, in
different positions on a lathe faceplate, for boring holes accurately
at given center-to-center distances, is illustrated in Fig. 16. The way
the size blocks are used in this particular instance is as follows: A
pair of accurate parallels are attached to a faceplate at right angles
to each other and they are so located that the center of one of the
holes to be bored will coincide with the lathe spindle. The hole which
is aligned in this way should be that one on the work which is nearest
the outer corner, so that the remaining holes can be set in a central
position by adjusting the work away from the parallels. After the
first hole is bored, the work is located for boring each additional
hole by placing size blocks of the required width between the edges of
the work and the parallels. For instance, to set the plate for boring
hole _D_, size blocks (or a combination of blocks or gages) equal in
width to dimension _A_₁ would be inserted at _A_, and other blocks
equal in width to dimension _B_₁ beneath the work as at _B_. As will be
seen, the dimensions of these blocks equal the horizontal and vertical
distances between holes _C_ and _D_. With the use of other combinations
of gage blocks, any additional holes that might be required are located
in the central position. While only two holes are shown in this case,
it will be understood that the plate could be located accurately for
boring almost any number of holes by this method.

[Illustration: Fig. 16. Method of setting Work on Faceplate with Size
Blocks or Gages]

Incidentally, such gages as the Johansson combination gages are
particularly suited for work of this kind, as any dimension within
the minimum and maximum limits of a set can be obtained by simply
placing the required sizes together. Sometimes when such gages are not
available, disks which have been ground to the required diameter are
interposed between the parallels and the work for securing accurate
locations. Another method of securing a positive adjustment of the
work is to use parallels composed of two tapering sections, which
can be adjusted to vary the width and be locked together by means of
screws. Each half has the same taper so that outer edges are parallel
for any position, and the width is measured by using a micrometer. The
size-block method is usually applied to work having accurately machined
edges, although a part having edges which are of a rough or irregular
shape can be located by this method, if it is mounted on an auxiliary
plate having accurately finished square edges. For instance, if holes
were to be bored in the casting for a jig templet which had simply been
planed on the top and bottom, the casting could be bolted to a finished
plate having square edges and the latter be set in the different
positions required, by means of size blocks. Comparatively large jig
plates are sometimes located for boring in this way and the milling
machine is often used instead of a lathe.


The Master-plate Method

When it is necessary to machine two or more plates so that they are
duplicates as to the location of holes, circular recesses, etc., what
is known as a master-plate is often used for locating the work on the
lathe faceplate. This master-plate _M_ (see Fig. 17) contains holes
which correspond to those wanted in the work, and which accurately fit
a central plug _P_ in the lathe spindle, so that by engaging first one
hole and then another with the plug, the work is accurately positioned
for the various operations.

When making the master-plate, great care should be taken to have the
sides parallel and the holes at right angles to the sides, as well as
accurately located with reference to one another. The various holes
may be located with considerable precision by the use of buttons as
previously described. Of course, it is necessary to have a hole in the
master-plate for each different position in which the work will have to
be placed on the faceplate; for example, if a circular recess _r_ were
required, a hole _r_₁ exactly concentric with it would be needed in
the master-plate. The method of holding the work and locating it with
reference to the holes in the master-plate will depend largely on its
shape. The cylindrical blank _B_ illustrated, is positioned by a recess
in the master-plate in which it fits. The work is commonly held to the
master-plate by means of clamps and tap bolts or by screws which pass
through the work and into the master-plate. Solder is sometimes used
when it is not convenient to hold the work by clamps or screws.

[Illustration: Fig. 17. Master-plate applied to a Bench Lathe Faceplate]

The plug _P_ which locates the master-plate, is first turned to fit
the spindle or collet of the lathe and the outer or projecting end
is roughturned for the holes in the master-plate, which should all
be finished to exactly the same diameter. The plug is then inserted
in the spindle and ground and lapped to a close fit for the holes in
the master-plate. The latter, with the work attached to it, is next
clamped to the faceplate by the straps shown, which engage a groove
around the edge of the master-plate. The first hole is finished by
drilling to within, say, 0.005 or 0.006 inch of the size, and then
boring practically to size, a very small amount being left for reaming
or grinding. The remaining holes can then be finished in the same
way, the work being positively located in each case by loosening the
master-plate and engaging the proper hole in it with the central plug.
It is apparent that by the use of this same master-plate, a number of
pieces _B_ could be made which would be practically duplicates.

The master-plate method of locating work can be applied in many
different ways. It is used for making duplicate dies, for accurately
locating the various holes in watch movements, and for many other
operations requiring great precision. Master-plates are quite
frequently used by toolmakers when it is necessary to produce a number
of drill jigs which are to be used for drilling holes in different
parts having the same relative locations, thus requiring jigs that are
duplicates within very close limits.

When a master-plate is required, that is to be used in making
duplicates of an existing model, the holes are bored in the
master-plate by reversing the process illustrated in Fig. 17. That is,
the central plug _P_ is turned to fit the largest hole in the model and
the latter with the attached master-plate blank is clamped to lathe
faceplate. The first hole is then bored to within say 0.002 inch of the
finish diameter, to allow for grinding, provided the master-plate is
to be hardened. The central plug is then turned down to fit the next
largest hole and the second hole is bored in the master-plate. This
method is continued until all the holes are bored. In order to prevent
any change in the position of the master-plate relative to the model,
it may be secured by inserting dowel-pins through both parts, the work
being held to the lathe faceplate by ordinary screw clamps. If the
holes in the model do not extend clear through, a flat plate having
parallel sides may be interposed between the model and master-plate to
provide clearance between the two and prevent cutting into the model
when boring the master-plate.




CHAPTER II

ACCURATE DIVIDING AND SPACING METHODS


Toolmakers and machinists occasionally find it necessary to locate a
number of equally-spaced holes on a straight line between two points,
or to divide a circle with holes which are equi-distant within a very
small limit of accuracy. Several dividing and spacing methods are
described in this chapter; some of these methods can, with slight
modification, be applied in various ways.

[Illustration: Fig. 18. Method of Drilling Small Equally-spaced Holes
in Rows]


Locating Small Equally-spaced Holes in Rows

It is sometimes necessary to drill one or more rows of small
equally-spaced holes. The best method of doing this work naturally
depends, to some extent, upon the accuracy required, but even when a
high degree of accuracy is not necessary, if an attempt is made to lay
out the holes and drill them in the ordinary way, considerable time
is usually required and the results are liable to be unsatisfactory.
For example, suppose a row of holes ¹/₁₆ inch in diameter and ⅛ inch
center-to-center distance were to be drilled in a flat plate. Some
machinists would proceed by first scribing a center-line and then
laying out the centers of the holes by means of dividers. A much easier
and accurate method is illustrated in Fig. 18, and is as follows:
Lay out the first hole and drill it; then secure a small piece of
flat steel for a drill guide, drill a hole through it, bevel one
corner and scribe a fine line on the beveled section, as shown in the
illustration. Align the hole drilled in the guide with the hole in the
work, by inserting a close-fitting plug, and clamp a scale against one
edge of the drill guide so that one of the graduation marks exactly
matches with the line on the guide. The edge of the scale must also be
located parallel to the center-line of the row of holes to be drilled.
Now proceed to drill the holes, setting the drill guide each time, to
whatever graduation line represents the required spacing or pitch of
the holes.

It is advisable to use a magnifying glass to accurately align the
graduation mark on the scale with the line on the drill guide. If two
or more rows of holes are to be drilled parallel, the guide block can
be drilled accordingly, so that the different rows of holes can be
finished at the same time. The drill guide block should be relieved
slightly in the center so as to insure the ends of the block bearing
against the edge of the scale. A toolmaker or machinist can drill a row
of holes accurately by this simple method, in the time required to lay
them out in the usual way, and even though accuracy is not necessary,
it is quicker to drill holes by this method than by the one more
commonly employed.


Use of Disks for Locating Equally-Spaced Holes

A simple method of spacing holes that are to be drilled in a straight
line is illustrated in Fig. 19. Two disks are made, each having a
diameter equal to the center-to-center distance required between the
holes. These disks must also have holes which are exactly central
with the outside to act as a guide for the drill or reamer. The first
two holes are drilled in the work while the disks are clamped so that
they are in contact with each other and also with the straightedge as
shown. One disk is then placed on the opposite side of the other, as
indicated by the dotted line, and a third hole is drilled; this process
of setting one disk against the opposite side of the other is continued
until all the holes are drilled. When it is necessary to drill a
parallel row of “staggered” holes, the second row can be located by
placing disks of the proper size in contact with the first row of disks.

[Illustration: Fig. 19. Locating Equi-distant Holes in a Straight Line
by Means of Disks and Straightedge]

A method of using disks, which is preferable for very accurate work, is
shown in Fig. 20. The disks are clamped against each other and along
straightedge _A_ by the screws shown, and if the outside diameters are
correct and the guide holes concentric with the outside, very accurate
work can be done. With this device there may be as many disks as there
are holes to be drilled, if the number of holes is comparatively small,
but if it is necessary to drill a long row of holes, the disks and
frame are shifted along an auxiliary straightedge _B_, the hole in one
of the end disks being aligned with the last hole drilled by inserting
a close-fitting plug through the disk and hole.


Adjustable Jig for Accurate Hole Spacing

An adjustable jig for accurately spacing small holes is shown in Fig.
21.

[Illustration: Fig. 20. Special Disk-jig for Precision Drilling]

This form is especially adapted for locating a number of equally
spaced holes between two previously drilled or bored holes, and the
accuracy of the method lies in the fact that a slight error in the
original spacing of the guide bushing is multiplied, and, therefore,
easily detected. There are two of these guide bushings _A_ and _B_
which are carried by independent slides. These slides can be shifted
along a dovetail groove after loosening the screws of clamp-gib _C_. To
illustrate the method of using this jig, suppose five equally spaced
holes are to be located between two holes that are 12 inches apart.
As the center-to-center distance between adjacent holes is 2 inches,
slides _A_ and _B_ would be set so that the dimension _x_ equals 2
inches plus the radii of the bushings. A straightedge is then clamped
to the work in such position that a close-fitting plug can be inserted
through the end holes which were previously drilled or bored. Then with
a plug inserted through, say, bushing _B_ and one of the end holes, the
first hole is drilled and reamed through bushing _A_; the jig is then
shifted to the left until the plug in _B_ enters the hole just made.
The second hole is then drilled and reamed through bushing _A_ and
this drilling and shifting of the jig is continued until the last hole
is finished. The distance between the last hole and the original end
hole at the left is next tested by attempting to insert close-fitting
plugs through both bushings. Evidently, if there were any inaccuracy in
the spacing of the bushings, this would be multiplied as many times as
the jig was shifted, the error being accumulative. To illustrate how
the error accumulates, suppose that the bushings were 0.001 inch too
far apart; then the distance to the first hole would be 2.001 inch, to
the second hole, 4.002 inch, and finally the distance from the first
to the sixth hole would be 10.005 inches; consequently, the distance
between the sixth and seventh holes would equal 12-10.005 = 1.995 inch,
or 0.005 inch less than the required spacing, assuming, for the sake
of illustration, that the first and last holes were exactly 12 inches
apart. In case of an error of 0.005 inch, the bushings would be set
closer together an amount equal to one-fifth of this error, as near as
could be determined with a micrometer, and all of the holes would then
be re-reamed.

[Illustration: Fig. 21. Adjustable Jig for Accurate Hole Spacing]


Methods of Accurately Dividing a Circle

Sometimes it is necessary to machine a number of holes in a plate so
that all the holes are on a circle or equi-distant from a central
point, and also the same distance apart, within very small limits. A
simple method of spacing holes equally is illustrated at _A_, Fig.
22. A number of buttons equal to the number of holes required are
ground and lapped to exactly the same diameter, preferably by mounting
them all on an arbor and finishing them at the same time. The ends
should also be made square with the cylindrical surface of the button.
When these buttons are finished, the diameter is carefully measured
and this dimension is subtracted from the diameter of the circle on
which the holes are to be located, in order to obtain the diameter
_d_ (see illustration). A narrow shoulder is then turned on the plate
to be bored, the diameter being made exactly equal to dimension
_d_. By placing the buttons in contact with this shoulder, they are
accurately located radially and can then be set equi-distant from
each other by the use of a micrometer. In this particular case, it
would be advisable to begin by setting the four buttons which are 90
degrees apart and then the remaining four. The buttons are next used
for setting the work preparatory to boring. (See “Button Method of
Accurately Locating Work.”)

[Illustration: Fig. 22. Four Methods of Accurately Dividing a Circle]


Correcting Spacing Errors by Split Ring Method

Another method of securing equal spacing for holes in indexing wheels,
etc., is illustrated at _B_, Fig. 22. This method, however, is not to
be recommended if the diameter of the circle on which the holes are
to be located, must be very accurate. The disk or ring in which the
holes are required, is formed of two sections _e_ and _f_, instead
of being one solid piece. The centers for the holes are first laid
out as accurately as possible on ring _e_. Parts _e_ and _f_ are then
clamped together and the holes are drilled through these two sections.
Obviously, when the holes are laid out and drilled in this way, there
will be some error in the spacing, and, consequently, all of the holes
would not match, except when plate _e_ is in the position it occupied
when being drilled. Whatever errors may exist in the spacing can be
eliminated, however, by successively shifting plate _e_ to different
positions and re-reaming the holes for each position. A taper reamer
is used and two pins should be provided having the same taper as the
reamer. Ring _e_ is first located so that a hole is aligned quite
accurately with one in the lower plate. The ring is then clamped and
the hole is partly reamed, the reamer being inserted far enough to
finish the hole in plate _e_ and also cut clear around in the upper
part of plate _f_. One of the taper pins is then driven into this hole
and then a hole on the opposite side is partly reamed, after which the
other pin is inserted. The remaining holes are now reamed in the same
way, and the reamer should be fed in to the same depth in each case. If
a pair of holes is considerably out of alignment, it may be necessary
to run the reamer in to a greater depth than was required for the first
pair reamed, and in such a case all the holes should be re-reamed to
secure a uniform size.

The next step in this operation is to remove the taper pins and clamps
or turn index plate _e_ one hole and again clamp it in position. The
reaming process just described is then repeated; the holes on opposite
sides of the plate are re-reamed somewhat deeper, the taper pins are
inserted, and then all of the remaining holes are re-reamed to secure
perfect alignment for the new position of the plate. By repeating this
process of shifting plate _e_ and re-reaming the holes, whatever error
that may have existed originally in the spacing of the holes, will
practically be eliminated. It would be very difficult, however, to have
these holes located with any great degree of accuracy, on a circle of
given diameter.


Circular Spacing by Contact of Uniform Disks

When an accurate indexing or dividing wheel is required on a machine,
the method of securing accurate divisions of the circle illustrated
at _C_, Fig. 22, is sometimes employed. There is a series of circular
disks or bushings equal in number to the divisions required, and these
disks are all in contact with each other and with a circular boss or
shoulder on the plate to which they are attached. The space between
adjacent disks is used to accurately locate the dividing wheel,
engagement being made with a suitable latch or indexing device. When
making a dividing wheel of this kind, all of the disks are ground and
lapped to the same diameter and then the diameter of the central boss
or plate is gradually reduced until all of the disks are in contact
with each other and with the boss. For an example of the practical
application of this method see “Originating a Precision Dividing Wheel.”


Spacing by Correcting the Accumulated Error

Another indexing method of spacing holes equi-distant, is illustrated
by the diagram at _D_, Fig. 22. An accurately fitting plug is inserted
in the central hole of the plate in which holes are required. Two
arms _h_ are closely fitted to this plug but are free to rotate
and are provided with a fine-pitch screw and nut at the outer ends
for adjusting the distance between the arms. Each arm contains an
accurately made, hardened steel bushing _k_ located at the same radial
distance from the center of the plate. These bushings are used as a
guide for the drill and reamer when machining the holes in the plate.

To determine the center-to-center distance between the bushings,
divide 360 by twice the number of holes required; find the sine
corresponding to the angle thus obtained, and multiply it by the
diameter of the circle upon which the holes are located. For example,
if there were to be eleven holes on a circle 8 inches in diameter, the
distance between the centers of the bushings would equal

      360
    ——————— = 16.36 degrees.
     2 × 11

The sine of 16.36 degrees is 0.2815, and 0.2815 × 8 = 2.252 inches. The
arms are adjusted to locate the centers of the bushings this distance
apart, by placing closely fitting plugs in the bushings and measuring
from one plug to another with a micrometer or vernier caliper. Of
course, when taking this measurement, allowance is made for the
diameter of the plugs.

After the arms are set, a hole is drilled and reamed; an accurately
fitting plug is then inserted through the bushing and hole to secure
the arms when drilling and reaming the adjacent hole. The radial arms
are then indexed one hole so that the plug can be inserted through one
of the arms and the last hole reamed. The third hole is then drilled
and reamed, and this operation is repeated for all of the holes.
Evidently, if the center-to-center distance between the bushings is
not exactly right, the error will be indicated by the position of the
arms relative to the last hole and the first one reamed; moreover,
this error will be multiplied as many times as there are holes. For
instance, if the arms were too far apart, the difference between
the center-to-center distance of the last pair of holes and the
center-to-center distance of the bushings in the arms, would equal, in
this particular case, eight times the error, and the arms should be
re-adjusted accordingly. Larger bushings would then be inserted in the
arms and the holes re-reamed, this operation being repeated until the
holes were all equi-distant.

As will be seen, the value of this method lies in the fact that it
shows the accumulated error. Thus, if the arms were 0.0005 inch too far
apart, the difference between the first and last hole would equal 8 ×
0.0005 = 0.004 inch. This same principle of dividing can be applied in
various ways. For instance, the radial arms if slightly modified, could
be used for drilling equally-spaced holes in the periphery or disk of a
plate, or, if a suitable marking device were attached, a device of this
kind could be used for accurately dividing circular parts.


Originating a Precision Dividing Wheel

There are various methods employed for making accurate indexing wheels
for a definite number of divisions. One of these methods, suitable
particularly for small numbers of divisions, employs a split wheel with
a series of taper holes reamed through the two divisions. By shifting
the two divisions from point to point (as explained in connection with
sketch _B_, Fig. 22) and reaming and re-reaming the taper holes at each
shifting, they may finally be brought very accurately into position.
Another method that has been employed consists in clamping about the
rim of the dividing wheel a number of precisely similar blocks, fitting
close to each other and to the wheel itself. These blocks are then used
for locating the wheel in each of its several positions in actual work.
A third and simpler method (a modification of the one last described)
consists in grinding a series of disks and clamping them around a
rim of such diameter that the disks all touch each other and the rim
simultaneously, as explained in connection with sketch _C_, Fig. 22.
The wheel described in the following, which is illustrated in Fig. 23,
was made in this way.

[Illustration: Fig. 23. Precision Dividing Wheel]

Disks _A_ are clamped against an accurately ground face of the wheel
_B_ and are supposed to just touch each other all around, and to be
each of them in contact with the ground cylindrical surface at _x_.
They are held in proper position by bolts _C_ and nuts _D_. The bolts
fit loosely in the holes of the disks or bushings _A_ so that the
latter are free to be located as may be desired with reference to the
bolts.

One or two improvements in the construction of this type of dividing
wheel may be noted before proceeding to a description of the way in
which it is made. For one thing, instead of having an indexing bolt
enter the V-space between two adjoining disks, a smaller diameter _y_
is ground on each of them, over which locking finger or pawl passes,
holding the wheel firmly from movement in either direction. This
construction has the advantage of a probable lessening of error by
locating on each bushing instead of between two bushings; moreover, it
gives a better holding surface and better holding angles than would be
the case if this smaller diameter were not provided.

A second improvement lies in the method of clamping the bushings _A_ in
place. Instead of providing each bolt with a separate washer, a ring
_F_ is used. This ring fits closely on a seat turned to receive it on
the dividing wheel _B_. When one bushing _A_ has been clamped in place,
the disk is locked from movement so that there is no possibility, in
clamping the remaining bushings, of having their location disturbed in
the slightest degree by the turning of the nuts in fastening them in
place.

The bushings _A_, of which there were in this case 24, were all ground
exactly to the required diameters on their locating and locking
surfaces. The important things in this operation are, first, that the
large or locating diameter of the bushing should be exactly to size;
and second, that this surface should be in exact alignment with the
diameter in which the locking is done; and, finally, that the face of
the bushing should be squared with the cylindrical surfaces. A refined
exactness for the diameter of the locking surfaces is not so important,
as the form of locking device provided allows slight variations at this
point without impairment of accuracy. This dimension was kept within
very close limits, however. The truth of the two cylindrical surfaces
and the face of the bushing was assured by finishing all these surfaces
in one operation on the grinding machine.

The sizing of the outer diameter of the bushing, which was 1.158 inch,
must be done so accurately that it was not thought wise to trust to
the ordinary micrometer caliper. An indexing device was therefore made
having a calipering lever with a long end, in the ratio of 10 to 1,
which actuated the plunger of a dial test indicator of the well-known
type made by the Waltham Watch Tool Co. The thousandth graduations
on the dial of this indicator would then read in ten-thousandths,
permitting readings to be taken to one-half or one-quarter of this
amount. The final measurements with this device were all taken after
dipping the bushings in water of a certain temperature, long enough to
give assurance that this temperature was universal in all the parts
measured. It will be understood, of course, in this connection, that
getting the diameter of these bushings absolutely to 1.158 inch was
not so important as getting them all exactly alike, whether slightly
over or slightly under this dimension; hence, the precaution taken in
measurement.

Wheel _B_ was next ground down nearly to size, great care being taken
that it should run exactly concentric with the axis. As soon as
the diameter of the surface _x_ was brought nearly to the required
dimension as obtained by calculation, the disks were tried in place.
The first one was put in position with its loose hole central on the
bolt and clamped in place under ring _F_. The next bushing was then
pressed up against it and against the surface _x_ of the wheel and
clamped in place. The third one was similarly clamped in contact with
its neighboring bushing and the wheel, and so on, until the whole
circle was completed. It was then found that the last disk would not
fill the remaining space. This required the grinding off of some stock
from surface _x_, and a repetition of the fitting of the bushings _A_
until they exactly filled the space provided for them.

[Illustration: Fig. 24. Precision Dividing Wheel and its Indexing
Mechanism]

This operation required, of course, considerably more skill than a
simple description of the job would indicate. One of the points that
had to be carefully looked out for was the cleaning of all the surfaces
in contact. A bit of dust or lint on one of the surfaces would throw
the fitting entirely out. The temperature of the parts was another
important consideration. As an evidence of the accuracy with which the
work was done, it might be mentioned that it was found impossible to
do this fitting on a bench on the southern or sunny side of the shop,
the variations of temperature between morning and noon, and between
bright sunshine and passing clouds, being such that the disks would
not fit uniformly. The variation from these minute temperature changes
resulted from the different coefficients of expansion of the iron
wheel and the steel bushings. The obvious thing to do would be to build
a room for this work kept at a constant temperature and preferably that
of the body, so that the heat of the body would make no difference in
the results. It was found sufficient in this case, however, to do the
work on the northern side of the shop where the temperature was more
nearly constant, not being affected by variations in sunshine.

The dividing wheel, the construction of which has just been described,
was made by the Fellows Gear Shaper Co. It is used for indexing the
Fellows gear cutters in the machine in which the teeth are ground. The
indexing mechanism of this machine is shown in Fig. 24. It is operated
by a handle or lever pinned to rock-shaft _H_, to which is keyed arm
_J_. Pivoted to _J_ is a pawl _K_ engaging the teeth of ratchet _L_,
which revolves loosely on shaft _H_. This ratchet _L_ controls the
movement of locking finger _E_. The parts are shown in their normal or
locked position in the engraving.

As the handle on shaft _H_ is pulled in the direction indicated by the
arrow, arm _J_ is raised, carrying the ratchet wheel around to the
right. This allows flat spring _M_ to drop off of the ratchet tooth,
permitting helical spring _O_ to raise latch _E_ and thus leave the
wheel free. The continued movement of the hand-lever and of rock-shaft
_H_, by means of gear _N_, intermediate pinion _P_ and gear _Q_, causes
the indexing pawl _R_, which is pivoted to gear _Q_ and acts on the
head of one of the bolts _C_ (see Fig. 23), to index the wheel one
step. Just before reaching its new location the new tooth of ratchet
wheel _L_ coming up, bears down on the top of spring _M_, pressing
latch _E_ into place against the tension of coil spring _O_. By this
means the wheel is locked in position.

When the operator pushes the handle on shaft _H_ back again to its
position of rest, the pawl _R_ is retracted into position to act on the
next bolt head for the next indexing. Star-wheel _L_ remains stationary
on this backward movement, being prevented from revolving by the notch
on the top of the tooth into which spring _M_ fits. Pawl _K_ on its
return engages with the next tooth of this wheel, ready for the next
indexing operation.

A slight rotary adjustment of dividing wheel _B_, independent of this
indexing mechanism, is required for the feeding of the machine. This
is accomplished by the end movement of latch _E_, which is pivoted in
slide _S_. This slide is pressed to the right by spring plunger _T_,
and is adjusted positively in the other direction by feed-screw _U_,
which is finely graduated to permit accurate adjustment. The accuracy
in indexing obtained by the use of a wheel thus made was required to
bring the finished cutters within the very narrow limits allowed for
them in the final inspection.




CHAPTER III

LOCATING WORK FOR BORING ON MILLING MACHINE


It is often desirable to perform boring operations on the milling
machine, particularly in connection with jig work. Large jigs, which
because of their size or shape could not be conveniently handled in
the lathe, and also a variety of smaller work, can often be bored
to advantage on the milling machine. When such a machine is in good
condition, the necessary adjustments of the work in both vertical and
horizontal planes, can be made with considerable accuracy by the direct
use of the graduated feed-screw dials. It is good practice, however,
when making adjustments in this way, to check the accuracy of the
setting by measuring the center distances between the holes directly.
For the purpose of obtaining fine adjustments when boring on the
milling machine, the Brown & Sharpe Mfg. Co. makes special scales
and verniers that are attached to milling machines, so that the table
may be set by direct measurement. By attaching a scale and vernier to
the table and saddle, respectively, and a second scale to the column
with a vernier on the knee, both longitudinal and vertical measurements
can be made quickly and accurately, and the chance of error resulting
from inaccuracy of the screw, or from lost motion between the screw and
nut, is eliminated.


Checking Location of Holes by Micrometer-and-plug Method

One method of checking the accuracy of the location of holes bored in
the milling machine, is to insert closely fitting ground plugs into
the bored holes and then determine the center-to-center distance by
taking a direct measurement across the plugs with a micrometer or
vernier caliper. For example, if holes were to be bored in a jig-plate,
as shown in Fig. 1, assuming that hole _A_ were finished first, the
platen would then be moved two inches, as shown by the feed dial; hole
_B_ would then be bored slightly under size. Plugs should then be
accurately fitted to these holes, having projecting ends, preferably of
the same size. By measuring from one of these plugs to the other with a
vernier or micrometer caliper, the center distance between them can be
accurately determined, allowance being made, of course, for the radii
of each plug. If this distance is incorrect, the work can be adjusted
before finishing _B_ to size, by using the feed-screw dial. After hole
_B_ is finished, the knee could be dropped 1.5 inch, as shown by the
vertical feed dial, and hole _C_ bored slightly under size; then by the
use of plugs, as before, the location of this hole could be tested by
measuring center distances between _C-B_ and _C-A_.

An example of work requiring the micrometer-and-plug test, is shown
set up in the milling machine in Fig. 25. The large circular plate
shown has a central hole and it was necessary to bore the outer holes
in correct relation with the center hole within a limit of 0.0005 inch.
The center hole was first bored and reamed to size; then an accurately
fitting plug was inserted and the distances to all the other holes
were checked by measuring from this plug. This method of testing with
the plugs is intended to prevent errors which might occur because of
wear in the feed-screws or nuts, that would cause the graduated dials
to give an incorrect reading. On some jig work, sufficient accuracy
could be obtained by using the feed-screw dials alone, that is, without
testing with the plugs, in which case the accuracy would naturally
depend largely on the condition of the machine.

[Illustration: Fig. 25. Example of Precision Boring on Milling Machine]

A method that is a modification of the one in which plugs are used
to test the center distance is as follows: All the holes are first
drilled with suitable allowance for boring, the location being obtained
directly by the feed-screw dials. A special boring-tool, the end of
which is ground true with the shank, is then inserted in the spindle
and the first hole, as at _A_ in Fig. 1 is finished, after which
the platen is adjusted for hole _B_ by using the dial as before. A
close-fitting plug is then inserted in hole _A_ and the accuracy of the
setting is obtained by measuring the distance between this plug and the
end of the boring-tool, which is a combination tool and test plug. In
a similar manner, the tool is moved from one position to another, and,
as all the holes have been previously drilled, all are bored without
removing the tool from the spindle.

Another modification of the micrometer-and-plug method is illustrated
in Figs. 26 and 27. It is assumed that the plate to be bored is
finished on the edges, and that it is fastened to an angle-plate, which
is secured to the table of the milling machine and set square with the
spindle. A piece of cold-rolled steel or brass is first fastened in the
chuck (which is mounted on the spindle) and turned off to any diameter.
This diameter should preferably be an even number of thousandths, to
make the calculations which are to follow easier. The turning can be
done either by holding the tool in the milling machine vise, or by
securing it to the table with clamps. In either case, the tool should
be located near the end of the table, so as to be out of the way when
not in use.

[Illustration: Fig. 26. Obtaining Vertical Adjustment by Means of Depth
Gage and turned Plug in Chuck]

After the piece in the chuck is trued, the table and knee are adjusted
until the center of the spindle is in alignment with the center of the
first hole to be machined. This setting of the jig-plate is effected
by measuring with a micrometer depth gage from the top and sides of
the work, to the turned plug, as illustrated in Fig. 26. When taking
these measurements, the radius of the plug in the chuck is, of course,
deducted. When the plate is set the plug is removed from the chuck
and the first hole drilled and bored or reamed to its proper size. We
shall assume that the holes are to be located as shown by the detail
view, Fig. 26, and that hole _A_ is the first one bored. The plug is
then again inserted in the chuck and trued with the tool, after which
it is set opposite the place where the second hole _B_ is to be bored;
this is done by inserting an accurately fitting plug in hole _A_ and
measuring from this plug to the turned piece in the chuck, with an
outside micrometer as indicated in Fig. 27. Allowance is, of course,
again made for the radii of the two plugs. The horizontal measurement
can be taken from the side of the work with a depth gage as before. The
plug is then removed and the hole drilled and bored to the proper size.
The plug is again inserted in the chuck and turned true; the table is
then moved vertically to a position midway between _A_ and _B_, and
then horizontally to the proper position for hole _C_, as indicated by
the depth gage from the side of the work. The location can be verified
by measuring the center distances _x_ with the micrometer. In a similar
manner holes _D_, _E_, _F_ and _G_ are accurately located.

[Illustration: Fig. 27. Adjusting for Center-to-center Distance by use
of Plugs and Micrometer]

If the proper allowances are made for the variation in the size of the
plug, which, of course, is made smaller each time it is trued, and if
no mistakes are made in the calculations, this method is very accurate.
Care should be taken to have the gibs on all sides fairly tight at the
beginning, and these should not be tightened after each consecutive
alignment, as this generally throws the work out a few thousandths.
If the reductions in the size of the plug, each time it is turned,
are confusing, new plugs can be used each time a test is made, or the
end of the original plug can be cut off so that it can be turned to
the same diameter for every test. If the center distances _x_ are not
given, it is, of course, far more convenient to make all the geometric
calculations before starting to work.


The Button-and-plug Method

The use of the button method as applied to the milling machine, is
illustrated in Fig. 28, where a plain jig-plate is shown set up for
boring. The jig, with buttons _B_ accurately located in positions
corresponding to the holes to be bored, is clamped to the angle-plate
_A_ that is set at right angles to the spindle. Inserted in the spindle
there is a plug _P_, the end of which is ground to the exact size of
the indicating buttons. A sliding sleeve _S_ is accurately fitted
to this plug and when the work is to be set for boring a hole, the
table and knee of the machine are adjusted until the sleeve _S_ will
pass over the button representing the location of the hole, which
brings the button and spindle into alignment. When setting the button
in alignment, all lost motion or backlash should be taken up in the
feed-screws. For instance, if the button on the jig should be a little
higher than the plug in the spindle, do not lower the knee until the
bushing slips over the button, but lower the knee more than is required
and then raise it until the bushing will pass over the button. This
same rule should be followed for longitudinal adjustments.

[Illustration: Fig. 28. Accurate Method of Aligning Spindle with Button
on Jig-Plate]

After the button is set by this method, it is removed and the plug in
the spindle is replaced by a drill and then by a boring-tool or reamer
for finishing the hole to size. In a similar manner the work is set for
the remaining holes. The plug _P_ for the spindle must be accurately
made so that the outer end is concentric with the shank, and the latter
should always be inserted in the spindle in the same relative position.
With a reasonable degree of care, work can be set with considerable
precision by this method, providing, of course, the buttons are
properly set.

Some toolmakers use, instead of the plug and sleeve referred to, a test
indicator for setting the buttons concentric with the machine spindle.
This indicator is attached to and revolves with the spindle, while the
point is brought into contact with the button to be set. The difficulty
of seeing the pointer as it turns is a disadvantage, but with care
accurate results can be obtained.


Size Block and Gage Method

Another method which can at times be employed for accurately locating
a jig-plate in different positions on an angle-plate, is shown in
Fig. 29. The angle-plate is, of course, set at right angles to the
spindle and depth gages and size blocks are used for measuring directly
the amount of adjustment. Both the angle-plate and work should have
finished surfaces on two sides at right angles to each other, from
which measurements can be taken. After the first hole has been bored,
the plate is adjusted the required distance both horizontally and
vertically, by using micrometer depth gages, which should preferably be
clamped to the angle-plate. If the capacity of the gages is exceeded,
measurements may be taken by using standard size blocks in conjunction
with the depth gages.

[Illustration: Fig. 29. Locating Work from Edges of Angle-Plate by
means of Depth Gages and Size Blocks]

It is frequently necessary to bore holes in cast jig-plates or machine
parts, which either have irregularly shaped or unfinished edges. A good
method of locating such work is illustrated in Fig. 30. The part to be
bored is attached to an auxiliary plate _A_ which should have parallel
sides and at least two edges which are straight and at right angles
to each other. This auxiliary plate with the work, is clamped against
an accurate angle-plate _B_, which should be set square with the axis
of the machine spindle. A parallel strip is bolted to the angle-plate
and the inner edge is set square with the machine table. After the
first hole is bored, the work is located for boring the other to the
edge of the auxiliary plate, and horizontal measurements _y_ between
the parallel and the plate. These measurements, if quite large, might
be taken with micrometer gages, whereas, for comparatively small
adjustments, size blocks might be more convenient.


Vernier Height Gage and Plug Method

When a vernier height gage is available, it can often be used to
advantage for setting work preparatory to boring in a milling machine.
One advantage of this method is that it requires little in the way of
special equipment. The work is mounted on an angle-plate or directly
on the platen, depending on its form, and at one end an angle-plate is
set up with its face parallel to the spindle. An accurately finished
plug is inserted in the spindle and this plug is set vertically from
the platen and horizontally from the end angle-plate, by measuring with
the vernier height gage. After the plug is set for each hole, it is, of
course, removed and the hole drilled and bored or reamed.

[Illustration: Fig. 30. Method of Holding and Locating Casting of
Irregular Shape, for Boring Holes]

The way the plug and height gage is used is clearly illustrated in
Figs. 31 and 32. The work, in this particular case, is a small jig.
This is clamped directly to the machine table and at one end an
angle-plate is also bolted to the table. This angle-plate is first set
parallel with the traverse of the saddle or in line with the machine
spindle. To secure this alignment, an arbor is inserted in the spindle
and a test indicator is clamped to it by gripping the indicator between
bushings placed on the arbor. The table is then moved longitudinally
until the contact point of the indicator is against the surface plate;
then by traversing the saddle crosswise, any lack of parallelism
between the surface of the angle-plate and the line of saddle traverse
will be shown by the indicator.

[Illustration: Fig. 31. Making a Vertical Adjustment by Measuring to
Ground Plug in Spindle]

[Illustration: Fig. 32. Making a Horizontal Adjustment by measuring
from Angle-Plate to Ground Plug]

When the work is to be adjusted horizontally, the vernier height gage
is used as shown in Fig. 32, the base of the gage resting on the
angle-plate and the measurement being taken to an accurately ground and
lapped plug in the spindle. For vertical adjustments, the measurements
are taken between this ground plug and the machine platen as in Fig. 31.


Locating Holes to be Bored from Center-punch Marks

The problem of accurately locating holes to be bored on the milling
machine has received much attention, and the method generally used when
accuracy has been required is the button method, which was previously
described. So much time is required for doing the work by this method,
however, that numerous efforts have been made to obtain equally good
results in other ways.

[Illustration: Fig. 33. Diagram Illustrating Rapid but Accurate Method
of Locating Holes to be bored on Milling Machine]

The increasing demand for rapidity combined with accuracy and a minimum
liability of error, led to the development of the system described in
the following: A center-punch mark takes the place of the button, from
which to indicate the work into the proper position for boring. The
fundamental principle involved is to lay out, accurately, two lines
at right angles to each other, and correctly center-punch the point
where they intersect. With proper care, lines may be drawn with a
vernier height gage at right angles, with extreme accuracy, the chief
difficulty being to accurately center the lines where they cross. For
semi-accurate work this may be done with a common center-punch but
where extreme accuracy is required this method is not applicable, as
the average man is incapable of marking the point of intersection
accurately.

The diagram, Fig. 33, illustrates, in a simple way, the procedure
adopted in laying out work by this system. The base _E_ is in contact
with a surface plate while the line _BB_ is drawn with a height gage;
then with side _F_ on the plate the line _AA_ is drawn. It will be
seen that these lines will be at right angles to each other, if the
bases _E_ and _F_ are square. Work done by this method must have two
working surfaces or base lines, and these must be at right angles
to each other. There is no difficulty in drawing the locating lines
_AA_ and _BB_ correctly, either with a vernier height gage or with a
special micrometer gage reading to 0.0001 inch, the only difficult
element being to accurately center-punch the lines where they intersect
as at _D_. It is assumed that two holes are to be bored, so that the
intersection at _C_ would also be center-punched.

The scriber point of the height gage should be ground so that it will
make a V-shaped line, as shown by the enlarged sketch _G_, rather than
one which would resemble a saw-tooth, as at _H_, if a cross-section of
it were examined with a microscope. This is important because when the
lines are V-shaped, an accurate point of intersection is obtained.

[Illustration: Fig. 34. Center Locating Punch]

[Illustration: Fig. 35. Center Enlarging Punch]

As it is quite or almost impossible to accurately center-punch the
intersection of even two correctly drawn lines, by ordinary means, the
punch shown in Figs. 34 and 36 was designed and an extended experience
with it on a very high grade of work has demonstrated its value for
the purpose. It consists essentially of a small center-punch _O_ (Fig.
36) held in vertical position by a holder _P_ which is knurled to
facilitate handling. Great care should be exercised in making this
tool to have the body of the punch straight, and to have it stand at
right angles to the surface to be operated upon, for the slightest
inclination will cause the finished hole to be incorrect, no matter
how carefully the lines are drawn. The 60-degree point must be ground
true with the axis. The holder for the punch stands on three legs,
located as indicated, and ground accurately to a taper fit in the
holder, where they are secured by watch screws bearing on their tops.
The lower ends are hardened, and terminate in an angular point of 55
degrees (the point of the vernier scriber being 60 degrees). The edges
are sharp, and slightly rounded at the ends, so that the legs will
slide along a line smoothly. The points _V_ and _U_ (Fig. 36) have
edges that are in line with each other, while the point _T_ has an edge
at right angles to the other two. The center of the punch is located at
equal distances from all the legs, and is held off the work normally by
a leather friction acted upon by a set-screw in the side of holder _P_.

[Illustration: Fig. 36. Section of Center Locating Punch]

[Illustration: Fig. 37. Section of Center Enlarging Punch]

If this tool is placed upon lines of the form shown at _G_, Fig. 33,
the legs _V_ and _U_ may be slid along horizontal line _B-B_, Fig. 33,
until the sharp edge of leg _T_ drops into line _A-A_. When this occurs
the punch _O_ is lightly tapped with a hammer, and the resulting mark
will be accurately located in the center of the intersection of the
lines. It is good practice to make the work very smooth before drawing
the lines, and after laying them out, to stone them so as to remove the
slight burr raised in drawing them. A drop of oil is then rubbed into
the lines, and the surplus wiped off. This procedure permits points
_V_ and _U_ to run very smoothly along the line, and the burr having
been removed, the edge of leg _T_ drops into the line very readily with
a slight click. As it is not advisable to strike punch _O_ more than a
very light blow, it marks the work but slightly, and a more distinct
indentation is made with the follower punch shown in Figs. 35 and 37.
This punch is made like the previous one, so that it will stand at
right angles to the work. The sectional view (Fig. 37) shows the punch
_A_ supported by the holder _E_ which has four legs cut away on the
sides so that the point of the punch may be seen. When this punch is in
position, it is struck a sufficiently heavy blow to make a distinctly
visible mark. The work is now ready to be placed upon the work table of
the milling machine, and indicated for boring the holes, an indicator
being used in the milling machine spindle.

[Illustration: Fig. 38. Indicator used for Aligning Punch Marks with
Machine Spindle]

An indicator which has been found especially valuable for this purpose
is shown in Figs. 38 and 39. It is of the concentric centering type,
and with it the work is brought concentric with the axis of the
spindle. The arbor _I_ is provided with a threaded nose on which disk
_D_ is screwed. This disk has four holes in its rim, equally-spaced
from each other. Hardened, ground, and lapped bushings _b_ are put into
these holes to receive plug _A_ which is made a gage-fit both in these
holes and in hole _B_ in the outer end of sector _C_. This sector is
held by a split sleeve to the barrel _L_ which carries the 60-degree
centering-rod _K_ that comes into contact with the work to be bored.
The spherical base of barrel _L_ fits into a corresponding concave seat
in the nose of the arbor at _H_, and is held in place by a spring _E_
which connects at one end to the cylindrical stud in the base of the
barrel, and at the other to the axial rod _M_ by which it and the other
connecting parts may be drawn into place, and held by the headless
set-screw _J_, bearing on a flat spot on the tang end of the rod.

Now, if plug _A_ is removed from bushing _b_ the point of the
centering-rod _K_ may be made to describe a circle. At some point
within this circle is located the center-punch mark on the work to
be bored. The holes in the rim of the faceplate all being exactly
the same distance from an axial line through both the arbor _I_ and
centering-rod _K_, it follows that the center mark on the work must
be so located by horizontal and vertical movements of the work table
that pin _A_ may be freely entered in all the four holes in the rim of
disk _D_. When that occurs, the center coincides with the axis of the
spindle.

The point of the center-punch _A_ (Fig. 37) should have an angle
slightly greater than the angle on the centering-rod _K_, as it is
impossible to locate the work in the preliminary trials so that the
center of the work will be coincident with the axis of the spindle, and
unless the precaution mentioned is taken, the true center on the work
is liable to be drawn from its proper location when trying to bring the
work into such a position that the plug will enter all the holes in the
disk. As the work being operated on is brought nearer to the proper
location by the movements of the milling machine table, spring _G_ will
be compressed, the center rod sliding back into barrel _L_. This spring
is made so that it will hold the center against the work firmly, but
without interfering with the free rotation of the sector _C_ around
disk _D_. When the work is located so that the plug enters the holes,
the gibs of the machine should be tightened up and the plug tried
once more, to make sure that the knee of the machine has not moved
sufficiently to cause the work on the table to be out of line. The work
table is now clamped to prevent accidental horizontal shifting, and the
work is drilled and bored.

[Illustration: Fig. 39. Sectional View of Indicator shown in Fig. 38]

In using this indicator the milling machine spindle is not rotated
together with arbor _I_, only the sector being turned around the disk.
The tool is set, however, in the beginning, so that the axes of two
of the bushings _b_ are at right angles to the horizontal plane of
the machine table, while the axes of the other holes in the disk
are parallel with the top of the work table. The centering-rods are
made interchangeable and of various lengths, to reach more or less
accessible centers. Fig. 38 shows the indicator with one of the long
center-rods in the foreground.

The only part of the milling machine on which dependence must be placed
for accuracy is the hole in the spindle, and this is less liable to get
out of truth, from wear such as would impair the accuracy, than are the
knee, table, or micrometer screws. The only moving part is the sector,
and this, being light, is very sensitive.

A series of 24 holes was laid out and bored in one and one-half day by
the method described in the foregoing. Measurements across accurately
lapped plugs in the holes, showed the greatest deviation from truth
to be 0.0002 inch, and running from that to accuracy so great that no
error was measurable. This same work with buttons would have required
considerably more time.




[Illustration: MACHINERY]


Machinery is the leading journal in the machine-building field and
meets the requirements of the mechanical engineer, superintendent,
designer, toolmaker and machinist, as no other journal does.
MACHINERY deals exclusively with machine design, tool design, machine
construction, shop practice, shop systems and shop management. The
reading matter in MACHINERY is written by practical men and edited by
mechanical men of long practical training.

Each number of MACHINERY contains a variety of articles on machine shop
practice. These articles include carefully prepared descriptions of
manufacturing methods and current mechanical developments. Shop systems
and shop managements are ably handled by the foremost writers. Every
number contains the most extensive and complete record published by any
journal, or in any form, of new machinery and tools and accessories
for the machine shop. A special department is devoted to “Letters on
Practical Subjects,” to which practical mechanics contribute their
experiences. There is a department of Shop Kinks—brief, concise little
contributions which contain ideas of value to the man in the shop or at
the drafting table.

The mechanical engineer, machine designer and draftsman are also well
provided for in MACHINERY. Every number contains articles on the theory
and practice of machine design, on the properties of materials, and
on labor-saving methods and systems. There are reviews of research
work in the mechanical field, and valuable results of carefully made
experiments are recorded.

The supremacy of MACHINERY in the mechanical field is due to the
care with which all matter offered for publication in its pages is
scrutinized. Only the _best_ of the material offered by mechanical
writers is published, and, as a result, its pages contain the most
authoritative, practical and up-to-date mechanical information.

    MACHINERY, 140-148 Lafayette Street,
          New York City 51 and 52,
        CHANCERY LANE, LONDON, W. C.

Heat-Treatment of Steel

[Illustration]

is one of a series of high-class authoritative, attractive and
well-bound books published by MACHINERY.

The strongest claim that can be made for these books is that they have
all the characteristics of MACHINERY itself.

These books cover comprehensively, and in a thoroughly practical
manner, the most important subjects in the metal-working field.

Each book comprises about 300 pages, printed on high-grade paper,
with engravings of the same superior type that has made MACHINERY
distinctive in its field.

The price of each book is $2.50. Special combination offers on a
monthly payment plan will be sent upon request.

                    MACHINERY
    140-148 Lafayette St.      New York City
     51 and 52, Chancery Lane, London, W. C.

The Five New Books

Brought Out by MACHINERY

SPUR AND BEVEL GEARING

A treatise on the principles, dimensions, calculation, design and
strength of spur and bevel gearing, together with chapters on special
tooth forms and methods of cutting gear teeth.

SPIRAL AND WORM GEARING

A treatise on the principles, dimensions, calculation and design of
spiral and worm gearing, together with chapters on the methods of
cutting the teeth in these types of gears.

TURNING AND BORING

By FRANKLIN D. JONES Associate Editor of MACHINERY

A specialized treatise for machinists, students in industrial and
engineering schools, and apprentices on turning and boring methods,
including modern practice with engine lathes, turret lathes, vertical
and horizontal boring machines.

PLANING AND MILLING

By FRANKLIN D. JONES Associate Editor of MACHINERY

A treatise on the use of planers, shapers, slotters and various types
of horizontal and vertical milling machines and their attachments.

HEAT-TREATMENT OF STEEL

A comprehensive treatise on the hardening, tempering, annealing and
case-hardening of various kinds of steel, including high-speed,
high-carbon, alloy and low-carbon steels, together with chapters on
heat-treating furnaces and on hardness testing.

Price of each book $2.50. Special combination offers on a monthly
payment plan will be sent upon request.

                    MACHINERY
    140-148 Lafayette St.      New York City
     51 and 52, Chancery Lane, London, W. C.



*** END OF THE PROJECT GUTENBERG EBOOK PRECISION LOCATING AND DIVIDING METHODS ***


    

Updated editions will replace the previous one—the old editions will
be renamed.

Creating the works from print editions not protected by U.S. copyright
law means that no one owns a United States copyright in these works,
so the Foundation (and you!) can copy and distribute it in the United
States without permission and without paying copyright
royalties. Special rules, set forth in the General Terms of Use part
of this license, apply to copying and distributing Project
Gutenberg™ electronic works to protect the PROJECT GUTENBERG™
concept and trademark. Project Gutenberg is a registered trademark,
and may not be used if you charge for an eBook, except by following
the terms of the trademark license, including paying royalties for use
of the Project Gutenberg trademark. If you do not charge anything for
copies of this eBook, complying with the trademark license is very
easy. You may use this eBook for nearly any purpose such as creation
of derivative works, reports, performances and research. Project
Gutenberg eBooks may be modified and printed and given away—you may
do practically ANYTHING in the United States with eBooks not protected
by U.S. copyright law. Redistribution is subject to the trademark
license, especially commercial redistribution.


START: FULL LICENSE

THE FULL PROJECT GUTENBERG LICENSE

PLEASE READ THIS BEFORE YOU DISTRIBUTE OR USE THIS WORK

To protect the Project Gutenberg™ mission of promoting the free
distribution of electronic works, by using or distributing this work
(or any other work associated in any way with the phrase “Project
Gutenberg”), you agree to comply with all the terms of the Full
Project Gutenberg™ License available with this file or online at
www.gutenberg.org/license.

Section 1. General Terms of Use and Redistributing Project Gutenberg™
electronic works

1.A. By reading or using any part of this Project Gutenberg™
electronic work, you indicate that you have read, understand, agree to
and accept all the terms of this license and intellectual property
(trademark/copyright) agreement. If you do not agree to abide by all
the terms of this agreement, you must cease using and return or
destroy all copies of Project Gutenberg™ electronic works in your
possession. If you paid a fee for obtaining a copy of or access to a
Project Gutenberg™ electronic work and you do not agree to be bound
by the terms of this agreement, you may obtain a refund from the person
or entity to whom you paid the fee as set forth in paragraph 1.E.8.

1.B. “Project Gutenberg” is a registered trademark. It may only be
used on or associated in any way with an electronic work by people who
agree to be bound by the terms of this agreement. There are a few
things that you can do with most Project Gutenberg™ electronic works
even without complying with the full terms of this agreement. See
paragraph 1.C below. There are a lot of things you can do with Project
Gutenberg™ electronic works if you follow the terms of this
agreement and help preserve free future access to Project Gutenberg™
electronic works. See paragraph 1.E below.

1.C. The Project Gutenberg Literary Archive Foundation (“the
Foundation” or PGLAF), owns a compilation copyright in the collection
of Project Gutenberg™ electronic works. Nearly all the individual
works in the collection are in the public domain in the United
States. If an individual work is unprotected by copyright law in the
United States and you are located in the United States, we do not
claim a right to prevent you from copying, distributing, performing,
displaying or creating derivative works based on the work as long as
all references to Project Gutenberg are removed. Of course, we hope
that you will support the Project Gutenberg™ mission of promoting
free access to electronic works by freely sharing Project Gutenberg™
works in compliance with the terms of this agreement for keeping the
Project Gutenberg™ name associated with the work. You can easily
comply with the terms of this agreement by keeping this work in the
same format with its attached full Project Gutenberg™ License when
you share it without charge with others.

1.D. The copyright laws of the place where you are located also govern
what you can do with this work. Copyright laws in most countries are
in a constant state of change. If you are outside the United States,
check the laws of your country in addition to the terms of this
agreement before downloading, copying, displaying, performing,
distributing or creating derivative works based on this work or any
other Project Gutenberg™ work. The Foundation makes no
representations concerning the copyright status of any work in any
country other than the United States.

1.E. Unless you have removed all references to Project Gutenberg:

1.E.1. The following sentence, with active links to, or other
immediate access to, the full Project Gutenberg™ License must appear
prominently whenever any copy of a Project Gutenberg™ work (any work
on which the phrase “Project Gutenberg” appears, or with which the
phrase “Project Gutenberg” is associated) is accessed, displayed,
performed, viewed, copied or distributed:

    This eBook is for the use of anyone anywhere in the United States and most
    other parts of the world at no cost and with almost no restrictions
    whatsoever. You may copy it, give it away or re-use it under the terms
    of the Project Gutenberg License included with this eBook or online
    at www.gutenberg.org. If you
    are not located in the United States, you will have to check the laws
    of the country where you are located before using this eBook.
  
1.E.2. If an individual Project Gutenberg™ electronic work is
derived from texts not protected by U.S. copyright law (does not
contain a notice indicating that it is posted with permission of the
copyright holder), the work can be copied and distributed to anyone in
the United States without paying any fees or charges. If you are
redistributing or providing access to a work with the phrase “Project
Gutenberg” associated with or appearing on the work, you must comply
either with the requirements of paragraphs 1.E.1 through 1.E.7 or
obtain permission for the use of the work and the Project Gutenberg™
trademark as set forth in paragraphs 1.E.8 or 1.E.9.

1.E.3. If an individual Project Gutenberg™ electronic work is posted
with the permission of the copyright holder, your use and distribution
must comply with both paragraphs 1.E.1 through 1.E.7 and any
additional terms imposed by the copyright holder. Additional terms
will be linked to the Project Gutenberg™ License for all works
posted with the permission of the copyright holder found at the
beginning of this work.

1.E.4. Do not unlink or detach or remove the full Project Gutenberg™
License terms from this work, or any files containing a part of this
work or any other work associated with Project Gutenberg™.

1.E.5. Do not copy, display, perform, distribute or redistribute this
electronic work, or any part of this electronic work, without
prominently displaying the sentence set forth in paragraph 1.E.1 with
active links or immediate access to the full terms of the Project
Gutenberg™ License.

1.E.6. You may convert to and distribute this work in any binary,
compressed, marked up, nonproprietary or proprietary form, including
any word processing or hypertext form. However, if you provide access
to or distribute copies of a Project Gutenberg™ work in a format
other than “Plain Vanilla ASCII” or other format used in the official
version posted on the official Project Gutenberg™ website
(www.gutenberg.org), you must, at no additional cost, fee or expense
to the user, provide a copy, a means of exporting a copy, or a means
of obtaining a copy upon request, of the work in its original “Plain
Vanilla ASCII” or other form. Any alternate format must include the
full Project Gutenberg™ License as specified in paragraph 1.E.1.

1.E.7. Do not charge a fee for access to, viewing, displaying,
performing, copying or distributing any Project Gutenberg™ works
unless you comply with paragraph 1.E.8 or 1.E.9.

1.E.8. You may charge a reasonable fee for copies of or providing
access to or distributing Project Gutenberg™ electronic works
provided that:

    • You pay a royalty fee of 20% of the gross profits you derive from
        the use of Project Gutenberg™ works calculated using the method
        you already use to calculate your applicable taxes. The fee is owed
        to the owner of the Project Gutenberg™ trademark, but he has
        agreed to donate royalties under this paragraph to the Project
        Gutenberg Literary Archive Foundation. Royalty payments must be paid
        within 60 days following each date on which you prepare (or are
        legally required to prepare) your periodic tax returns. Royalty
        payments should be clearly marked as such and sent to the Project
        Gutenberg Literary Archive Foundation at the address specified in
        Section 4, “Information about donations to the Project Gutenberg
        Literary Archive Foundation.”
    
    • You provide a full refund of any money paid by a user who notifies
        you in writing (or by e-mail) within 30 days of receipt that s/he
        does not agree to the terms of the full Project Gutenberg™
        License. You must require such a user to return or destroy all
        copies of the works possessed in a physical medium and discontinue
        all use of and all access to other copies of Project Gutenberg™
        works.
    
    • You provide, in accordance with paragraph 1.F.3, a full refund of
        any money paid for a work or a replacement copy, if a defect in the
        electronic work is discovered and reported to you within 90 days of
        receipt of the work.
    
    • You comply with all other terms of this agreement for free
        distribution of Project Gutenberg™ works.
    

1.E.9. If you wish to charge a fee or distribute a Project
Gutenberg™ electronic work or group of works on different terms than
are set forth in this agreement, you must obtain permission in writing
from the Project Gutenberg Literary Archive Foundation, the manager of
the Project Gutenberg™ trademark. Contact the Foundation as set
forth in Section 3 below.

1.F.

1.F.1. Project Gutenberg volunteers and employees expend considerable
effort to identify, do copyright research on, transcribe and proofread
works not protected by U.S. copyright law in creating the Project
Gutenberg™ collection. Despite these efforts, Project Gutenberg™
electronic works, and the medium on which they may be stored, may
contain “Defects,” such as, but not limited to, incomplete, inaccurate
or corrupt data, transcription errors, a copyright or other
intellectual property infringement, a defective or damaged disk or
other medium, a computer virus, or computer codes that damage or
cannot be read by your equipment.

1.F.2. LIMITED WARRANTY, DISCLAIMER OF DAMAGES - Except for the “Right
of Replacement or Refund” described in paragraph 1.F.3, the Project
Gutenberg Literary Archive Foundation, the owner of the Project
Gutenberg™ trademark, and any other party distributing a Project
Gutenberg™ electronic work under this agreement, disclaim all
liability to you for damages, costs and expenses, including legal
fees. YOU AGREE THAT YOU HAVE NO REMEDIES FOR NEGLIGENCE, STRICT
LIABILITY, BREACH OF WARRANTY OR BREACH OF CONTRACT EXCEPT THOSE
PROVIDED IN PARAGRAPH 1.F.3. YOU AGREE THAT THE FOUNDATION, THE
TRADEMARK OWNER, AND ANY DISTRIBUTOR UNDER THIS AGREEMENT WILL NOT BE
LIABLE TO YOU FOR ACTUAL, DIRECT, INDIRECT, CONSEQUENTIAL, PUNITIVE OR
INCIDENTAL DAMAGES EVEN IF YOU GIVE NOTICE OF THE POSSIBILITY OF SUCH
DAMAGE.

1.F.3. LIMITED RIGHT OF REPLACEMENT OR REFUND - If you discover a
defect in this electronic work within 90 days of receiving it, you can
receive a refund of the money (if any) you paid for it by sending a
written explanation to the person you received the work from. If you
received the work on a physical medium, you must return the medium
with your written explanation. The person or entity that provided you
with the defective work may elect to provide a replacement copy in
lieu of a refund. If you received the work electronically, the person
or entity providing it to you may choose to give you a second
opportunity to receive the work electronically in lieu of a refund. If
the second copy is also defective, you may demand a refund in writing
without further opportunities to fix the problem.

1.F.4. Except for the limited right of replacement or refund set forth
in paragraph 1.F.3, this work is provided to you ‘AS-IS’, WITH NO
OTHER WARRANTIES OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT
LIMITED TO WARRANTIES OF MERCHANTABILITY OR FITNESS FOR ANY PURPOSE.

1.F.5. Some states do not allow disclaimers of certain implied
warranties or the exclusion or limitation of certain types of
damages. If any disclaimer or limitation set forth in this agreement
violates the law of the state applicable to this agreement, the
agreement shall be interpreted to make the maximum disclaimer or
limitation permitted by the applicable state law. The invalidity or
unenforceability of any provision of this agreement shall not void the
remaining provisions.

1.F.6. INDEMNITY - You agree to indemnify and hold the Foundation, the
trademark owner, any agent or employee of the Foundation, anyone
providing copies of Project Gutenberg™ electronic works in
accordance with this agreement, and any volunteers associated with the
production, promotion and distribution of Project Gutenberg™
electronic works, harmless from all liability, costs and expenses,
including legal fees, that arise directly or indirectly from any of
the following which you do or cause to occur: (a) distribution of this
or any Project Gutenberg™ work, (b) alteration, modification, or
additions or deletions to any Project Gutenberg™ work, and (c) any
Defect you cause.

Section 2. Information about the Mission of Project Gutenberg™

Project Gutenberg™ is synonymous with the free distribution of
electronic works in formats readable by the widest variety of
computers including obsolete, old, middle-aged and new computers. It
exists because of the efforts of hundreds of volunteers and donations
from people in all walks of life.

Volunteers and financial support to provide volunteers with the
assistance they need are critical to reaching Project Gutenberg™’s
goals and ensuring that the Project Gutenberg™ collection will
remain freely available for generations to come. In 2001, the Project
Gutenberg Literary Archive Foundation was created to provide a secure
and permanent future for Project Gutenberg™ and future
generations. To learn more about the Project Gutenberg Literary
Archive Foundation and how your efforts and donations can help, see
Sections 3 and 4 and the Foundation information page at www.gutenberg.org.

Section 3. Information about the Project Gutenberg Literary Archive Foundation

The Project Gutenberg Literary Archive Foundation is a non-profit
501(c)(3) educational corporation organized under the laws of the
state of Mississippi and granted tax exempt status by the Internal
Revenue Service. The Foundation’s EIN or federal tax identification
number is 64-6221541. Contributions to the Project Gutenberg Literary
Archive Foundation are tax deductible to the full extent permitted by
U.S. federal laws and your state’s laws.

The Foundation’s business office is located at 809 North 1500 West,
Salt Lake City, UT 84116, (801) 596-1887. Email contact links and up
to date contact information can be found at the Foundation’s website
and official page at www.gutenberg.org/contact

Section 4. Information about Donations to the Project Gutenberg
Literary Archive Foundation

Project Gutenberg™ depends upon and cannot survive without widespread
public support and donations to carry out its mission of
increasing the number of public domain and licensed works that can be
freely distributed in machine-readable form accessible by the widest
array of equipment including outdated equipment. Many small donations
($1 to $5,000) are particularly important to maintaining tax exempt
status with the IRS.

The Foundation is committed to complying with the laws regulating
charities and charitable donations in all 50 states of the United
States. Compliance requirements are not uniform and it takes a
considerable effort, much paperwork and many fees to meet and keep up
with these requirements. We do not solicit donations in locations
where we have not received written confirmation of compliance. To SEND
DONATIONS or determine the status of compliance for any particular state
visit www.gutenberg.org/donate.

While we cannot and do not solicit contributions from states where we
have not met the solicitation requirements, we know of no prohibition
against accepting unsolicited donations from donors in such states who
approach us with offers to donate.

International donations are gratefully accepted, but we cannot make
any statements concerning tax treatment of donations received from
outside the United States. U.S. laws alone swamp our small staff.

Please check the Project Gutenberg web pages for current donation
methods and addresses. Donations are accepted in a number of other
ways including checks, online payments and credit card donations. To
donate, please visit: www.gutenberg.org/donate.

Section 5. General Information About Project Gutenberg™ electronic works

Professor Michael S. Hart was the originator of the Project
Gutenberg™ concept of a library of electronic works that could be
freely shared with anyone. For forty years, he produced and
distributed Project Gutenberg™ eBooks with only a loose network of
volunteer support.

Project Gutenberg™ eBooks are often created from several printed
editions, all of which are confirmed as not protected by copyright in
the U.S. unless a copyright notice is included. Thus, we do not
necessarily keep eBooks in compliance with any particular paper
edition.

Most people start at our website which has the main PG search
facility: www.gutenberg.org.

This website includes information about Project Gutenberg™,
including how to make donations to the Project Gutenberg Literary
Archive Foundation, how to help produce our new eBooks, and how to
subscribe to our email newsletter to hear about new eBooks.