IMPROVEMENTS IN MACHINERY FOR WINDING YARN OR THREAD UPON CONICAL SURFACES
Year: 1869

page_text: LETTERS PATENT to John Boyd, of Glasgow, in the County of Lanark,
North Britain, Engineer, for the Invention of "IMPROVEMENTS IN
MACHINERY FOR WINDING YARN OR THREAD UPON CONICAL SURFACES,"
Sealed the 31st May 1870, and dated the 4th December 1869.
PROVISIONAL SPECIFICATION left by the said John Boyd at the
Office of the Commissioners of Patents, with his Petition, on the
4th December 1869.
I, JOHN BOYD, of Glasgow, in the County of Lanark, North Britain,
Engineer, do hereby declare the nature of the said Invention for "IM-
PROVEMENTS IN MACHINERY
IN MACHINERY FOR WINDING YARN
FOR WINDING YARN OR THREAD UPON CONICAL
SURPACES," to be as follows, that is to say :-
This Invention has for its
winding machinery in such a
-
object the shaping of certain wheels in
way that the winding spindles may have
the varying velocity necessary to draw the yarn or thread at a practically
uniform rate whilst winding it up and down the conical surface of the
pirn or equivalent detail.

page_text: The wheels referred to are in such a position in the driving train of
the machinery that they each make half a turn whilst the yarn or thread
is winding up the cone, and half a turn whilst the yarn or thread is
winding down the cone again.
Two different forms of wheel are used in carrying out the Invention,
the driving wheel being of one form, and gearing into one or two driven
wheels which are of the other form. The form of the pitch line for the
driven wheels is defined by making the lengths of any convenient
number of equidistant radii equal severally to lengths obtained by
substracting from the length, measuring the distance between the
centres of the two wheels that are to gear together, portions equal to
equidistant ordinates drawn from a hyperbola to its asymptote. These
radial lengths may also be obtained numerically by calculations consistent
with the known properties of the hyperbola.
The form of the pitch line for the driving wheel is defined by taking
the lengths of the hyperbola ordinates herein-before referred to for those
of radii placed at suitably varying angular distances apart. To obtain
the varying angles a four-sided figure is taken equal or similar to an
axial section of the conical part of the pirn, and the area of it is divided
by lines parallel to the base into as many equal parts as there are
angular spaces. The division lines cut the side line of the figure into
unequal portions, which are severally of the proportion to the whole
side line that the several angles should be to 180 degrees of the circle
The same angles may be got by other geometrical methods or by
numerical calculation or by geometrically constructing the triangles
formed by the several pairs of radii and the portions of the circum-
ference joining their ends, which circumferential portions are equal
to and can be measured with great accuracy from the corresponding
circumferential portions of the other wheel.
SPECIFICATION in pursuance of the conditions of the Letters Patent, 3
filed by the said John Boyd in the Great Seal Patent Office on
the 3rd June 1870.
TO ALL TO WHOM THESE PRESENTS SHALL COME, I, JOHN.
BOYD, of Glasgow, in the County of Lanark, North Britain, Engineer,
3
send greeting.

page_text: two different forms, the driving wheel being of one form, and gearing
into one or two driven wheels which are of the other form.
My Invention consists in shaping the wheels in such a way that if
certain radii are drawn to the pitch line of the driving wheel they will
be equal to a series of equidistant ordinates drawn from a hyperbola
to its asymptote, whilst if the lengths of those ordinates be severally
deducted from the distance between the centres of the two wheels the
remainders will be equal to radii drawn equidistantly to the pitch line
of the driven wheel.
And in order that my said Invention and the manner of performing
the same may be properly understood I have hereunto appended a Sheet
of explanatory Drawings to be herein-after referred to, and representing
a pair of spur wheels as constructed according to my Invention. The
Drawing also comprises two explanatory diagrams.
The wheels represented in the Drawing are designed to suit a conical
surface, of which the ratio of the largest diameter to the smallest is
as 2 to 1. The pitch lines of the two wheels and sets of radii to the
pitch lines are shown by dotted lines. The radii divide each semicircle
of each wheel into sixteen sectors, the sectors of the driving wheel
having unequal angles, whilst those of the driven wheel have equal
angles. The formulæ herein-after given are constructed to suit any
number of divisions of the semicircle, and any ratio between the
extreme diameters of the conical surface for which the wheels are
designed.
in which A represents the distance between the centres of the two
wheels ; R, the higher term of the ratio (the lower term being 1);
N the number of sectors into which the semicircle is divided by the radii;
and 22, the number of sectors between the shortest radius and the
particular radius that is being calculated. The shortest and longest
radii may be calculated by the simple formulæ, 2A and 2AR
Various
R+3
3R + 1'

page_text: 2 A
2 AR
R+1
hyperbolas may be used for determining the lengths of the radii
geometrically or graphically; but it is convenient to use a rectangular
hyperbola, such as is shown in diagram i, in which the square between
the curve and its asymptotes and y has its side C, D, equal to the
distance A between the centres, or representing that distance on a
convenient scale. Diagram 1 is delineated to a scale one-sixth of the
full size. Having calculated the shortest and longest radii for the
driven wheel mark them off on E, F, from the point E, and draw straight
lines through the marks from C to G and H. Or E, G, and E, H, may
be calculated from the formulæ R1 and RTI, to which they are
respectively equal. Divide G, H, into N parts (N being made = 4 in
the diagram for simplicity), and through G and H and the divisions,
draw lines G, K, H, L, &c., at right angles to the asymptote a. Also
draw straight lines from C to all the divisions on G, H, and mark on
the respective lines at right angles to a lengths from G, H, equal to the
distances from E on E, F, of the intersections of the respective oblique
lines from C. The points so marked will be in the hyperbola z, and the
lengths measured from H, G, will be those for the equidistant radii of
the driven wheel. The remainders of the lines are ordinates between
the curve and its asymptote x, and are the proper lengths for the radii
of the driving wheel at the points of its pitch line, which have in
succession to coincide or gear with the points already found for the
driven wheel. Whilst, however, the points found for the driven wheel
are separated by equal augles the corresponding points for the driving
wheel must necessarily be separated by unequal angles. The first and
smallest of these unequal angles for the driving wheel may be calculated
numerically by the following formula (the letters representing the same
quatities as before):-
R (2N-2)+R2(2 N - 1.) x180° first angle of driving wheel.
=
The angles for the driving wheel, shown in the Drawing, are as follows,
the numbered liues showing the angle each radius measures from the
starting point, whilst the intermediate lines are the separate angles

page_text: K, L, and from K and L, and the divisions draw at right angles to the
last drawn lines straight lines K, M, L, N, &c., when those lines will
cut M, N, so as to divide it in the required manner. On the other hand
if it is desired to find the lengths of equidistant radii for the driving
wheel the length M, N, may be divided into equal parts, and from the
divisions lines such as the dotted lines in the diagram may be drawn by
well-known geometrical methods so as to cut K, L, in points such that
lines drawn thence to P will be at right angles to them; then if through
these last points lines (such as the dotted ones) are drawn at right
angles to a, the portions of those lines between the curve z and the
asymptote will be the lengths required. Also the line K, L, will be
divided in the same proportion as a semicircle will be by the unequal
angles, which will then in the driven wheel correspond to the equal
angles of the driving wheel. The unequal angles for the driven wheel
(to correspond with equal angles for the driving wheel) may be obtained
by taking a four-sided figure, diagram 2, equal or similar to an axial
section of the conical part of the pirn or equivalent detail, upon which
the thread or yarn is to be wound, and by dividing its area by lines
parallel to the base into as many equal parts as there are angular spaces.
The division lines wi" cut the side line of the figure into unequal
portions, which are severally of the proportion to the whole side line that
the several angles should be to 180 degrees of the circle. The mode
already herein-before described by which the line K, L, diagram 1, is to
be divided in the required manner is simply an adaptation of a known
geometric process for dividing a figure, such as diagram 2, into a number
of spaces of equal areas. The same angles may also be got by other
geometrical methods, or by geometrically constructing the triangles
formed by the several pairs of radii and the portions of the circumference
joining their ends, which circumferential portions are equal to and
can be measured with sufficient accuracy from the corresponding
circumferential portions of the driven wheel.
It is not necessary in practice for the conical surfaces of the pirns or
other details on which the yarn or thread is wound to be precisely of the
proportion for which the improved wheels on the machine happen to
have been designed, but when there is a difference I prefer that the
wheels should be adapted for a smaller ratio than the actual one between
the extreme diameters of the cone,

page_text: The usual "heart" cam for working the traverse motion by which the
thread guide is moved so as to lead the yarn or thread successively upon
the different parts of the conical surface is to be fixed upon the driven
one of my improved wheels. The yarn or thread is laid or wound
approximately in the form of a continuous conical spiral, and the
formulæ and methods of designing herein-before given are based on
the assumption (taken for simplicity) that the length of such spiral is
equal to the sum of the circumferences of the mean circles of the several
convolutions. This assumption though not strictly correct differs from
mathematical accuracy to an extent which in the conditions of actual
practice is quite inappreciable, and which is the less the greater the
number of the convolutions of the yarn or thread between the two ends
of the conical surface.
Having thus particularly described my said Invention, and the manner
in which the same is to be performed, I have to state that what I believe
to be novel and original, and claim as the Invention secured to me by the
herein-before in part recited Letters Patent is, the applying of wheels
substantially such as are herein-before described in machinery for winding
yarn or thread upon conical surfaces.
In witness whereof, I, the said John Boyd, have hereunto set my
hand and seal, this Second day of June, in the year of our Lord
One thousand eight hundred and seventy.
Witness,
EDMUND HUNT,
Patent Agent,
Glasgow.
JOHN BUYD. (L.S.)