Apparatus for Drawing Spiral Curves.
Year: 1896

page_text: Date of Application, 24th July, 1896-Accepted, 21st Nov., 1896
COMPLETE SPECIFICATION.
Apparatus for Drawing Spiral Curves.
I, WILHELM KIELHORN, of Blüthenstrasse No. 3, Munich in the Kingdom of
Bavaria, German Empire, Sculptor, do hereby declare the nature of my
invention and in what manner the same is performed to be particularly described
and ascertained in and by the present statement:-
The present invention consists of an apparatus for drawing all kinds of spirals,
whether composed of a series of arcs of circles or of a series of elliptical ares, or
whether the coils are equidistant or arranged at increasing distances one from the
other.
The device consists of a cross piece as hereinafter specified, having slides which
are so arranged as to allow of the spiral being drawn either with a compass or with
a graduated bar in combination with a bifurcated scale or by means of the graduated
bar alone, without the assistance of the cross piece.
And in order to render the present specification more easily intelligible reference
is had to the accompanying drawing in which similar letters of reference denote
similar parts throughout the several views:-
Fig. 1 is a plan view of a device consisting of a number of small discs pivotally
connected to a common axis and confined between two slides which are shown in
side elevation in Figure 2.
Fig. 3 is a plan view of the cross piece,
Fig. 4 a cross section through one of its arms,
Fig. 5 shows side and end elevations and plan view of a slide for retaining one
leg of the compass,
Fig. 6 is a plan view showing the apparatus in operative position when describing
a spiral having the coils equidistant,
Fig. 7 is a similar view when describing a spiral having the coils at varying
distances apart,
Fig. 8 is a plan view of the cross piece used with an apparatus for describing
elliptical spirals,
Fig. 9 is a cross section through one of its arms,
Fig. 1 shows side and end elevations and plan view of a slide used in connection
with the cross piece as hereinafter more particularly described,
Fig. 11 shows similar views of a second slide,
Fig. 12 is a plan view of a graduated bar used in connection with this
apparatus,
Fig. 13 side and end elevations and plan of a slide for the said bar,
Fig. 14 perspective elevation and plan of a pen holder for the apparatus,
Fig. 15 plan of a U-shaped scale also employed in some cases,
Fig. 16 shows the apparatus in operative position when describing an elliptical
spiral of Archimedes,
Fig. 17 similar view of the apparatus when employed to describe a geometrical
spiral,
Fig. 18 is a plan of a graduated bar which may be employed in connection with
a compass for describing spirals,
and
Fig. 19 is an end elevation of Figure 18,
Fig. 20 shows the bar in operative position to describe a spiral of Archimedes
Fig. 21 similar view of the bar in position to describe a geo.netrical spiral.

page_text: Referring to Figures 1 to 7:-The apparatus consists of a cross bar a having
dovetail grooves arranged along its arms as at a and having ears with orifices at
the ends of its longer arms by means of which the said cross piece may be attached
to the sheet of paper on which it is desired to describe the spiral.
A spindle (Fig. 1) is provided at each end with a stop p mounted on the same
and having a foot to engage the groove a' of the cross piece as will be seen from
Figure 2. In the centre of the said spindle is arranged a fork piece having
arms adapted to close down at each side of one of the cross bars and retain the
longitudinal spindle o in position along the longer bar of the cross as shown at
Figure 6. Between the fork and each stop p are arranged a series of discs a
pivoted at one end to the spindle and normally covering the groove a² of the longer
bar of the cross piece as at Figure 6, but being capable of movement round the
spindle o so that they can be thrown over as at Figure 7 to leave the groove free.
A slide m is adapted to slide in the groove a¹ said slide having a dovetail foot to
fit the groove and a horizontal disc m' having orifices m 2 to receive one leg of a
compass.
The device operates in the following manner :-
The slide m is placed in the groove of the longer bar of the cross piece and slid
into the middle of the same as shown at Figure 6.
The spindle o is then placed along the long bar of the cross piece as shown at
the same figure, the fork r being turned over to engage at either side of the
transverse arm, and an equal number of discs being at each side of the slide. The
slide is now pushed against the end disc at one side, the leg of a compass inserted
in the central hole of the same and a semicircle described at one side of the
longitudinal bar of the cross. The slide is now pushed to the opposite end of the
space between the two series of discs and a semicircle described at the opposite side
of the centre line, said semicircle being a continuation of the first one from one end
of the same. One or more discs n are now thrown over to leave the travel for the
slide greater at the opposite end of the space and a further semicircle described,
then an equal number of discs at the other end are thrown over and the slide slid
up against this end and a semicircle again described, if it is required to form a
spiral of Archimedes but if on the other hand it is required to describe a
geometrical spiral one or more discs more should alternately be thrown over at
each end as shown at Figure 7 and the operation be carried out as above
described.
Referring to Figures 8 to 17: which illustrate a device for describing elliptical
spirals, the cross piece a has arms of equal length or thereabout and grooves al
as stated with regard to the cross of Figure 3 and means for securing the
said cross to the surface on which the spiral is to be described. This cross may,
as illustrated, be composed of a series of sections or may be of one piece. The
transverse grooves arranged at the under side of the cross serve as
guides for the U-shaped scale us hereinafter described. The slide b (Fig. 10)
having set screw is adapted to slide in the groove a'. The slide e (Fig. 11) is
also adapted to slide in the groove a' and provided with an upwardly projecting
guide pin c'. A slide e is arranged to slide on the graduated bar d which has a
cross section to fit the opening of said slide, whilst the slide has an orifice at its
under surface adapted to engage over the pin cl of the slide c. The pen or pencil
holder (Fig. 14) is pivoted to a socket at h which socket is provided with an
orifice through which the bar d passes so that the whole device is moveable on said
bar, the said pen as shown at g may be held in any desired position on its pivot by
means of a spring catch i, after the desired position has been adjusted. The
U-shaped scale k (Fig. 15) is provided along each leg with an upwardly projecting
rib said ribs fitting the guide slots 11 of the under side of the cross a.
The parts operate in the following manner :-
The cross is attached to the surface, on which the elliptical spiral is to be
described, by means of drawing pins or other suitable arrangement, and the slides a
and b are each arranged in one of the grooves a' of the cross a so as to run or slide

page_text: at right angles one to the other. The graduated bar d is then fitted to turn on the
slide by means of the screw on the latter which is passed through the hole d' at
the end of said bar, and the slide e of the bar d is fitted to the slide c by means of
the pin e' of the latter being inserted into the orifice or depression el of the former.
After adjusting the pen or pencil holder on the bar d elliptical figures of a great
variety of sizes and axial proportions may be produced in the well known manner.
If the bar d is not long enough, suitable extensions may be applied to the
same.
If it is desired to describe elliptical spirals having a substantially oval appearance,
the U-shaped scale k should be passed underneath the cross a with its ribs k' in the
guide grooves Il so that the zero point of the graduations or a graduation corre-
sponding to a desired curve lie underneath the point of intersection of the arms of
the cross, the rows of figures of the scale being to the right and left or above and
below the said point. The slide e is now adjusted to the desired point of the bar d,
and the pen or pencil adjusted to the desired graduation of the scale k and half an
ellipse described, as may be required to the right or the left of the row of
graduations. After this the cross is slid along the bifurcated scale-as will be
shown in connection with one or two examples hereafter-a few graduations above
or below the starting point, according to requirement, the marking device-pen or
pencil-is again adjusted so as to join and continue the end of the first curve and the
second semi-ellipse struck. The cross is then slid along the scale a few graduations
in the opposite direction to the other side of the zero point the marking device
again adjusted to continue the curve last struck and the next semi-ellipse, struck
and so on until the spiral required has been described. If the cross is moved an
unequal distance to each side of the zero point at each operation, a geometrical
elliptical spiral will be the result, but if moved an equal distance at each stroke of
the ellipse an elliptical spiral of Archimedes will be obtained. A geometrical
elliptical spiral may also be obtained by adjusting the slide e further along the rod d
at each stroke but in this case the curve will be gradually flattened.
Examples of curves of this description are shown at Figures 16 and 17. Figure 16
shows an elliptical spiral of Archimedes which is described by keeping the slides
on the trammel rod or bar d the same distance-say 8 graduations-apart, and by
moving the whole apparatus at equal intervals along the U-shaped scale, say
from 5 to 0 or rice versa.
Fig. 17 shows a geometrical curve which is produced as shown in the figure by
placing the slides of the bar d 3 graduations apart and the cross on the lower
6th graduation of the U-shaped scale for the first curve and for the second by
placing the slides four graduations apart and sliding the cross to the 4th upper
graduation of the U-scale and so on, as will be readily understood by reference to
the drawing.
In Figures 18 to 21 a graduated bars having a suitable pivot t is employed to
describe spirals of Archimedes and geometrical spirals with the aid of a compass.
In this case centre lines at right angles to each other or a series of lines all cutting
at one point and producing equal angles with each other-according to the
accuracy with which it is required to produce the spiral-are drawn and the
graduated bar is radially affixed by means of its pivot t to the centre point as
shown at Figure 20. A portion of a circle corresponding to one of the angles
formed is then struck from the desired graduation of the bar and the bar shifted to
the next position i.e. to the next radial line, the compass is then adjusted to continue
the part of the circle begun and this are is then continued to the next radial line
when the compass is again shifted after the bar has been removed to the next line
and so on until the desired spiral has been described.
In order to produce a geometrical spiral with the aid of the bars only, the same
operation is performed but the leg of the compass is shifted one or more graduations
at each alteration or progressive step of the bar instead of remaining at the same
point as with the Archimedean spiral.

page_text: Having now particularly described and ascertained the nature of my said
invention and in what manner the same is performed I declare that what I
claim is :-
1. A device for describing spirals, according to which the spirals described are
composed of semi-circles in the well known manner, the transit of one compass leg
from one circle centre to the other, as is necessary by this kind of drawing, by
means of a slide on which said leg is supported, the path of said slide being limited
by a series of pivoted discs, suspended on a spindle o and capable of being swung
out of said path substantially as described.
2. A device for describing spirals, according to which a U-shaped scale is
arranged underneath the cross of the apparatus for describing the ellipse, said
cross being adjusted on said scale after each part of the ellipse has been described
substantially as described.
3. Device for describing spirals consisting of a graduated bars having a pivot
pint and graduations for the reception of the leg of the compass as specified.
Dated this 24th day of July 1896.
BOULT & WADE,
Agents for the Applicant.