Improved Harmonic Apparatus for the Drawing, Cutting, or Marking of Mathematical Figures.
Year: 1894

page_text: COMPLETE SPECIFICATION.
Improved Harmonic Apparatus for the Drawing, Cutting, or
Marking of Mathematical Figures.
I, HENRY HARRER of Allegheny, County of Allegheny and State of
Pennsylvania, United States of America, being by occupation a Gentleman, do
hereby declare the nature of this invention, and in what manner the same is to
be performed, to be particularly described and ascertained in and by the following
statement:-
This invention has relation to simple harmonic machines and is particularly
adapted and designed to produce an almost limitless number of mechanical
motions.
This invention has for its object the provision of novel means for producing
a mechanism for drawing, carving, marking or producing mechanical motion along
circles of any desired diameter, ellipses of any major or minor axis, lines at any
angle to a fixed right line, within the limits of 0°, an 180°, parabolas, and many
other curves whose equations may be readily calculated; furthermore, for
converting the motion of a point or pin moving in the path of the above mentioned
curves into two circular motions; furthermore, in combination with a uniform
motion along a right line to draw a cycloid and an in lefinite number of other
mathematical curves; furthermore, to produce an innumerable number of designs
consisting of curves and lines of different degrees and angles.
With these objects in view, the invention consists in the novel construction,
combination and arrangement of parts, more particularly hereafter described and
specifically pointed out in the claims.
Referring to the accompanying drawings which form part of this Specification
and wherein like letters of reference indicate corresponding parts in the several
views,
Fig. 1, is a plan view of my machine,
Fig. 2, is a bottom view of the same and
Fig. 3, is a side view, taken on the line x, x, of Fig. 1.
In these drawings, M, represents the base plate supported on four standards F, F,
F, F; on the upper side of said plate are arranged the cranks C C¹, carrying the
slides D, and D', along which the pins P and P₁, may be adjusted. The said
cranks C, and C', are fixed to the same shaft with the gear wheels W' and W,
respectively. A third gear wheel W', carried in a bearing adjustable along the
semi-circular slot B, in order that it will gear with the wheels W, and W', whatever
be the diameter of the former, may be revolved by the crank H. Two arms A,
aud A', bearing on one end the transverse slotted heads S, and S', (which are
respectively perpendicular to A, and A',) are reciprocated by means of the rotation
of the pins P and P', which are free to move from right to left in the transverse
slotted heads S, and S. The slots E, and E', are of such length and proportion
and so arranged that at every possible position of the arms A, and A', the slot E,
will be over some portion of the slot E. The arms A, and A', are guided
in slides V', and V, respectively, said slides being so arranged that they may be
adjusted in the slots N₁, and N, so that the motion of the arms A, and A', will
always be along the radii of circles whose centers are the centers of motion of the
cranks C and C¹. The arms A, and A', may be placed at different angles to each
other as will be obvious.
About the center of motion of C, and C', degree scales are marked, also on the
sides of the slots N, and N¹. The slides D and D', likewise carry lineal scales.

page_text: At the intersection of the slots E, and E', a suitable bearing K, is provided,
through which a pencil, marker, cutter or crank pin L may be placed.
Operation:-When it is desired to give a certain movement to L, I set the arms
at the required angle, then place a wheel of the required diameter at W, W., and
adjust W, accordingly; the cranks C, and C', are next set at the proper angles and
lastly the crank pins P, and P1, are adjusted.
To draw a circle for example, let the diameters of W, and Ws, be the same,
adjust the arms A, and A', at 90°, each and adjust the pins P, and P1, at equal
distances (a), place the crank C, at 90°, and C₁, at 180°. On rotating H, a circle
of a diameter 2a, will be described by L. To prove this, let the center of
co-ordinates be at the center of figure; let the horizontal axis be the axis of . and
the vertical, that of y; let 0 equal the angular velocity, and t, the time; and let
a=rading

page_text: If it is desired to carve, a cutter is inserted at L, and the suitable mechanism
attached.
The above calculations are illustrative of the great variety of curves that may
be produced by this mechanism.
If a set of rolls operated by a set of gear wheels, one of which gears with W³,
cause the paper to move across the board parallel with the arm A, when the
crank H, is set in motion another set of curves will be produced which will differ
from those just considered.
If the machine is set to describe a circle and the velocity with which the paper
moves be equal to that of the crank pins P and P1, and is uniform, a cycloid will
be described. It becomes evident therefore that the variety of curves that may be
described by means of this mechanism are practically limitless.
For the purpose of more clearly illustrating the practical application of my
invention, I wish to call particular attention to the fact, that instead of causing a
piece of paper to move laterally under the mechanism, by proper arrangement
may cause a board to move so, and have a rotating cutter head guided by the
mechanism in K. All kinds of ornamented curves may thus be carved out on its
surface. When the lateral motion is stopped while the mechanism continues to be
operated, another set of curves is carved by the cutter.
If it be desired to transform the motion of a pin along an ellipse, into a circular
motion, or that of a pin vibrating in a parabola or right line at any angle, into
circular motion, such motion may be converted by causing the pin to act on L, and
adjusting the mechanism as heretofore described.
The arrangement of the slotted arms E and E', which are set at right angles to A,
and A', may be changed to suit the particular demands of the mechanism. Thus
where greater strength is required as in guiding a cutter head, the slots E, and E',
should be arranged perpendicular to A and A', and so arranged that the center of
the said slots E, and E', are in the axial lines of A, and A', as in the case of the
transverse slotted heads S, and S', and the said arms A, and A', should be of such
lengths that when the slots of heads S, and S', are directly over the center of
motion C, and C', at the same time the centers of slots E, and E', will be directly
over each other.
Instead of the wheel W', to drive W, and W2, two shafts at right angles to each
other and carrying mitre gear wheels meshing with each other, may be employed to
connect with the primary source of power; furthermore, instead of the transverse
slotted heads S, and S¹, connecting rods might be used, but inasmuch as these
would have to be adjusted in length for each change of position of P, and P', or
otherwise shift the center of figures, I find it preferable to employ the arrangement
as illustrated in the drawings.
It will be obvious in view of the above, that various changes may be made in the
detail construction of my machine without departing from the general idea
involved; also that the mechanism may be employed with great advantage to an
innumerable number of machines.
Having now particularly described and ascertained the nature of my said inven-
tion, and in what manner the same is to be performed, I declare that what I
claim is:
1. In a machine for combining simple harmonic motions to act together on a
point, a base plate M, supported by standards F, F, F, F, the arms A, and A',
having slots, cranks C and C', carrying slides D, and D', pins P, and P¹, the gear
wheels W, W', and W', the crank H, attached to the shaft and carrying the
wheel W, the transverse slotted heads S, and S', and the marker L, substantially
as described.
2. In a simple harmonic machine, the combination of the base plate M, having
arranged thereon cranks C, and C¹, carrying the slides D, and D', the pins P,
and P, the wheels W, and W, fixed to the same shaft as the said cranks C, and C',
semi-circular slot B, the wheel W₁, the crank H, the arms A, and A', carrying on

page_text: their one end the transverse slotted heads S, and S', and the other extremity the
slots E, and E', the slides V, and V, the slots N, and N', substantially as
described.
3. In a simple harmonic machine, the combination of the arms A, and A',
operating in conjunction with each other and arranged at right angles, greater than
right angles or less than right angles to each other, the base plate and a train of
gear wheels, the slides and slots, substantially as described.
4. In a simple harmonic machine, consisting of a base plate M, mounted on
suitable supports, and having arranged thereon arms A, and A', carrying on their
free ends the transverse slotted heads S, and S₁, and at their other extremity the
slots E, and E', the slides V, and V, moving in slots N, and N', a series of gear
wheels and suitable means for operating the same, the cranks C, and C₁, the
slides D, and D', and the pins P, and P¹, substantially as described and for
the purpose set forth.
5. In a simple harmonic machine, the combination of the base plate M, having
arranged thereon arms A, and A', carrying on their free ends the transverse slotted
heads S, and S', and at their other extremity the slots E, and E', and marker L,
the cranks C, and C¹, carrying the slides D, and D', and the pins P, and P,
a series of wheels W, W', and W', the crank H, the slides V, and V', adjustable
in the slots N, and N', the semi-circular slot B, the bearing K, carrying the
marker L, all parts being arranged substantially as described and for the purpose
set forth.
6. In a simple harmonic machine, the combination of the arms A, and A',
operating in conjunction with each other and arranged at right angles, greater than
right angles or less than right angles to each other, the base plate and a train of
gear wheels, the cranks and slides with suitable means for operating the same,
substantially as described.
7. In a simple harmonic machine, the combination of the base M, mounted on
suitable supports, arms A, and A', arranged on said plate forming at their free ends
the transverse slotted heads S, and S₁, and at their other extremity the slots E,
and E, and the bearing K, and marker L; the cranks C, and C, carrying the
slides D, and D', having scales, the pins P, and P', a train of gear wheels, the
crank H, the slides V, and V₁, the slots N, and N', having scales and the semi-
circular slot B, substantially as described.
8. In a simple harmonic machine, the combination of the base M, mounted on
suitable supports, arms A, and A', arranged on said plates, forming at their free
ends the transverse slotted heads S, and S', and carrying at their other extremity
the slots E, and E', the bearing K, and marker L, the cranks C, and C¹, carrying
the slides D, and D', the pins P, and P¹, the wheels W, W', and W³, the
crank H, the slides V, and V₁, the slots N, and N', and the semi-circular slot B, as
set forth.
Dated the First day of January 1894
HENRY HARRER,
By W. Fairburn-Hart,
Agent.