Curves of the Conic Sections.
Year: 1889

page_text: Curves of the Conic Sections.
I, SIGMUND SCHUCKERT, of Nürnberg, in the Empire of Germany, Manufacturer, do
hereby declare the nature of this invention and in what manner the same is to be
perfomed, to be particularly described and ascertained in and by the following
statement:
This Invention relates to apparatus for producing, grinding, or polishing curvilinear
forms or surfaces such as are generated by the revolution of certain conic sections, vizt.
spherical, paraboloidal, hyperboloidal, and ellipsoidal forms or surfaces whether convex
or concave.
The essential feature of this class of machine is that the cutting, grinding, or other
tool is guided in a twofold manner vizt. in the side of an imaginary cone and in a plane
cutting the side of the cone whereby it is constrained to follow the curve of the conic
section by whose revolution the form to be produced is generated.
Such is the kind of machine described in my previous application for Letters Patent
dated May 29th 1888 No. 7836, and the present invention relates to improvements in
the construction and operation of such machines.
Reference is to be had to the accompanying drawings forming part of this specifica-
tion, in which figure 1 is a diagram illustrating the principle of operation, and figures 2
and 3 are respectively front and side elevations, partly in section, of the improved
machine.
Referring to figure 1, which illustrates the principle of the machine forming the
subject of my former application and of the present invention, A A is the axis of a right
cone and may have any desired inclination to the horizon and L L is the generatrix
This cone is cut on
which by its revolution about A describes the side of the cone.
the curved line a b c d e by a plane which is perpendicular to a plane (E E' E' E³ for
example) cutting the axis A and the vertical line D D which intersects the axis of the
cone.
Let the surface to be produced be that generated by the rotation of the conic
section a b c d e about the vertical line D D as an axis. It will be obvious that the
curve a b c d e will be described by the point c, if that point be constrained to move
both in the side of the cone and in the plane of the said conic section.

page_text: In the improved machine of this invention, as in that before described, there is a
guide rod L L which is at an angle to, and movable about, an axis A A so as to
describe part of the surface of an imaginary cone, this guide arm L being connected to
the tool-holder by a universal joint permitting of the angular motion of the guide rod
with regard to the tool holder and also the sliding motion of the tool-holder along the
rod consequent on the tool holder being constrained to move in one plane only. In
this improved machine, the universal joint is of the gimbal, instead of the ball and
socket, type. It comprises two rings 18, 19, through the former of which the guide
rod L passes with freedom to slide, said ring being pivoted by trunnions 20, 21, in the
outer ring 19 which is pivoted by trunnions 22, 23, at right angles to 20, 21, in the
sides of a frame 14, 15, 16, 17, which is itself free to slide up and down on a pair of
vertical guide pins 12, 13.
a
In lieu of the ordinary compound slide rest described in the said former application
whereby the tool holder is constrained to move in one plane, the machine comprises a
combined means of guiding the tool holder and of imparting the angular motion to the
guide arm. This means of guiding and operating comprises a parallel motion frame
formed by a pair of equal radius links 5, 6, pivoted at 1, 2, to the main frame G and a
transverse member 7 pivoted at 3, 4, to the ends of, and connecting, said radius
links 5, 6, so that said transverse member 7 will be movable in its own vertical plane,
the joints 1, 2, being of sufficient length to prevent it moving out of that plane so that
its successive positions are parallel to one another and its motion is similar to that of
one of the members of a parallel ruler. To this transverse member are fixed the pair of
guide pins 12, 13, lying in the said plane of motion and upon which is free to slide the
frame 14, 15, 16, 17, above referred to. This parallel motion frame 5, 6, 7, receives
motion in its own plane from a leading screw 11, mounted in the crosshead 40 of the
main frame and working through a nut 10 whereby a saddle piece 9 is traversed across
the main frame, this saddle piece 9 being fitted to slide in a straight guide in the cross
head 40 of the main frame G, the screw 11 and guide for the saddle piece 9 being
horizontal and parallel to the transverse member 7 of the parallel motion frame. This
saddle is connected with the parallel motion frame by a pin and roller 8 working in a
vertical slot in the face of the saddle piece 9 so as to allow of the difference of motion
of the rectilinear moving saddle 9 and of the curvilinear moving point of connection
with the transverse member 7 of the parallel motion frame. Thus the links 5, 6, are moved
about their centres, and the parts 5, 6, 7, 12, 13, are all moved in one plane by the
revolution of the leading screw 11, and the frame 14, 15, 16, 17, is also movable in the
same plane and being free to slide on the pins 12, 13, it can take up any desired position
within a limited plane.
The axis AA of oscillation of the guide arm 1. is mounted in a bracket 27 adjustable
about an axis 28 at right angles to the axis A A and is fixed in the
desired position by a set screw 29 passing through a slot 32 in the
bracket. By this adjustment, the axis A A of the imaginary cone can be set at
different inclinations to the axis of revolution of the work and thus a paraboloid or an
ellipsoid can be produced, as may be required. The axis of adjustment 28 of this
bracket 27 is carried by an car 30 on a slide 31 movable on a guide 33 on the main
frame in a direction towards or away from the axis of revolution of the work in order
to vary the dimensions of the imaginary cone and consequently the size of the conic
section whose outline the tool is to be caused to follow.
The guide rod L is firmly attached to the axis A by the bracket 34 and bolts 35, 36,
37, 38, and 39. But the guide arm L, instead of being rigidly connected to its axis A,
may work on a joint at the apex of the cone and may be guided in its oscillation by
being caused to bear against the periphery of a fixed segment of a circle perpendicular
to the axis of the cone. In any case, every part of the frame 14, 15, 16, 17, is con-
strained to move in the curve of a conic section, and this frame may therefore be used.
as the holder for the tool (which may be a cutting or turning tool or a grinding ring
or disc) with which the desired surface of revolution is to be produced.
Instead of guiding the tool by an arm moving about the axis and in the side of an
imaginary cone, as above described, a material cone may be used as a pattern, as

page_text: illustrated diagrammatically in figures 4 and 5, in front and side view. The parallel
motion guiding frame is the same as before, but upon the side of the pattern cone bears
a feeler roiler 25 carried by an arm 24 affixed to the tool carrier frame 14, 15, 16, 17,
whereby the tool 26 will be caused to describe the curved outline of the conic section
in the plane of which the feeler roller moves, the pattern cone being fixed adjustably to
the main frame to enable the conic section to be varied as required. These two curves
are coincident when the roller 25 and the tool 26 are situated in one and the same plane
parallel to the plane of motion of the frame 5, 6, 7, and they are similar when the tool 26
and roller 25 are situated in two distinct parallel planes.
In conclusion, I may remark that the ball and socket form of universal joint,
described in my former specification, may be used with the parallel motion frame 5, 6, 7,
and the gimbal form of universal joint herein described and shewn in figures 2, 3, as
also the pattern cone and feeler herein described and shewn in figures 5, 6, may be used
with the compound slide described in the aforesaid previous specification. These various
combinations of the parts described in this, and my former, application require no special
description.
Having now particularly described and ascertained the nature of the 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 producing or machining the curvilinear surfaces herein specified,
the combination with the guide rod L (mounted to oscillate about the axis of, and in or
describe the side of, an imaginary cone) of a universal joint free to slide on the guide
rod as herein described and of the parallel motion frame composed of radius links 5, 6,
transverse member 7, and guide pins 12, 13, and of the tool holder frame 14, 15, 16, 17,
fitted to slide on said pins, the whole arranged to operate substantially as specified.
2. In the herein described machine, the combination with the parallel motion frame
and its adjuncts of the leading screw and saddle piece or carrier connected to, and
actuating the said frame, as and for the purpose specified.
3. In the machine as herein described with reference to figures 4 and 5, the com-
bination with the said parallel motion frame and the tool carrier of the pattern cone and
feeler roller whereby the tool carrier is guided in the curve of the conic section, as
specified.
4. In the machines herein described the substitution for parts herein described of the
equivalent parts of the machine described in my aforesaid specification.
.
101
1
1000
S. SCHUCKERT.
By A. M. & Wm. Clark,
53 Chancery Lane, London,
Patent Agents.