Hyperboloidal, and Ellipsoidal Surfaces.
Year: 1888

page_text: Hyperboloidal, and Ellipsoidal Surfaces.
I, SIGMUND SCHUCKERT, of Nürnberg, in the Empire of Germany, Dynamo-
Electric Machine Maker, do hereby declare the nature of this invention to be as
follows:-
This Invention relates to a machine for grinding, polishing, etc., surfaces of
curvilinear forms such as are generated by the revolution of the conic sections, that
is to say, spherical, paraboloidal, hyperboloidal, and ellipsoidal surfaces, whether these
surfaces be convex or concave.
The Invention consists in guiding the cutting, grinding, or other tool, first by
an arm at an angle to, and movable about, an axis, which arm would, by turning round
the axis, describe the surface of an imaginary cone; and secondly by a compound
slide rest whose guides are at right angles to one another and coincident or
parallel with the plane of the imaginary conic section whose outline the tool is
required to follow, the connection of the tool with these two guiding mechanisms being
made through the agency of a ball and socket joint. The work to be machined is
revolved upon an axis which is coincident with the axis of the imaginary conic section,
that is to say, at an angle to the axis of the cone depending on the surface to be
produced. To enable this to be varied, the axis of the above mentioned guide arm
is carried by a frame movable on a pivot which is perpendicular to the said axis, so
that the said axis may be adjusted at various angles relatively to the axis of rotation
of the work. The tool being constrained by the compound slide rest to move in the
plane of the conic section, and being also constrained to move with the guide arm
in its partial rotation about its axis, the tool will by the conjoint action of said guide
arm and of the compound slide rest, be so guided as to move around the side of the
cone and in the plane of the conic section and will so be caused to describe :-
a circle if the above mentioned angle is a right angle ;
a parabola if the axis of the cone makes the same angle with the axis of
revolution of the work as with the tool guide arm;

page_text: (c) a byperbola if the axis of the cone is parallel to the axis of revolution of
the work;
(d) an ellipse in all other cases.
These motions of the tool in conjunction with the rotary motion of the work will
result in the production respectively of spherical, paraboloidal, hyperboloidal, or
ellipsoidal surfaces.
S. SCHUCKERT.
By A. M. & Wm. Clark,
53, Chancery Lane, London,
Patent Agents.
Hyperboloidal, and Ellipsoidal Surfaces.
I, SIGMUND SCHUCKERT, of Nürnberg, in the Empire of Germany, Dynamo-
Electric Machine Maker, 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 relates to a machine for grinding, polishing, etc., surfaces of
curvilinear forms such as are generated by the revolution of the conic sections, that
is to say spherical, paraboloidal, byperboloidal, and ellipsoidal surfaces whether these
surfaces be convex or concave.
The Invention consists in guiding the cutting, grinding, or other tool first by an
arm at an angle to and movable about an axis which arm would, by turning round the
axis, describe the surface of an imaginary cone and secondly by a compound slide rest
whose guides are at right angles to one another and coincident or parallel with the
plane of the imaginary conic section whose outline the tool is required to follow,
the connection of the tool with these two guiding mechanisms being made through the
agency of a ball and socket joint. The work to be machined is revolved upon an axis
which is coincident, or in line, with the axis of the imaginary conic section, that is to
say at an angle to the axis of the cone depending on the surface to be produced. To
enable this angle to be varied, the axis of the above mentioned guide arm is carried
by a frame movable on a pivot which is perpendicular to the said axis so that the said
axis may be adjusted at various angles relatively to the axis of rotation of the work.
The tool, being constrained by the compound slide rest to move in the plane of the

page_text: conic section and being also constrained to move with the guide arm in its partial
rotation about its axis, will by the conjoint action of the said guide arm and of the
compound slide rest be so guided as to move around the side of the cone and in the
plane of the conic section and will so be caused to describe :-
:-
(a) a circle, if the above mentioned angle is a right angle ;
(b) a parabola, when the axis of the cone makes the same angle with the axis of
revolution of the work as with the tool guide arm :
(c) a hyperbola, if the axis of the cone is parallel to the axis of revolution of
the work;
(d) an ellipse, in all other cases;
These motions of the tool, in conjunction with the rotary motion of the work, will
result in the production respectively of spherical, paraboloidal, hyperboloidal, or
ellipsoidal surfaces.
Reference is to be had to the accompanying drawings forming part of this
specification, wheroin figure 1 is a diagram illustrating the principle of the invention.
Figures 2 and 3 shew part sectional elevations of practical forms of the apparatus for
producing convex and concave surfaces. Figures 4 and represent the ball and
socket joint on a large scale.
Referring to figure 1, A A is the axis of a right cone which may be inclined at any
angle to the horizon, the line L L being the generatrix by whose revolution about A
the conical surface is produced. Suppose this cone to be cut in a curve a bed by a
plane which is perpendicular to the plane (for example E E E E³) that passes through
the axis A of the cone and through the vertical line D which cuts the axis of the
cone. Suppose the figure of the surface to be produced to be that generated by the
rotation of the curve a b c d about the axis D. This curve will be described by a
point, such as c for example, being constrained to move both in the surface of the cone
and in the plane which cuts the cone.
Referring now to figures 2, 3, 4, 5, L is the guide rod which if it were rotated
about the axis A A would describe an imaginary cone. This rod receives an oscillating
motion about the axis and its free end passes through the ball K fitted in a ball and
socket joint on the tool carrier V. The latter is fitted to work up and down in a
guide in a slide rest or carrier F fitted to work along a horizontal guide H attached
to the standard G G. V is therefore constrained to move in a vertical plane but being
connected by means of the spherical joint with the guide rod L L, which moves in the
surface of an imaginary cone, the joint (on the tool carrier receiving motion in the
guides Hand F) will describe a curve lying both in the imaginary cone and in a vertical
plane cutting this imaginary cone this curve is therefore the figure of a conic section.
If now the surface to be machined be rotated about D D, it will be worked by the
cutting or grinding tool to the surface of revolution of the conic section a bed
(figure 1) assuming that the axis D D lies in that plane in which the cutting points
of the tool are moved. According to the inclination of the axis A A of the cone to
the axis of rotation, the tool will describe the curve of:
a circle when the axis A A is perpendicular to D D.
:-
a parabola when the axis A A makes the same angle with DD as with the guide
rod L. L.
a hyperbola when the axis A A is parallel to D D.
an ellipse in all other cases.
In these cases then, the tool will produce the surface of a sphere, a paraboloid, a
hyperboloid, or an ellipsoid respectively.
The arrangement of the various parts of the machine above described may be
modified in various ways (for instance, the axis of rotation D D of the surface to
be machined may be horizontal instead of vertical) and the constructional details of
the machine may be varied. The employment of the apparatus above described for
producing a concave surface is shewn in figure 3, which will be readily understood
without further description, as the same letters refer to similar parts.
The construction of the above mentioned ball and socket joint is more particularly
shown in figures 4 and 5. Unlike figures 2 and 3, the guide rod L L in these two

page_text: figures is supposed to be in a horizontal position to which it may be brought by
suitably inclining the axis A. A. This guide rod slides through the diametrical hole
in the ball K. The tool carrier V fitted to slide up and down in the saddle F,
is formed with the socket Z Z and gland W both turned spherical internally to fit the
ball K, the two parts being connected by screws R so that ball K will turn in the
socket with a moderate amount of friction. Below the socket is an extension F upon
which is mounted a bracket T having a socket wherein the stem of the tool $ is
fitted.
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. The herein described apparatus for producing grinding or polishing spherical,
paraboloidal, hyperboloidal, and ellipsoidal surfaces, the apparatus consisting essentially
in the means whereby the tool is caused to follow the outline of the conic section
corresponding to the surface of revolution to be produced, said means consisting
in :-
(a) a guide rod which is movable about an axis and in so moving generates or
describes part of the surface of an imaginary cone and (b) a compound slide rest by
which the tool holder is guided in two rectilinear directions at right angles to each
other and in, or parallel to, the plane of the said conic section, as specified.
2. The combination, with the guide rod movable about an axis so as to describe
part of the surface of an imaginary cone as specified and with the tool holder mounted
in a compound slide rest permitting rectilinear motion of the tool in two directions at
right angles to each other as described, of the ball and socket joint connecting the
guide rod to the tool holder the ball being free to slide on the rod and to turn in its
socket, as specified.