the Formation of Parabolic Surfaces.
Year: 1885

page_text: [Communicated from abroad by Messrs. Wirth & Co., of Frankfort-on-the-Main,
in the Empire of Germany, acting as Agents of Georg Munker, Professor,
and Siegmund Schuckert, Manufacturer, both of Nürnberg, in the Empire
of Germany.]
the Formation of Parabolic Surfaces.
I, HENRY HARRIS LAKE, of the firm of Haseltine, Lake, & Co., Patent Agents,
Southampton Buildings, in the County of Middlesex do hereby declare the nature
of my invention for "IMPROVEMENTS IN TURNING AND GRINDING APPARATUS FOR
USE IN THE FORMATION OF PARABOLIC SURFACES" to be as follows:-
This invention relates to apparatus for grinding and turning parabolic surfaces.
The construction of this apparatus is based upon the following facts.
Referring to the drawing, suppose to be any point in a parabola, x y the axis
of the latter, o its focus, y y¹ a line perpendicular to the axis and x¹ y'a line parallel
to the latter, then o x + x y = 0x¹ + x² y¹. If therefore a cord of the length
ox+xy is fixed with one end at o, and its other end is moved upon the straight
line y y¹, the cord being stretched by a point so that the part x'y' of the cord
always remains parallel to the axis a y, the said point describes a parabola having
the focal distance o x.
If the cord is fixed to the circumference of a fixed disc 8, whose axis passes
through the focus o and the cord is stretched by a movable disc 8¹ of equal size
under the conditions above stated, while the other end moves upon the straight
line y y¹, the centre of the movable disc describes the same parabola as that before
mentioned; the cord must however be longer by half the circumference of the disc.
The said apparatus comprises a vertical spindle which carries a flanged disc upon
which the piece of material to be ground can be turned or fastened with either its
convex or its concave face uppermost. Above the said disc is supported a horizontal
guide bar upon which a slide-rest is adapted to be moved to and fro by means of a
screw. The said slide rest has a groove, in which a slide block moves vertically.
At the lower end of this slide-block are arranged either turning tools or grinding
devices.
The means for guiding the said sliding-block and the tools thereon in a parabolic
curve are as follows:-
In the middle of the length of the horizontal bar is fixed a disc. A rotary disc
of equal size and arranged in the same plane as the said fixed disc is mounted upon
the said slide-block. To a small cylinder in proximity to the feed disc is fixed one
end of a steel band which passes over the said fixed and movable discs and is
fastened at the other end to the slide-block.
Upon the said slide-block is fixed a fork carrying two discs or pulleys capable of
being turned upon the common axis to which they are firmly connected.

page_text: One pulley is circular and has passing over it a band attached at one end to the
slide-block and tools, and at the other end to a counterweight. The other disc is
cam shaped and has suspended from it a weight which keeps the steel band of the
slide block at equal tension at every position."
Now if the slide rest is moved towards the centre of the horizontal bar the slide
block gradually rises as the distance between the ends of the steel band is
diminished, so that the centre of the disc on the slide block, is caused to move in
a parabolic curve by means of the counterweight together with the tools connected
with the said slide block.
If the apparatus is to be used for grinding the grinding device hereinafter
described is used. Independent apparatus termed a bow serves to apply grinding
devices which can be adjusted and used for the preliminary grinding.
In order to operate upon a concave surface the movable disc is arranged lower
down upon the sliding block, the steel band is passed below the said fixed and
movable discs and the cam-shaped pulley with its tension weight placed inversely
upon its axis.
In this case the bow used for the preliminary grinding and the grinding devices
must be curved in a reverse direction to those before described. The said grinding
devices turn in use in two directions upon a ball-joint, the centre of which must be
as near as possible to the working surface.
This ball joint is arranged as follows, that is to say: At the lower end of the
slide block is fixed a disc which has a lateral projection. Through a hole in the
latter passes a spindle to which is screwed a spherical segment. Upon this segment
is a segment of a hollow sphere; to the edge of which is fastened the grinding
device. The said two spherical segments are held in contact with one another by
springs and thus the grinding device can move in every direction and also turn with
the said spindle. The centre of this ball-joint lies perpendicularly below the centre
of the movable disc upon the slide-block in proximity to the surface to be operated
upon. The grinding device must therefore, when it is worn a little be replaced by
another of suitable thickness.
In order to relieve the apparatus as much as possible, the preliminary work is
performed not only by the grinding devices on the said bow but also in the
following manner, that is to say:-The steel band, the movable disc on the slide
block and the cylinder to which the band is attached are removed. A guide bar
having a parabolic curve which by the aid of the present apparatus can be accurately
obtained is fixed adjacent to the traversing screw to the supports of the horizontal
guide bar. At the lower end of the slide bar is arranged, instead of the grinding
device before described, a grinding roll in perpendicular line below the movable roll
upon the slide block and of diameter equal to that of the latter roll.
The slide-block must not in this case be quite equilibrated so that it presses by
reason of its weight, the grinding-roll upon the surface to be operated upon. The
grinding-roll may be set in rotation by any driving mechanism. The movable roll
of the slide block serves as a guide along the parabolic guide bar. If the slide rest
is moved horizontally while the grinding-roll rotates, the latter grinds a surface, the
curve of which is similar to the curve of the parabolic guide-bar.
The guiding-roll is provided with a device for adjusting it, and when it is much
worn it must be replaced by a new one.
Instead of using the movable roll, the guiding may be effected by means of a
small lug attached to the slide-block in which case the above described grinding
device with its ball-joint must be employed.
Noted thin and dow of October 1885
HASELTINE, LAKE & Co.,
For the Applicant.

page_text: Upon the said slide rest is fixed a bracket 10 carrying two discs or pulleys 11 12
capable of being turned upon their common axis to which they are firmly
connected.
The pulley 11 is circular and has passing over it a band attached at one end to
the sliding block 5 and at the other end to a counterweight 13. The other
pulley 12 is cam shaped or of a helicoidal section; at right angles, to its axis, and
has suspended from it, by means of a band, a weight 14.
This pulley 12, with its counter weight 14, serves to keep the steel band 6* of
the slide block at equal tension at every position of the latter.
Now if the slide rest 4 is moved from the position shown in the drawing
towards the centre of the bar 3 the sliding block 5 and the parts connected there-
with rise by reason of the counter weights as the distance between the ends of the
steel band is diminished, so that the centre of the disc 7 on the slide block, is
caused to move in a parabolic curve together with the tools connected with the
said slide block.
If the apparatus is to be used for grinding, the grinding device Figures 5 and 6
hereinafter described is used.
In order to operate upon a concave surface the disc 7 is arranged lower down
upon the sliding block than previously described and the steel band 6* is passed
below the discs 6 and 7. The pulley 12 also with its tension weight 14 is placed
inversely upon its axis.
In this case the grinding devices on the slide block 5 must be curved in a reverse
direction to that before described.
The grinding devices turn, in use, in two directions upon a ball-joint, the centre
of which must be as near as possible to the working surface. This ball joint
shown in figures 5 and 6 is arranged as follows that is to say:-At the lower end
of the sliding block 5 is fixed a disc 16 which has a lateral projection. Through a
hole in the latter passes a spindle 17 to which is screwed a spherical segment 18.
Upon this segment is a segment 19 of a hollow sphere to a flange on the edge of
which is fastened the grinding device 20. The said two spherical segments are
held in contact with one another by the springs 21, and thus the grinding device
can move in every direction and also turn with the said spindle 17. The centre
of this ball-joint lies perpendicularly below the centre of the disc 7, upon the
surface to be operated upon. The grinding-device must therefore, when it is worn
a little, be replaced by another of suitable thickness.
In order to relieve the apparatus as much as possible, the preliminary work is
performed by the following means that is to say:- -The steel band, the disc 6 and
the pin 8 are removed. A guide bar 22 having a parabolic curve, (which by the
aid of the present apparatus can be accurately obtained) is fixed in axial alignment
with the spindle 1 to both supports of the horizontal slide bar 3. At the lower
end of the sliding-block 5 is arranged, instead of the grinding device before
described a grinding-roll 23 in perpendicular line below the roll 7, and of a diameter
equal to that of the latter roll.
The sliding-block 5 must not in this case be quite equilibrated, in order that it
may by reason of its weight press the grinding roll 23 upon the surface to be
operated upon,
The grinding-roll 23 may be set in rotation by any suitable driving mechanism.
The roll 7 serves as a guide along the parabolic guide bar 22.
If the slide rest 4 is moved horizontally while the grinding-roll 23 rotates, the
latter grinds, apart from its wear, a surface, the curve of which is similar to the
curve of the parabolic guide-bar 23.
The grinding roll is provided with a device for adjusting it, and when it is much
worn it must be replaced by a new one.
Instead of using the roll 7, the guiding may be effected by means of a small
lug 24 attached to the slide block 5 and bearing against the under side of the
bar 22. In this case the above described grinding device with its ball-joint must
be employed.

page_text: Having now particularly described and ascertained the nature of the said
invention and in what manner the same is to be performed as communicated to
me by my foreign correspondent I declare that what I claim is:-
First. Apparatus for grinding or turning parabolic surfaces, consisting of the
sliding block 5 which can be moved vertically in the slide-rest 4 on the slide-bar 3,
in combination with a band which is fixed at one end to the fixed disc 6 the axis
of which intersects the axis of the spindle 1, and at the other end to the slide rest 4,
which band is always held in tension, through the medium of a roll 7 of the same
diameter as the disc 6 and arranged on the tool-holder, by the weight 14 acting
upon the tool-holder.
Second. Apparatus for the preliminary grinding of parabolic surfaces, compressing
the parabolic guide-bar 22 which guides the tool-holder 5, the said tool-holder
being vertically movable on the slide-rest and having the roller 7 or lug 24 adapted
to bear against the said guide bar and being provided at its lower end with the
grinding-roll 23 of the same size as the roll 7, or with the grinding device shewn
in Figures 5 and 6 of the drawing.
Third. The grinding-tool for use in combination with the apparatus hereinbefore
described, and consisting of a spindle 17 turning upon its axis and having the
spherical segment 18, upon which the segment of a hollow sphere can move in any
direction, the segment 19 carrying the grinding device 20, the centre of this ball-
joint being always in a perpendicular line below the middle of the disc 7 and
simultaneously upon the surface to be ground.