Improvements in or relating to the Mechanism used in Grinding Machines for Producing Parabolic Conoidal Surfaces.
Year: 1892

page_text: Date of Application, 19th Oct., 1892
Complete Specification Left, 19th July, 1893-Accepted, 14th Oct., 1893
PROVISIONAL SPECIFICATION.
[Communicated from abroad by Messrs. SCHUCKERT & Co., Nürnberg,
Germany, Engineers.]
Improvements in or relating to the Mechanism used in Grinding
Machines for Producing Parabolic Conoidal Surfaces.
I, JOSEPH SINCLAIR FAIRFAX, of 433 Strand, in the County of London,
Patent Agent and Consulting Engineer, do hereby declare the nature of this
invention to be as follows:-
In order to produce parabolic conoidal surfaces, or surfaces generated by the
revolution of a parabola, it is necessary that the grinding tool shall slowly pass
along the path of a parabola, while the material to be acted upon is rapidly rotated
upon its own axis.
The geometric principle upon which the present invention is based, is stated by
my foreign correspondents to be the following; reference being had to the
accompanying drawings.
When two straight lines a and b (Fig. 1) respectively turn upon points A and B
in such a way that their angular velocities are in proportion to each other
as 1 is to 2, and further, a system of any number of parallel lines d' d² d³ d' d³ and do
are projected through the lines a, a, a², a³, a, a, a, upon their intersecting points
with a fixed line cc, then the cutting points of this system with the corresponding
lines b, b, 3, 3, 4, 6, and 66 produce a parabola E' E E³ E' E' and E.
Both the turning lines a and b are hereinafter termed connecting rods a and b
respectively.
As the focus of the parabolic surface or shell to be ground must be known, the
following suppositions are made for the geometric construction which determines
the position of the focus and the directrix, namely; first, that the third line c-c
(see Fig. 8) is perpendicular to the connecting line of both turning points; and
secondly, that at the beginning of the movement both connecting rods and the
connecting line just mentioned cover each other.
In Figs. 2, 3, 4, 5, 6, 7, and 13, are shown the kinematic systems which in
Figs. 9, 10 and 11 respectively indicate the resulting forms. A uniform indication
by letters is used throughout; therefore, as in Fig. 1 so in Fig. 2, the letters A
and B are the turning points of the connecting rods a and b, (shown as forked),
D corresponds to the parallel system in Fig. 1, which-as in Fig. 2-is understood
to be a cross piece moving on a straight bed or rail, parallel to itself. In order to
obtain the proportion of the angular velocities, as determined before, a pin F is
fixed in the connecting rod 6 so that it describes a circle while the forked
connecting rod a slides under this pin. As under these conditions the one connecting
rod moves upon an angle drawn from the centre of the same circle, then the
proportion of the angular velocities must be as 1 is to 2; and consequently they
describe a parabola.
Fig. 3 shows how the proportions of the angular velocities are obtained in another
way, and directly, wherein both connecting rods a and b turn upon the same point
and are fixed to independent pulleys, one of which has twice the diameter of the
other while an equal length of cord runs over them.
A modification of the latter mechanism is shown in Fig. 4. The connecting rod b
is removed and replaced by a moving element of equal value. Below the upper
straight line cc is arranged a second one c¹, c', parallel thereto, and equidistant

page_text: between the same and the central point A. A guiding cross bar is moveable on the
line c', c, and also along the line of the connecting rod a. It will be seen how this
change is carried back to the first when it is considered that the right angle
triangles DFE and EFA are congruent, (as D F is equal to F A, and E F is
equal to itself) consequently angle ay, but (as alternate angles are equal) also
equal to that is the connecting rod a has to move twice the angle
a.
This parabolic guide in Fig. 4 may also be directly produced exactly as the
former, if (as shown in Fig. 5) the continuation of the connecting rod a is removed,
and the straight movement of D and F brought about by means of two screw
spindles of equal pitch, one making twice the revolutions of the other, or having
equal revolutions and of double the pitch; so that D moves twice the
distance of F.
If the connecting rod b is again introduced, (see Fig. 6) then an arrangement with
pulleys, analogous to Fig. 3, is employed, by which the movement along the line c―c
in Fig. 4 becomes superfluous.
The employment of the bed or rail has a special advantage, inasmuch as that f
is a tangent to the parabola and the grinding tool. The latter works most advan-
tageously in a normal or right angle position to the surface to be ground, and should
be so placed.
Figs. 9 and 10 are mechanical devices corresponding to the kinematic methods
indicated in Fig. 4 and 5, the straight guides c-c and c-c² being represented by
planed beds or rails having slides thereon. To simplify construction, the point F is
directly guided in a horizontal straight line (see Fig. 9) by means of a screw
spindle and nut. The pivot D, however, is attached to a carriage or slide which
, encloses a screw spindle above and below, and is capable of sliding parallel there-
with. A vertical slide J is mounted in the horizontally moving slide and carries a
tool at its lower end, which, with all other points of the slide J, is capable of
describing parabolas, as at E. The distance of the turning point A from the screw
spindle (whereby AF: FD, while as described with reference to Fig. 4, c¹—c¹
has the same distance from e-c as from A) determines the focal distance, so that
by changing the points named, the distance of the focus may be changed at
pleasure.
-
The arrangement shown in Fig. 10 corresponds to that of the diagram Fig. 5,
and will be understood from that; it being noted that the two screw spindles c-c
and cc partly cover each other in Fig. 10, but in Fig. 5 they are some distance
apart from each other.
When the grinding machine is used for grinding small objects, such as lenses, it
may be of advantage to raise or lower the material acted upon while the tool moves
in a straight line. This leads to the construction shown in Figs. 7 and 11. This
raising and lowering is effected by a circular guide rod or arm attached to the
point H, and moving vertically. In this, and all arrangements shown, it will be
readily understood that the parts indicated in the kinematic sketches must not
interfere with each other in the planes of their motion; and the same remark
applies to the more detailed arrangements shown.
A final arrangement is indicated to ensure the required movement, in Figs. 12
and 13. The tangent marked always cuts off by its forward movement equal
parts of the angle g-O-g standing symmetrically to the axis, (see Fig. 12); as
for instance, the length 1-0-1 is equal 8-0-8.
In the figure, the reference letters ab DF ED &c. have the same meaning as
before the construction has regard to the points 10 and 10 in Fig. 12.
If the moving part corresponding to the tangent f engages two more pivots
(according to this geometric construction) which pivots are connected by means of
a cord or belt of a certain length running over a pulley O, and guided in the
straight guides 9-0 and O-g, then the position of the point F of the tangent
and of the point E of the parabola, in the continuation of f, are given. As
before stated, one or other of the elements of the earlier mechanism may be
removed, for instance in Fig. 13, which corresponds to Fig. 12, the straight guide F

page_text: is removed, so that the band from 10 over 0 to 10 plays the part of an independent
moving element.
Dated this 19th day of October 1892.
FAIRFAX & WETTER,
433, Strand, London, Agents for the Applicant.
COMPLETE SPECIFICATION.
Improvements in or relating to the Mechanism used in Grinding
Machines for Producing Parabolic Conoidal Surfaces.
I, JOSEPH SINCLAIR FAIRFAX, of 433 Strand, in the County of London,
Patent Agent and Consulting Engineer, 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 :-
In order to produce parabolic conoidal surfaces, or surfaces generated by the
revolution of a parabola, it is necessary that the grinding tool shall slowly pass
along the path of a parabola while the material to be acted upon is rapidly rotated
upon its own axis.
The geometric principle upon which the present invention is based is stated by
my foreign correspondents to be the following, reference being made to the
accompanying drawings.
When two straight lines a and b (Fig. 1) respectively turn upon points A and B
in such a way that their angular velocities are in proportion to each other as 1 is
to 2, and further, a system of any number of parallel lines d' d² d³ d² d³ d® and d'
are projected through the lines a¹ a² as a¹ as a and a' upon their intersecting points
with a fixed line c-e, then the cutting points of this system with the corresponding
lines and 6 produces a parabola E E E E E E and E. Both the
turning lines a and b are hereinafter termed connecting rods a and b respectively.
As the focus of the parabolic surface or shell to be ground must be known, the
following suppositions are made for the geometric construction which determines
the position of the focus and the directrix, namely, 1. That the third line c-c
(Fig. 8) is perpendicular to the connecting line of both turning points; and 2. That
at the beginning of the movement both connecting rods, and the connecting line
just mentioned, cover each other.
In Figs. 2, 3, 4, 5, 6, 7 and 13, are shown the kinematic systems which result in
the forms indicated in Figs. 9, 10, and 11. The reference letters apply uniformly
throughout; therefore the points A and B are the turning points of the connecting
rods a and b (shown as forked), D corresponds to the parallel system in Fig. 1
which, as in Fig. 2, is to be understood as a cross piece capable of movement along
a straight bed or rail parallel to itself. In order to obtain the proportion of the
angular velocities - -as before determined-a pin F is fixed in the connecting rod b
so that it describes a circle while the forked connecting rod a slides upon this pin, as
in Fig. 2. Under these conditions, as the one connecting rod moves upon an angle
drawn from the periphery, and the other upon an angle drawn from the centre of
the same circle, then the proportion of the angular velocities must be as 1 is to 2;
and consequently the point E describes a parabola.
Fig. 3 shows how the proportions of the angular velocities are obtained in another
and direct way, in which both connecting rods a and b turn upon the same point,
and are fixed to independent pulleys, one having twice the diameter of the other,
while a corresponding length of cord, equally stretched, runs over them.
A modification of the latter mechanism is shown in Fig. 4. The connecting rod b
is removed and replaced by an element of equal value. Below the upper horizontal
line c-c is arranged a second one c¹¹, parallel thereto, and equidistant between
the upper line and the central point A. A guiding cross bar is moveable on the
line c, and also along the line of the connecting rod a. It will be seen how this

page_text: 'change is carried back to the first when it is considered that the right angle
triangles D F E and E FA are congruent (as D F is equal to FA, and E Fis
equal to itself); consequently angle = y, but (as alternate angles are equal) also
equal to ß; that is, the connecting rod a has to move twice the angle x.
This parabolic guide in Fig. 4 may also be directly produced, exactly as the
former, if the continuation of the connecting rod a is removed, (as shown in Fig:5)
and the horizontal movement of both D and F is brought about by means of the
two screw spindles, c, and c', of equal pitch, c making twice the revolutions of c';
or, both screw spindles having equal revolutions but c having double the pitch, so
that the nut and pin D would move twice the distance of the nut and pin F.
If the connecting rod is again introduced, then the arrangement with pulleys
shown in Fig. 6 is employed (analogous to Fig. 3), by which the movements along
the line ce in Fig. 4 becomes superfluous. The employment of the bed or rail f
in some of these figures has a special advantage, inasmuch as y' is a tangent to the
parabola and grinding tool. The latter works most advantageously in a normal or
right angle position to the surface to be ground, and should be so placed.
Figs. 9 and 10 are mechanical devices corresponding to the kinematic methods
indicated in Figs. 4 and 5, the straight guides e-c and cel in those figures, being
represented by planed beds or rails having slides thereon, distinguished by the same
reference letters. To simplify construction, the point F is directly guided in a
horizontal straight line upon a suitable bed (in Fig. 9) by means of a screw spindle
and nut. The pivot D, however, is attached to a carriage or slide which in itself
encloses the screw spindle c'e' above and below as shown, and is capable of sliding
parallel therewith. A vertical slide J is mounted in the horizontally moving slide,
and carries a tool at its lower end which, with all other points of the slide J, is
capable of describing parabolas, as at E. The distance of the turning point A from
the screw spindle c'-c' (whereby A F FD, while as described with reference
to Fig. 4, is midway between c-c and A) determines the focal distance; so
that by changing the points named, the distance of the focus may be changed at
pleasure.
==
The arrangement shown in Fig. 10 corresponds to that of the diagram Fig. 5, and
will be understood therefrom, it being noted that the two screw spindles c-c
and cc', with their respective beds are shown on the same horizontal level
in Fig. 10, so that e-c¹ covers or is in front of c-c, while in Fig. 5 they are
shown at some distance apart (vertically) from each other.
When the grinding machine is used for grinding small objects such as lenses, it
may be of advantage to raise or lower the material acted upon while the tool moves
in a straight line. This leads to the construction shown in Figs. 6 and 11 wherein
the raising and lowering is effected by a circular guide rod or arm attached to the
point H (Fig. 11) and moveable vertically. In this and all other arrangements
shown, it is to be understood that the parts indicated in the kinematic sketches must
not interfere with each other in the planes of their respective motions, and the same
remark applies to the more detailed arrangement shown.
A final arrangement is indicated to ensure the required movement in Figs. 12
and 13. The tangent marked f (in other figures) always cuts off by its forward
movement equal parts of the angle g-0-g, standing symmetrically to the axis, as
in Fig. 12 where the length 1-0-1 is equal to 8-0-8. In Fig. 13 the reference
letters a D F E D &c. have the same meaning as before; the construction shown
refers to the points 9 and 9 in Fig. 12. If the moving part corresponding to the
tangent engages two more pivots 9, 9, (in the slides g, according to the geometric
construction) which pivots are connected by a cord or belt of a certain length
running over a pulley O, and guided in the straight slides 9-0 and O-g, then the
position of the point F. of the tangent and of the point E of the parabola in the
continuation of F are given. As before stated, one or other of the elements of
the earlier mechanism may be removed; for instance in Fig. 13, which corresponds
to Fig. 12, the straight guide F is removed, so that the band from 9 over 0 to 9,
plays the part of an independent moving element.

page_text: 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 ;-
A mechanism for guiding the grinding tool in a parabolic path for acting upon
shells or surfaces, consisting of the following principal parts;
(a) Two connecting rods each turning round a fixed point and having their
angular velocities as 1 is to 2.
(b) A straight guide on which
(c) A slide carriage moves, which carries
(d) A slide holding the grinding tool and adapted to move vertically to the
straight guide, the slide and carriage being so connected that one guiding
bar determines the position of the carriage on the straight guide and the
second the position of the slide in the carriage, whereby every point of the
vertical slide moves in a parabola, in accordance with Fig. 1.
2. In the mechanism specified in Claim 1, the substitution for the second
connecting rod of a right angled cross piece moveable on the first connecting rod
and whose middle point is moved in a straight line, parallel to the said cross piece
guide (Figs. 4 and 10) so that the arm indicated by f is a tangent to a parabola, as
herein described.
3. In the mechanism specified in Claim 1, the reversal of the movement of the
grinding tool so that it is moved in a straight line, while the material acted upon
is raised or lowered during the progress of the movement sufficient to produce
a relative motion on their respective paths to obtain the required parabolic shape,
as herein described.
4. In the mechanism specified in Claim 1, the arrangement of a cross piece
placed symmetrically to the axis of the parabola, and in whose right lined path
two slides are moving so that the axis of the connecting rod of the tangent is forced
to go through the middle point of the slide mentioned, as herein described.
Dated this 19th day of July 1893.
FAIRFAX & WETTER,
433, Strand, London, Agents for the Applicant.