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Патент USA US2403668

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July 9, 1946,
2,403,668’
c. B. MADDO‘CK
APPAfiATUS FOR FORMING SURFACES OF REVOLUTION
Filed July 20,_1939
5 Sheets-Sheet l
MBMwzm/a,
MW‘
July 9, .1946.
2,403,668
c. B. MADDOCK
APPARATUS FOR FORMING SURFACES OF'REVOLUTION
‘ Filed ‘July 20. 1959
5 Sheets-Sheet 2
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July 9, 1946.
c. B. MADDOCK
‘2,403,668 ’ v
APPARATUS FOR ‘FORMING SURFACES OF REVOLUTION
Filed Juiy 20, 1959‘
5 Sheets-Sheet 5
July 9, 1946.
c. B. MADDOCK '
2,403,668
APPARATUS FOR FORMING SURFACES OF REVOLUTION’ ,
Filed July 20, 1959
5 Sheéts-Sheet 4
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July 9, 1946.
c. B. MAl-DDOCK_
- 2,403,668
APPARATUS FOR FORMING SURFACES OF REVOLUTION
1 "Filed July 20, 1959
_F|G.6..
5 Sheets-sheaf 5
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2,403,668
Patented July 9, 1946
* UNITED 5 STAfES PATENT , OFFICE. j
" 2,403,668
. < ‘
YAPPsRATUsFoR FORMING SURFACESOF
>,
-
REVOLUTION
>
‘
Y
Charles B. Maddock, St. Louis, Mo., assignor to
'_ Baker"& Company; Inc., Newark, N. J., a cor
poration' of New Jersey
'
Application July, 20, 1939, Serial No. 285,482
'
I ‘22 Claims.
(01. 82-511)
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1
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sections, and with regard to’cert‘ain more Speci?c
features, to apparatusjo-f the ‘class described which
form
paraboloids.
.
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"
2
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Similar reference characters indicate corre
sponding" parts vthroughout‘ the several views .of
;, v[I‘h'i'sinvention relates toapparatus for. forming
surfaces of revolution "having conic, longitudinal
will
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the drawings.
Li,
' Among the several objects . of the invention
may be noted the provision of apparatus forrform
ing paraboloids and the like‘which accomplishes
‘
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Oneway in which to cut or ‘spinor similarly
‘form a paraboloid or the'like is _jto mount the
material/from which it is‘ to be made upon a. ro
tary device such as alathe and then" work upon
a it with suitable tools, using a template as a guide.
the desired result with a high degree of’ overall
This ‘procedure.’ is essentially no more accurate
accuracyfbu't particularly ina region where prior
than the template. _ The template in turn de
pends upon manual operation for its accuracy,’
apparatus 'failed, namely, near the vertex} and
and the accuracy of manual operations obviously
the provision of’ apparatus of the class described
which will reduce the cost of high-accuracy prod
ucts such as‘searchlight,‘ telescopic and other re
isnot consistent at all times. _
‘
p
._
,
f
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‘_
Various linkages have been ‘suggested for form
ing conicsurfaces of revolution, such as parab
oloids; ellipsoids and 'hyperboloids, but they are
?ectors and permitthemto beft'urned out “satis
v,;_I"a'ctorily in‘vquantity; Other objects will be in
-_open ‘to ,a' commondefect, namely- that the‘cut
'pa'rt‘obvious' and ‘in part pointed out hereinafter.
The invention accordingly comprises the'elej
ting or forming tool, as it proceeds through its
.ments and combinations of elements, features ,of
operations, has, a__ varying angular aspect with
which will berindicate'diin the following claims.
accuracies are introduced into the surface. For
example, if a point is used at,v the; end of the
construction, and arrangements of ‘- parts which; respect to the curved. longitudinal sectionl'de
will be’ exempli?ed in the structures hereinafter
sired. {This means that, "if- ‘the cutting edge of
described, and the scope of the application of
the tool is anything except a point, inherent in
In the accompanying'drawings, in which are
illustrated several various possible embodiments
ofthe'i'nvention,
‘
j"
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'
.forming tool, in order to'eliminate the undesir
able result. of .a-varying aspect-of forming the
,
" Fig..1'is a diagram, illustrating certain basic
geometricy’concepts,"
_‘
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‘
'
tool, the surface becomes a series. of,‘ de?nite
‘spiral or circulargrooves, makingit di?icul/t
_
Fig.2 is a geometric diagranisimilar to
1
‘thereafter- to " applylla proper '?m'sh to the sur
but showing ‘superimposed a‘jkinernatic. diagram;
face, or at leastv requiring a costly ?nishing op
Fig. '3 isa View’ similar 'to Fig1 .2‘, but shown ‘on '
eration"!
‘an enlarged scale and _ illustrating vadditional
‘
»
f‘ In‘ order to provide a smooth “?nish,” a.cut-’
kinematicfeature's of a 'bisecting mechanis'm;_
ting or'forming tool ordinarilymu'st have a con
‘Fig. '4 is ‘a plan view of the mechanism applied
vex or curvilinear cutting edge rathenthan a
to a‘lathe embodying the principles of the inven,-.
theoretical point, cutting or forming edge or end.
'Such aniedgeorend permits“ of approaching with
one operation more closely to the ?nal ?nish de
sired without any, or at least'y'only an‘ easy, ?nish
tion‘fthe view beingtaken on line 4-‘44 of vFig. 5
.so as to maintain all projections orthographic;
Fig. 5 is a‘ vertical section taken on line 5-5
ing operation.
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Fig. 6 is a fragmentary enlarged plan‘ view of . 4,0 The present invention'n'ot only provides an im
certain parts of Fig. 4 vshowing alternate posi
proved linkage for moving a cutting or, forming
tions of parts j
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tool
generally, but includes a ‘mechanism for
,Fig. 7 is a vertical detail section‘taken‘ on, line
maintaining the tool at the proper aspect angle
with respect to the surface to be worked, so that
'I-—'!
‘Fig.
ofF'ig.4;
Bis a vertical detail
‘'1
section
'
"taken
"j;
on
H line
'8—‘—8ofFig.7;
‘
“‘
the desired edge may bev employed‘ for smooth
'
Fig. 9 is a'ver'tical detai1 section'takenxon line
9-9 of‘Fig. 4;’
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?nish-h.‘
t‘ Fig. ‘10' is a verticalsection taken on'linejvll_l—l?
‘cussed._"'’
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7:;
a
V
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01mg.
‘11.
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nates onjX-Y axes; If a width W and a height
H'be assumed for, a desired parabola P, the ver
v
.
_
1 is shown a set ofrectangular coordi
tain ‘operating parts‘v removed and an alignment
a Fig. 12 is a vertical‘s'ectiont'aken on line I2‘—lj2
.~
50 mg? of p'arabolas ‘In a plane will ?rst be dis
ofFig.9;)
Fig. 11 is'a
' plan
'
view of a carriage with cer
jig shown in position; and, _
.
In orderthat the invention may be better un-7
derstood; some theoretical aspects of the outlin
'
55
tex-will" be at'V, and theparabola'may be_;con~
2,403,668
4.
3
structed geometrically by using this vertex V as
vertex V.
a pole and employing radial lines R as follows:
The horizontal axis is divided into a predeter
ing a pin 23 on a coordinate slider 25. The
slider 25 moves parallel to the Y axis in a longi
tudinal guide 21.
mined number of equal divisions, for example,
eight on each side of the center of the ?gure,
in
scribed. In the guide 29 is a slider 3|, which
slides at right angles to the slider 25.
Various ways may be used for coordinating the
desired proportional movements between the slid
The radial lines
R are then drawn from the vertex V to the re
spective vertical edge divisions |—8. Where
these respective radial lines cross the respective
horizontal division lines |’-8', intercepts K are
ers 25 and 3|.
»- so that the screw 31 travels faster but propor
time the drawing :plane is rotated, a‘paraboloid
of revolution will theoretically be generated in
the space manifold of that plane.
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. Furthermore, by laying off equal distances D
parallelto the Y axis, a second parabola P—2
will be determined, which is the same as P but
simply displaced the distance D. The focus F—2
of this parabola P—2 will be displaced from the
focus F an equal distance D.
For the purpose of the diagram
matic Fig. 2, I have illustrated these coordinator
blocks 25 and 3| as driven by lead screws 35 and
31, geared at 39 in the ratio of 1:2 respectively,
determined ‘which form the locus of the desired
parabola, as shown.
The focus F of this parabola P may be found
by known methods, and it is as indicated in the
drawings. It is not necessarily on the exact axis,
but has been so chosen in the present example,
From the above it will be clear that if a point
proceeds along the parabola, and at the same
At right'angles to the guide 21_ is a guide 29
corresponding to the X axis hereinbefore de
as shown. The vertical or Y axis is divided into
an equal number of divisions (of equal or dif
ferent size) above the X axis.
The rod includes a guide 2| surround
‘
tionally to the screw 35, thus moving the block 3|
throughout its range of movement which in the
examplechosen is double the range of movement
of the block 25.
'
From the above it will be seen that, if the screw
35 is driven, the screw 31 moving in relation there
to, the pin 23 will assume ‘at successively equal
time intervals successive equal intervals on the
Y axis.
At the same time the'block 3| will as
sume proportional positions at equal intervals
on the X axis. Thus, the center line of the tool
holder 33 becomes positioned at successive equal
intervals along the X axis. The intersection ll
'of the center line of the radius rod IS with the
center line of the'tool holder 33 ful?lls the neces
sary conditions referred to in connection with
It will also be clear that if a cutting tool such
as illustrated at T be moved with’ its center line
Fig. l.
"
C—L parallel to itself, a theoretical cutting point
ill thereon will generate a paraboloid of revolu
The above construction solves the problem of
tion in a solid if said solid be turned relatively
providing a mechanism to drive a theoretical
around the Y axis ‘shown. Thus, it will be'seen A, point such as H along a parabola P. However,
since it is impracticable to place a cutting tool
that so long as the cutting point l0 remains
theoretically an absolute point, the aspect of the
at the point H which is already occupied by a
tool T with respect to the parabola P—2 will not
pin, it is necessary to project the actual cutting
affect the theoretical form of the p'araboloid.
tool beyond the point I | and to generate at point
*However, if any attempt be made to employ a 40 C—P a parallel parabola P—2, the actual focus
linear tool face on said tool, such as for-example
of which is at F-—2. If the tool holder 33 were
at N, the face will necessarily intersect ‘the de
merely extended to a point C—P, as shown, it
sired curve as shown and generate an improper
would in its various lateral positions assume, with
surface. It will also'be seen that the only way
respect to the parabola P—2, various and differ
in which such an improper aspect of thetool can .,
ent angular aspects which have been above desig
be avoided is always to maintain the desiredface
N of the tool tangent to the curve P—2 at point
|ll.. This involves varying the angle ‘of the center
line of'the toolxas it traverses the curve,__P—2
nated as undesirable. That is, the problem could
not be successfully solved by simply providing a
pointed tool on the tool holder 33 extending so
that its point is on the parabola P—2, because
this would introduce the ‘inability to provide a
One of the advantages of this inventioncon
sists in causing said tool to angle properly to
maintain a constant aspect of the cutting tool
satisfactory ?nish,
.
Therefore, in orderto use a round-nosed tool
extending to a position in the clear where it can
face such as N, as indicated for example at N’, J
cut the parabola P—2 and remain constantly
wherein a constant tangency is ‘always main- '1,» normal (at ?xed aspect) to a tangent'on the
tained at a center point I0. By this means very
?ne, broad» ?nishing cuts may be taken, provid
ing mirror-like surfaces of great accuracy with—
out consequential circular or spiral ridges there
in, as would occur with a point cutting tool.
In the above method for generating the para
bola P—2 (which may be considered as a section
of the desired paraboloid of revolution) ,the mo
tions of the coordinates of the loci K’ along the
X—Y axis are proportional.
In Fig. 2 is shown the part of the mechanism
of the invention which traces by means of a
desired parabola P—2, I provide a swinging tool
block 4| (Fig. 3), which, with respect to the tool
holder 33, always swings around the cutting point
C—P on the parabola P--2. Since the cutting
point C-P needs to remain clear for cutting
within a bowl-shaped surface, it cannot be used
as a point for a pivot pin, and rotation of the
block 4| around the center C—P is therefore
managed by arranging a circular slide 43 to work
in 'a circular guide 45 in the tool holder 33. The
radii of the circular forms for the parts '43 and
45 have centers at C—P.
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point the geometric construction outline incon
At the actual focus F—2 of the parabola.P—2
nection with Fig, 1. In this ?gure is shown the
is provided a pin I51. This pin is in aguide E9
theoretical parabola P generated by what will H of a drag link 5|. ‘The center line of the‘ link 5|
hereinafter be referred to asa virtual (not real)
passes through the focus P—2 and point ’C»-P.
generating point II. This point || consistsin the
The link’5l is made rotary about the center C—l?
center of a pin l3 which is rotary in a toolho‘lder
33 and supportsa rotary slider I5. ‘The; slider
is slidable upon a radius rod |9 pivoted at the 75
by providing it with a circular slide 53 .in a cir
cular guide 55 of the tool holder 33.
.
Connected between the tool holder 33 and the
2,403,668
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"drag link ‘.5I are bisecting links 51 and.59 respec
tively. ‘- The" links'51v and 59 are pivoted in com
-. ‘Adjustmentfor?the‘ assembly of the unit 81,’
88 is obtained by means of the‘two sets of right
center line of~the tool blockJI. .
' From the above it will be clear that,’ as the/tool
angularly located set screws 89 threaded through
holder 33 "moves (under "the influence of the» co
ordinator blocks 25. and 3| and radius rod I9),
the center line ofthe block 4| will-always bisect
behaped-members 90, at opposite cornersof the
7 support 88. The -members. 90 are attached to
the carriage ‘65.- Itwill be seen that by means
of the set screws 89 the support 88 andattached
the angle formed by the centerlines of the tool > v
platen 81 may bemoved longitudinally,‘laterally,
andiangularly- Itis heldlin any given adjusted
position by means of. locking and elevating-studs
9I and 93.5 The studs 9|v work in'compression
and the studs 93 in tension, havingheads 95
holder
center line
33 and
willthe
always
dragpass
link'5I.
through
This
thebisecting
cutting
pbintC-P, and thus the arcuate face of the tool
'Talways remains with afixed aspect'with respect
‘to the parabola,that is, the tool holder face and
"the face of the parabola always have. coincidental
loosely located in TIT-slots 91'. The .?t between
the heads .95 and the T-slots 91 is loose enough
Inormals G to commonv tangents H’ at C-—P, re
gardless of the position of C--P onthe desired
.
.
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to accommodate the angular motion needed for
making centeringadjustments, as follows:
.
It will be understood that the geometric and’
datingdowel pins I02 v(Figs. 11 and 12). The
trated symbolically. In ‘the remaining ?guresof
‘the case is shown actualapparatus for carrying
out the principles describedtin connection with
. points 99 and HM‘ at the start‘ of a‘ cut lieupon
the center line of the‘desired .paraboloid. The
point .99 is establishedat what is to become the
focusF-2, and the'point IIII is established at
the vertex V of a parallel paraboloid such as
Figs; l-3, and so'far as possible similar reference
characters and description ofparts will be used.
It should be noted, however, that the lead screw
and gear drive for theJcoordinator blocks Hand
3]. (shown in Figs. 2 and 3) are not'used inthe
remaining ?gures, a set of ninety-degree, phased
PinFigs.land:2.'-v
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My.
.3.
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J Aljig I03-havingholes I85 is applied to the
platen‘81 on the pins'I82 and establishes linear
points I81 and: I89 onwthe same line‘ as points
slider-crank; mechanisms being v"used for-this
2
.
and‘ vII'II are established thereon for accommo
'andxthat the various mechanical pairs are illus
§P—2 and V.‘ ‘The platen support .88 and platen
.'
. ‘I Referring ,now to Figs. 4-12, there=isishown at
,
In order to set the platen. 81, twoholes 89
kinematic showings of Figs. i-3 are diagrammatic '
purpose.
6
tolset the platen 81 into a position which will
vplace the box 85 clear'of thelathe bed.
mon to a pin!“ which works in a'slot 63 on the
parabola.
a
thereon; 'The purpose 'of .the anglesupport is
81 are then adjusted as a unit so that the. point
V
numeral 5I§an ordinary lathebed'on whichis a
rotary or live spindle 53 carrying'a face plate 55
"adapted to function as a chuck‘te support the
I89 is at.- the exact center of the livespindle
and isat .a- point which will become the actual
, vertex of the actuallparaboloid; The point I01
is placed -at'the point-of the center ‘III in the
material 151 (preferably generally cup-shaped)
tail: stock II3. By this means theidesired point
of real focus 31-2 is established on the'center
line ‘of-lthe- lathe; After adjustments for the
which. is to be ?nished inside tothe- exact form
of a-parabola. ‘Holding .clamps are shown at .59.
The lathe‘ is .drivenlin» the usual way,.for ex-»
platen are made; it- is tightened down and the
ample. by a'beltin connection withthe live/spin,
dle, andhas the ‘usual gear train 6| from the live
spindle to a splined'lead' screw 63, thelatter
“passing through the'control apron 84 of the .car
riage 55. ,;;The .screw' 63, among other things, 1
serves‘ toefurnish, through the;usual clutchland
;gear,trainrin ‘the apro'ngIiA, .a drive for the cross
_jig I03isremoved.‘
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The'parts carried upon the. platen 81 consist '
of ‘the driving shaft H5, splined for example at
four slots II1, and adapted‘ to be keyed
by means of one of saidslots- II1 to one
Slots'J I 9 in a bell-crank I2I. The choice
' slots H1 in. the shaf-tII5. and; ?ve slots
at IIB _
of ?ve
of four
H9 in
feed shaft 68021 the carriage 55., Further, details
bell-crankJI2-Iallows fora large number of
of thisgear'train-are believed to be unnecessary 3 the
keyed‘ relative adjustments vbetweenuthe bell
because the ‘drive forthe present attachment-isv
crank?l and theshaftiI I5. .
'. '
' '
taken from. said cross-feedshaft 66.. In the’ case
At Hand’ 29 are-shown the right-angular slots
of the present invention, the lead screw servesto
in platen 81 f0r:.a‘ccommodating-thecoordinator
drive the mechanism herein described which:is
- mounted on the carriage.
:For manually. moving the carriage independ
‘ ently of the lead screw 83 there is provided the
usual hand‘ feed wheel 61.functioning='jthrough
(a gear train in the apron. Elli-to rotate ‘a pinion~1I
along a rackr13,,the latter being. attached rigidly . .
be: manually movedlback and-forth. along the bed
by means of the hand wheel 51, andithe lead screw
63 furnishes the drive to parts mountedon the
“on the .lathe bed 5|.- > Thus, the carriage 65 ‘may L
carriage. The present apparatus being mounted
upon the carriage 65, the drive therefor is picked 1 ~
up at an extension‘ 15 from the cross-feed shaft
66-
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- The shafti?licarries apulley 11 fora quarter
blocks 25 and3l ‘respectively.
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The arms- of the bell-crank I2I are phasedat
ninety degrees as shown. The bell-crank is
pivoted ‘at I23 to a connecting rod‘ I25 which in
turn is pivoted at I21 to the slider‘ 25 (see also
Figs. '7 and 8). ~ Thus, it will be seen that» there
is substituted for the screw-operationsof block
25 the bell-crank 'I2I with the connecting rod
I25.
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To obtain a connection between “the radius
rod I9 and the pin 23 a slot I29 is employed,
but it is" relied upon for-clearance and not for
guiding. "This is’ to increase accuracy, there
‘ being'a shoe’ I3I formed around the pin 23which
has guidelsurfaces I33 on'theroutside of. the
radius'rod- I9.-‘
a more accuratebeari'ng
turn .belt-rdrive??- to pulley‘ ill. The pulley 8i , I'is'obtained, but the motionis equivalent to that
drivesa double reduction-gear ‘83 in‘ a1gear~box - .
indicated in the kinematic diagram (Fig. .3) ' at
.85, the latter being attached to a main ‘platen/'81;
vThe platen 81 is shown iwithoutsuperimposed
‘parts -in.,Fig. 11. The platen gisifastened at‘ 84
to . an angle; support 88 which in-turn. is: carried
upon the‘ carriage,“ and is adjustableilniposition 1"
"numerals2l,<23.._
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1 In order to ' operate‘the, slide 3 I , there is. pro.
~videda second arm‘ Chef/he. belt-crank al 2 I . phased,
at ninety degrees, which is pivoted at. I35 toia
'1
2,403,668
7
connecting rod I31 which in turn is pivoted at
I39 to the second sliding block 3|.
The sliding
block in Figs. 4 and 6 is of triangular form and
has a dove-tailed connection on its bottom with
the platen 81 at the guide 29 (see Fig. 9).
Since the pins I35 and I23 of the bell-crank
I2l have a crank phase of ninety degrees, and
since they work sliders 25 and 3| at a ninety
degree angle, the displacements of» said sliders
Figs. 9 and 10 show also how the radius bar I9
is pivoted at the vertex V (of the parallel parab
oloid P), a pin I13 being used for the
These ?gures also showhow the slider
bearing engagement with the radius bar
top and sides. The pin I3 at the pivot
between the tool holder 33 and the slider
purpose.
I5 has a
I9 at the
point II
I5 is also
indicated. When the mechanism moves from the
vposition of Fig. 4 to that shown in Fig. 6, the con
are always proportional. Other schemes may be 10 centric relationship of Figs. 4, 9 and 10 between
employed .for obtaining this proportional move
' pins I3 and I13 disappears.
ment besides the screw mechanism shown .in
To operate the device, the jig I03 is ?rst applied
Fig. 3 and the phased slider-crank mechanism
to the platen 81, after the parts above described
of'Fig. 4. The screw mechanism has one ad
have been removed (Figs. 11 and 12). This is
vantage however, and that is uniformity of mo 15 done by applying the holes I35 to the pins I52 at
tion as well as proportionality.
the focal point F—2 and vertex V. The focal
The tool support 33 has a dove-tailed slide
point F~2 is that of the actual curve which is cut,
connection with the slider 3|. The relative slid
and the vertex V is that of the equivalent-parallel
ing possible vmay be seen by comparing Figs. ,4
parabola P. Then adjustments are made so that
and 6 (see also Fig. 9) .
‘the platen 81 is moved to bring the jig points I01
The practical manner of mounting the swing
and I09 into line respectively with the point of
ing tool block M is .best indicated in Fig. .6
the lathe tail stock center III and the center of
wherein said block will be seen to have an
the live spindle 53. ‘The jig is then removed, and
arcuate shaped end bearing portion I4I having
the parts shown in Figs. 4 and 6 are applied.
a dove-tailed bearing connection I43 with the ..
It will be understood that the angle of the
tool support 33 (see also Fig. 9). The purpose
platen 81 may be other than as shown, or the de—
of this is to obtain a rotary connection between
vice may even be horizontahthe criterion bein
the tool block 4| and the tool support 33 which
simply that the tool works in a plane which in
shall have a virtual center at C-P, which is
cludes the longitudinal axis of the desiredpara
the theoretical point above discussed on the tool. III.) bola.’
"
The tool itself consists of a small block of suit
After the parts are mounted and set into the
centered position shown in Fig. 4, the entire car
riage 65 is manually moved forward by means of
ably hard cutting material, numbered I45 and
held rigidly in position on the tool block 4| by
means of a clamp bolt I4]. In order to maintain
wheel 61 until the tool I45 assumes a ‘depth of
the tool block M as rigid as possible in all of .? penetration desired into 51 for the depth of cut to
its rotary positions, the tail is provided with a
be used. Rotation of the live spindle 53 will then
tongue I49 which rides in .a slot I5I of a guide
result in causing turning of the material 57 with
a drive through the gear BI to the lead screw 63.
I53, the latter forming a part of the tool sup
port 33.
.
;
The drag link 5I which is shown with an offset
(to effect clearances) is slotted asshownat 155
to slide on a pin block I 51 at the focus ,F—,+2. The
center line of the slot I55 passes through the point _
0-? and focus F-—2.
The end of the drag link 5I near the tool I45
is also arcuately dove-tailed with respect to 33,- as
shown at I59, to effect arota-ry relationship be
tween the drag link 5i and the tool support '33.
This is done indirectly, without obtaining inter
ference‘ from other parts, by making the slotted
connection as shown at I59 withthe tool bar 4|,
a
which, it is clear, is the equivalent of a- direct ro
tary connection with the tool support 33.
The
center of curvature of the dove-tailed, slotted
connection I59 also is the point C—-P on the face
of the tool I45.
To maintain the tool I45 normal to the surface
being cut, the bisector links 5'! and 59 are used,
the former being pivotedto the tool support 33
at I53 and the latter to the drag links 5I at I55.
The two bisector links 51 and 59 are joined at a
pin I61 which rides in a slot vI53 of the tool bar M.
The center line of the slot 63 also passes through
the point C—-:-P.
‘
'
at
The lead screw drives through'the gears in the
apron 64 to rotate the cross-feed shaft’ 66 and
hence to drive the gear reduction unit 85 through
the quarter-turn belt ‘I9. This causes movement
of the linkage from the position shown in Fig. 4
to that shown in Fig. 6, the lateral traversebeing
slow enough toe?’ect a desirable feed.
At numeral I8I is shownan oil sump for con
taining cutting oil, with a suction pipe I 83 leading
to a pump I85 driven from a belt drive I81 from
the live spindle. A ?exible hose I89'leads to a
nozzle I9I which is caused to project cutting lu
bricant upon the tool as it advances. It is clear
that the nozzle I9I may be manually controlled to
follow the tool, or connected with the tool.
The following will serve to indicate the scope
that is intended for claims that follow: A parabola
may be thought of as an especial case of an ellipse
or a hyperbola. One of the conjugate foci of the
parabola is at in?nity, the other focus being that
at F—2. An ellipse happens to haveboth con
jugate foci ?nite, as also» does the hyperbola. In
all three cases of the parabola, ellipse and hyper
bola, lines drawn from the fool to any point on
the curve will determine an angle Q, the bisector
G of which. is a normal to the tangent of the curve
Fig. 9 makes clear how the dove-tailed connec 65 at that point.
.
tions I43 and I59 are on-opposite sides of the tool
Thus,
in
Fig.
3,
the
center line of the tool holder
bar 4| so as to avoid interference between the two.
33 passes through the point C—P and to a focus
This ?gure also clari?es the steadying bearing‘
I51. It also indicates that the pin block I51 at
point at in?nity (not shown), 'and'the center line
of the drag link 5| passes through the ?nite locus
the focus F—2 is supported upon a. C;-.shaped 70
F—2 and. the point C-—-P. The center 'line'of the
member I'Il, which in turn is supported on the
tool block 4| is the bisector and'ls'normal to the
platen 81.
The member I ‘II hasa C-shape in’
order to clear and accommodate the tool ‘holder
'33 in the centerediposition of the latter v(see also
.tangent to the curve at point C--P.
Thus, the center line of the link 5f is parallel
to: alight ray‘ which would emerge from a point
75 source of light. at F'—2,. and the centerline of the
‘2,403,668
the toolbeing rotary with respect to the support
about said point on the tool, a link also rotary
with respect to said support about said point, a
center ‘line of the cutting tool bisects. the angle
formed between the hypothetical rays in, any
given plane.
10
a traverse movement with respect to said axis,
vtool support 33 is, parallel to the emerging direc
tion of said my from the resulting re?ector. The
sliding arrangement for said link with respect to
It'is the constant ‘arrangement
of .
_
‘ the focal point of ‘the section line, and a propor
the tool in this manner that accounts for the
inherent accuracy of the resulting paraboloid,
tioning vlinkage between the link and vtool holder.
4. A parabolic section line generatorcompris
particularly'when applied tomaking light re
ing a tool having a smooth convex forming edge
'
The amount of advance of the tool along the . 10 ‘in whichis a point adapted to traverse the sec
tion, :a support for the tool having movement
. parabola P—2 per revolution of the work on the
?ectors'.
along ,a- line passing through said point and par
allel tothe axis ofthe parabola,means for giv
live spindle of the lathe is arranged; by means-of
the gear reduction unit 83, 85 in view of the
curvature of the tool face, that only the most in
ing the support‘ a longitudinal and a traverse
15 movement with respect to said axis; the tool be
consequential, if any, ridges are left.
ing rotary with respect to the support about said
Curve generating systems of the class herein
point on theltool, a link also rotary with respect
described, involving linkages which, inherently
to said support about said, point, a ‘sliding ar
produce the desired results, are to-be distin-.
rangement for said link with. respect to the focal
guished from non-generating systems in which
dependence is placed upon manually made tem v20 point of the parabolic'section, and a bisecting
linkage between the link, and tool holder to main
tain'the tool in a predetermined bisecting posi
The bisecting'linkage, above described, between
plates.
}
.
_
r
i
~
tion between said holder and link.
the tool support and the drag link to maintain the
tool holder at a given aspect with respect tov a
parabola is only one example of various propor
'tioning means that may be usedyfor maintaining
said constant aspect of the tool.
,
5.1 A parabolic section line generator compris- '
ing a tool havingya forming edge in which isv a
point adapted to traverse the section, a support
for the toolhaving movement along a line pass
ing through said point and parallel to the axis
of the parabola, means for giving the support a
.
The radius of curvature at the tip of the tool
145 should be less than the minimum radius of
curvature of the curve which is being cut.
. J30 longitudinal and‘ a traverse movement with re
In ,view of the above, it will be seen that the ' ' spect to said axis comprising a transversely slid
ing block slidingly supporting the tool holder for
its longitudinal movement, a longitudinally slid
ing" block, aradial arm pivotedv at the vertex
several objects of the invention are achieved and
other advantageous results attained.
‘ As many changes could be made in the above
constructions without departing from the scope ;_.. of- a parallel parabola‘ and having a slide con
nection with the last-named block, and also a
of the invention as setrforth in the claims, it is
connection'with the. tool holder to control its
intended that all matter contained in the above
longitudinal movement. ,
description ‘or shown in the accompanying draw
,6. Av parabolic section line generator compris
ings shall be interpreted as illustrative andnot [
in a limiting sense. A circle is not considere , in ing a tool having'a smooth convex forming edge
in which isa point adapted to traverse the sec
a conic section in the appended claims.
,
~ 7
.
' ,-tion, a support for the tool having movement
along a line passing through said point and par
I allel to theaxis of the parabola, means for giv
I'claim;
1. A section line generator
for conic
g
, sections
having a plurality of foci comprising‘ a tool hav
ing a forming edge which includes a point'adapted 45 ing the support a longitudinal and atraverse
movement with» respect to said axis comprising
to traverse the section, said tool having its form
_a transversely sliding block slidingly supporting
ing edge lying substantiallyin the plane of the
section, and means for maintaining constant an
aspect between said edge and the section line ‘dur
the tool holder for its longitudinal movement,
a longitudinally sliding block, a radial arm vpiv
oted at the vertex of a parallel ‘parabola and
having a;slide. connection with the last-named
ing traverse, such that a line on the tool which .
' is normal to the common tangent between the
blockland also a slide connection with‘ the tool
holder to control its longitudinal movement, and
forming edge and the'section line, and which‘
passes through said point, shall always bisect the
means.,for_maintaining a predetermined aspect
angle between lines passing from the point to said
foci.
.
"
._
55
2. A section line generator for conic sections
having a plurality of foci comprisingadcutting
between said convex forming edge and the sec
,tion line.
-,
.
,
.
.
'
h
. 7. A parabolic :section linegenerator‘compris
mg ‘a tool havingv a ‘forming edge in which is a
I point adapted to traverse the.section,.a support
tion, ‘said tool having its cutting edgelying sub‘ 60 "for the toolmovable along a line passing through
said point and parallel to the axis of the parabola,
‘stantially in the plane of the section, and a link
tool having a cutting edge of arcuate shape'and
including a point adapted to traverse ‘the sec.
age for maintaining constant an aspect between
means’ ‘for giving the support .a longitudinal and
said edge and the section line during traverse,
independently of templates or the like, such that
a traverse movement with‘ respect to said axis
tangent between the forming edge, and the sec
,ment, a longitudinal sliding block, a pivoted arm
tion line, and which passes through said. point,
shall always bisect the angle between lines pass- I
.blockand also a slide connection with'thetool
comprising a transversely sliding'block slidingly
a line on the tool which is normal to the common 65 guiding the, tool holder for its longitudinal move
having'a slide connection with the. last-named
I holder to.v control its longitudinal movement,.and
‘
l
V
. I >
3. A generator for section'lines having-fool, 70 ‘means for proportionally moving said blocks, the,
transversely sliding block/providing transverse
comprising a tool having a forming edge, in which
ing from the pointto said foci.
is a point adapted to, traverse a line, av support
‘for the tool having a line passing throughwsaid
point and parallel to the axis of the section line,
__mo,vemen_t of the tool holder.‘
' f f
"
1
, > 8.,_A parabolic section line generator compris
ing a tool having'a forming edge in ,which is a
,means for giving the support a’ longitudinal and ;7‘5 ,point adapted to traverse the section‘, "a support
"2,403,668
l2
for the tool movable along a line passing through
said point and parallel to the axis of the parabola,
means for giving the support a longitudinal and
a traverse movement with respect to said axis
comprising a transversely sliding block slidingly
guiding the tool holder for its longitudinal move
ment, a longitudinal sliding block, a pivoted arm
having a slide connection with the last-named
block and also a slide connection with the tool
holder to control its longitudinal movement, and
means for proportionally moving said blocks,
comprising a double slider-crank mechanism hav
ing connections with the sliders which are phased
at ninety degrees.
'
9. A parabolic section line generator compris- '
ing a tool having a forming edge in which is a
point adapted to traverse the section, a support
for the tool having longitudinal movement along
a line passing through saicl'point and parallel
to the axis of the parabola, means for giving the
support a longitudinal and a traverse movement
with respect to said axis comprising a trans
versely sliding block slidingly guiding the tool
holder in its longitudinal movement, a longitu
dinal sliding block, a pivoted radial arm having ;
a slide connection with the last-named block and
also a connection with the tool holder to control
said longitudinal movement, the tool being rotary
crank mechanism having connections with the
sliders phased at ninety degrees, the tool being
rotary with respect to the support about said
point on the tool, a link also rotary with respect
to said support about said point, a sliding ar
rangement for said link with respect to the focal
point of the parabola, and a bisecting linkage
between the link and the tool holder to maintain
the tool in a predetermined bisecting position be
tween said holder and link.
.
12. A parabolic section line generator compris
ing a tool having a forming edge in which is
a point adapted to traverse the section, a support
for the tool having motion along a line passing
through said point and parallel to the axis of the
parabola, means for giving the support a longi
tudinal and a traverse movement with respect to
said axis comprising a transversely sliding block
slidingly guiding the tool holder in its longitudi
nal movement,’ a longitudinal sliding block, a
pivoted arm having a slide connection with the
last-named blockand also a sliding connection
with the tool holder to control its longitudinal
movement, means for proportionally moving said
blocks, comprising a double slider-crank mecha
nism having connections with the sliders phased
at ninety degrees.
13. A parabolic section line generator compris
with respect to the support about said point on
ing a tool having a forming edge in which is a
the tool, a link also’rotary with respect to said ‘
point adapted to traverse the section, a support
for the tool having motion along a line passing
support about said point, a sliding arrangement
for said link with respect to the focal point of
the parabola, and a bisecting linkage between the
link and the tool holder to maintain the tool in
a predetermined bisecting position between said
holder and link.
'
10. A parabolic section line generator compris
1, through said point and parallel to the axis of the
parabola, means for giving the support a longi
tudinal and a traverse movement with respect to
said axis comprising a transversely sliding block
slidingly guiding the tool holder in its longitu
dinal movement, a longitudinal sliding block, a
ing a tool having a smooth convex forming edge
pivoted arm having a slide connection with the
in which is a point adapted to traverse the sec~
last-named block and also a sliding connection
tion, a support for the tool having motion along 40 with the tool holder to ‘control its longitudinal
a line passing through said point and parallel
to the axis of the parabola, means for giving the
support a longitudinal and a traverse movement
with respect to said axis comprising a trans
versely sliding bl'ock slidingly guiding the tool
holder in its longitudinal movement, a longi
tudinal sliding block, a pivoted arm having a slide
connection with the last-named block and also
a slide connection with the‘tool holder to; control
its longitudinal movement, means for proportion
ally moving said blocks, the tool being rotary
with respect to the support about said ‘point on
the tool, a link also rotary with respect to said
support about said point, a sliding arrangement
for said link with respect to the focal point of
the parabolic section, and a bisecting linkage be
tween the link and tool holder to maintain the
tool in a predetermined bisecting position between
said holder and link. ,
11. A parabolic section line generator compris
ing a tool having a smooth convex forming edge
in which is a point adapted to traverse the sec
tion, a support for the tool having movement
along a line passing through said point and paral
lel to the axis of the parabola, means for giving
the support a longitudinal and a traverse move
ment with respect to said axis comprising a trans
versely sliding block slidingly guiding the tool in
its longitudinal movement, a longitudinal sliding
block, a radial arm pivoted at the vertex of a >
parallel parabola and having a slide connection
with the last-named block and also a slide‘con
nection with the tool holder to control its longi
tudinal movement, means for proportionally
moving said blocks, comprising a double slider
movement, means for proportionally moving said
blocks, comprising geared screw connections with
said blocks.
14. Apparatus for generating conic sections
Li having two foci, comprising a tool support hav
ing a line passing through successive points on
the section and through one focus, a rotary tool
on the support movable about said successive
points on the section as centers, a rotary drag
link on the support also movable about said
points as centers, said drag link having a sliding
relationship with respect to means at the other
focus, and a bisecting mechanism between the
holder and the drag link adapted to maintain the
tool at predetermined positions between said
lines.
’
,
'
15. Apparatus for generating conic sections
having two foci, comprising a tool support hav
ing a line passing through successive points on
the section and through one focus, a rotary tool
on the support movable about the successive
points on the section as centers, a rotary drag
link on the support also movable about said
points as centers,‘ said drag link having a sliding
relationship with respect to center means at the
other focus, a bisecting mechanism between the
holder and the drag link adapted to maintain
the tool at a predetermined bisecting position be
tween said lines, said bisecting mechanism com
prising a slot associatedwith the tool, the slot
having a center line passing through said point
on the section, slide means in said slot, and links
of equal lengths pivoted at the same point to said
last-named slide means and-at their other ends
to the tool support and drag link respectively on
, 2,403,668
'
,13w
,
,
lines which always cross on said successive points
on a section.
V
16. Means for centering a device of theeclass
described on a lathe bed,;comprising an adjust
able support on the bed, a jig adapted to be sup
ported upon the support and having two gauging
points, said jig being adapted to be placed on
the support with said points being located on the
v14
connection with said linkage, said driving con~
nection comprising related splined members, one
of which has an even number of splinesand the
other an odd number of splines, and a single key
e?ecting a connection between a single pair of
said splines.
-
20. In combination, a driving element provided
with slots, a driven element provided with slots
having different displacement from the driving
same line with a hypothetical focus point and
a hypothetical vertex point of a section to be 10 element, and a key engaging one slot in the driv
ing ‘element and one slot in the driven element,
made.
'
said key being removable, and replaceable in
1'7. Means for centering a device of the class
other slots of the driving and driven elements to I
described on a lathe, comprising a support on the
bed having rotary, vertical and lateral adjust:
ments, a jig adapted to be supported upon the,
secure accurately phased, positive, and variable
connection between the drivingpand driven ele
platen and having two gauging points,,said jig, '
being adapted'to be placed on the platen with
said points being located on the same line with a
ments.
hypothetical focus point and a hypothetical
'
21. In a kinematic chain for generating a
parabola, a base, a straight bar pivoting on a
point in’ said base, means revolvingv said bar
' vertex point of a conic section to be made, said 20 about said point, a slider, and means moving said
platen being adjustable as to any of said adjust-_
ments to bring the gauge points on the jig into
‘ alignment with the center line of the jig.
, 18. In apparatus of the class described, a
linkage to be driven, a shaft having a ‘driving .
connection with said linkage, said driving con
nection comprising related splined members, one
slider along said bar as said bar revolves so that
' a predeterminedwpoint on said slider traces a
parabolic path relative to the base.
22; A conic section line tracer comprising a
forming tool having a forming edge including a
point adapted to traverse the section, said form
ing tool having its forming edge lying substan-,
tially in the plane of the section, and means for
maintaining constant a predetermined aspect be
other another number of. splines, and a key
effecting a driving connection between less than 30 tween said edge and the section line during
of which has one number of splines and the
all of said splines.
,
a
19. In apparatus of the class described, a
linkage to be driven, a shaft having a driving
traverse.
‘
CHARLES B. MADDOCK.
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