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Патент USA US2410888

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Nov. 12, 1946.
o H, LUCY
2,410,888
METHOD AND APPARATUS FOR MOLDING THREE-DIMENSIONAL
SHAPES FROM DRAWINGS
Filed March 31, 1944
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INVENTOR.
Oh‘: I: :Hi. LUCL/
Nov. 12, 1946.
o. H. LUCY
2,410,838
METHOD AND APPARATUS FOR MOLDING THREE-DIMENSIONAL
J
SHAPES FROM DRAWINGS
Fil'ed March 31, 1944
4 Sheets-Sheet 2.
INVENTOR.
U H0 i-l ., L u c: L/
Nov. 12, 1946.
_
' '
o. H‘. LUCY
2,410,888
' METHOD AND APPARATUS FOR MOLDING THREE-DIMENSIONAL
‘
SHAPES FROM DRAWINGS
Filed March 51, 1944
4 Sheets-Sheet 5
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INVENTOR.
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NQV. 12, 1946.-
O H, LUCY
-
-
2410,888
9
METHOD AND APPARATUS FOR MOLDING THREE~DIMENSIONAL
SHAPES FROM DRAWINGS
Filed March 31, 1944
4' Sheets-Sheet 4
Patented Nov. 12, 1946
2,410,888
IU'NlTED STATES‘ PATENT OFFICE",
METHOD'AND APPARATUS FOR MOLDING
THREE-DIMENSIONAL‘ SHAPES FROM
DRAWINGS
Otto H. Lucy, Los Angeles, Calif., assignor t0
Murray-Lucy-Marvosh - Company,
Pasaden
Calif., a partnership
Application March 31, 1944,‘ Serial No. 525L033
17 Claims. (o1. 2'5_118)
1
,
This invention has to do with the art of pro-'
ducing shapes or contours and has for one of its
objects the developing andproducing of . any de
sired contour or shape without the use of con
ventional templates.
~
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,
2
‘
-
.
?ecl; form," of contour-de?ning pin, inside eleva
tion;
.
Fig. 11 is a fragmentary section showing- an
otherv modi?ed form of contour-de?ning pin;v
Figs. 12,13 and Marc perspective, side eleva
tion and end views, respectively, showing a fur
ther variational v‘form ~of contour-de?ning pin;
'
It is another object of my invention to provide
apparatus for transferring ?at drawings or refer
ence- lines to three-dimensional shapes.
Another object of the invention is to provide
novel ‘apparatus for producing a shape and pro
Fig. 15 is a fragmentary-view of amodi?edform ‘
of pin-locking means; »
-
Figs. 16 and 17 are side elevation and longitu
vidingin the produced shape reference indicia to
dinal sectional'views,trespectively, of a further’
be subsequently employed as a ?nishing guide
variational form ofv contour-de?ning pin;
Fig. 18 isa view similar to» Fig. 17 showing a
and forother checking purposes.
.
Another object is to provide method and appa
ratus for producing from ?at drawings three
drill disposed axially of the pin;
dimensionalshapes which'conform in contour to
the drawings with extreme accuracy.
Another object is to provide in such apparatus
means for providing the shape with a base which
-
Fig- 19 is- astill further variational form of
15'
pin; and
._
.
Figs. 20,- 21'and 22 are perspective, side eleva
' tion andend elevations, respectively, showing a
modified form of setting block. .
may be employed as a, reference for checking and 20.
,
Referring now tothe drawings,- I show a body
or frame providing channeled side members 5.
The frame is here ‘illustrated as being of metal,
cast in one integral piece, but, of course, may be
composed. of separate frame members suitably
measuring layout Work in relation thereto.
My invention has still further objects and cor
responding advantages, the nature and‘ identity
of which will become apparent to those skilled in
assembled. The frame is'supported upon corner
the art‘ from the following detailed description
legs 6 which may be secured to the frame asb-y
of a‘presently preferred embodiment which I have
dowels ‘l.
'
chosenlfor purposes of' explanation. In this con
Along the top‘ surface, adjacent the inner edge,
nection, however, I wish it understood that my
of. each of the sides 5,_I provide- a scale of cali
invention, in ‘its broader aspects as de?ned by the
appended claims, is not‘ to be con?ned to the 30 brations 9, here shown as being formed into the
sidesalthough, of course, the scale may be other
details'and association of parts now to be par
wise applied.
ticularly described, since it is'capable of being
A plurality of pin-retaining contour transfer
ring elements or frames generally designated at
Illv are disposed in parallel relationship trans
practiced in~other modi?ed forms of apparatus
which the following description will suggest to
those working in the‘ art;
'
For purposes of the ensuing description I shall
refer to the accompanying drawings, in which:
Fig. 1~is a’perspective of'my apparatus with a
matrix- and a shape disposed thereon, some parts
40
being broken away for'illustra'tive purposes;
Fig52 ‘is a top plan'view; '
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,
,
,
.
Y
,
Fig. 9 is a perspective view showing a setting’
.
Fig. 10 is a fragmentary view showing- a modi
to the top- barlby anattaching flange I8a (Fig. 4).
Each collar is split and .is adapted to be clamped
’
,
H . ,
, The top end... of each of‘ the vpinsor spikes, I'l
tapers to a point as shown at Ila, and ,a washer‘
23 maybe loosely placed over the pointedendso
as ‘to. be rockable thereon Whenever necessary,
to accomplish the proper-contour as will be here
Fig. 7 is a view taken on line 1—1 of Fig. 6;
Fig. 8 is a View taken on line 8-—8 of Fig. 6;
block;
adapted to be clamped in any set position relative
to the bars by means o-fa clamp collar. l8 secured
about ya pin'as by a screw. [81).
Fig. 6 is a top plan View showingv the setting
element;
Spaced-pairsofregisteringhole-s iii are provided
throughthe bars l5,‘ 15a and through each ‘pair
of registering holes a contour-de?ning pin or ‘
Fig. F'is'anfenlarged fragmentary view show- 8
mg, in side elevation, one of the conto-ur-éde?ning
pins;
larframe having- a top bar 15 and a bottom-bar
15a secured together ,,by- end members [5b.
spike i‘l adjustably extends... Eachof the pins is
Fig‘. 4’is ‘an‘enlarged‘section taken on line li—4
of'Fig. '3‘;
Versely. between the sides 5..
Each. of the elements I 0. consists of a rectangu
inafter explained. .
55
e
, »
,
.
Theiendsuof' the. top bars l5 have extensions 25
2,410,888
3
resting on the sides 5 and the inner edge 25 of
each of the extensions is alined with the longi
tudinal axis of the openings 15 and the pins l1.
4
the setting block is adapted to be registered with
the contour line 51 and disposed normal to the
drawing. As shown in Fig. 9, the front face of
the block 54 has a perpendicular reference line
Thus the edge 26, when registered with the scale
55 with which the pointed ends of the respective
9, permits the operator to accurately aline the
pins ‘ll are brought into contact when the block
axes of'the pins with the desired indicia on the
is registered with the contour line 5| at the end
scales 9.
of the pin being set, to thereby register the pin
As best shown in Fig. 3, each of the side mem
end with the line. As each pin 11 is thus set
bers 5 has a depending ?ange 30 whose inner
side surface 3| is beveled. To the left-hand end 10 in the desired position relative to the contour
line, the clamp screw itlb of the collar I8 is
I5b of each frame I pivotally secure, as by a pin
tightened to secure that pin in the set position,
32, an eccentric clamp 33 having a handle por
and the block 54 is manually moved to the next
tion 33a, which clamp eccentrically engages the
adjacent pin and the same setting procedure is
undersurface of the depending ?ange on the
left-hand frame member 5 to positively retain 15 there followed. This pin-setting procedure con
tinues until all the pins ll of a given frame 10 are
the bar extension 25 against the top surface of
the side 5. To the right-hand end |5b of each
frame, I pivotally secure, as by a pin 34, an.
eccentric clamp 35 whose inner side face is bev
eled to cooperate with the beveled surface 3| 20
of the ?ange 30, so as not only to hold the ex-_
tension 25 in engagement with the top surface of
the right-hand frame member 5, but also to pull
the right-hand end I5b of the frame into engage
ment with the ?ange v3|]. Since the frames in
?t between the sides 5 with suf?cient looseness
set and secured at the desired position, after
which the frame In is removed from the table 42
and placed between the sides 5 as shown in
Figs. 1 and 2, with the bar extension edges 26
registering. with the appropriate reading of the
scales 9, which correspond to the relative posi
tion ‘of the contour line on the drawing with
which'those pins have been coordinated.
Then a different contour line on the drawing
50 is used for the setting of the pins of the next
frame and this procedure is followed until there
to permit of free insertion and removal, this co
is a frame If] in position between the sides 5
operation of ‘clamp 35 with the beveled surface 3|
corresponding to all‘the desired contour lines
insures uniform positioning of all the frame ele
ments Ill between the sides 5. To prevent swing 30 on the drawing. Thus, when the pins and frames
are positioned as shown in Fig. 1, the pointed
ing of the elements 10 relative to the sides 5,
ends of the pins I1 collectively de?ne the contour
I provide a third eccentric clamp 3‘! pivotally
of the shape which it is desired to produce.
secured to an extension of one of the ends l5b
Next the washers 23, which function as stop
of a pin 38 for eccentric clamping engagement
with the upper surface of a ?ange 39 provided 35 guides and supports, are placed loosely over the
pointed ends of the pins and a matrix is mounted
on the side 5. Spacers 40 may be provided be
thereon. First, in forming the matrix, I place a
tween the ends I 5b and the clamps 33, 35, 31.
sheet of pliant screen wire 50 over the pointed
It will be observed that the several top bars l5
ends of the pins I ‘I and force the screen down
of the frames I0 are thus disposed in a common
plane on the sides 5 and the pointed ends of the 40 against the washers 23, thus conforming it to
the contour defined by the pins. Next a matrix
pins are adjusted relative to that plane. Before
sheet ‘62, such as a sheet of pliant modeling clay,
mounting the frames ID, with their carried pin
is formed over and conformed to the screen, the
elements, between the sides 5, the pins I‘! are
sheet 52 being forced over the pointed ends of
adjusted so that their pointed ends register with
the respective contour lines of a ?at drawing to 45 the pins until the points of the pins project above
the top surface of the sheet 62 to a slight extent,
be followed, and in Figs. 6, '7 and 8 I show what
of the order of ‘(112 inch. The extent of this pro
I term the setting table for accomplishing this
jection is determined by the extent of final ?nish
adjustment. Here vI show a table or ?at plate
ing which it is desired to perform on the shape
42 whichoppositely disposed angle iron guide
brackets 45 secured thereto adjacent its opposite 50 to be formed on the matrix. I
Before forming, the ?nal shape 65 to be de
side edges by their attaching flanges 46 and bolts
scribed, I provide a suitable base-locating struc
41. I show one of the frames III with its carried
ture for the shape by placing on the sides 5 a
pins laid flatly against the table, with the bar
pair of height blocks 68 upon the tops of which
extensions 25 bearing against the front faces of
the guide brackets. The frame is secured in 55 I rest a straight edge 69. To the straight edge
I secure, as by C-clamps ‘l0, leg members ‘I! whose
position by the clamp 33, engaging the adjacent
free ends are disposed in position'spaced slightly
face of one of the guide brackets and by the
above the matrix surface so as to become em
beveled clamp 35 engaging the beveled adjacent
bedded in the shape 65 when the latter is formed.
surface 46a of the other guide bracket, which
Next the material of which the shape 65 is to
cooperating beveled surfaces draw the left-hand 60
be formed—which typically may be plaster-of
end [51) of the frame against the left-hand guide
bracket 45.
.
.
The drawing or “left”. to be followed, here
Paris or other suitable plastic-is poured or other
wise applied over the matrix 62 and allowed to set
or harden, the free ends of the legs 1| becoming
denoted by thenumeral 50, is placed ?atly against
the table 42 under the adjacent pointed ends of
the pins [1. _First the clamp screws I81) of the
may be desirable to first coat the matrix 52 with
collars are loosened so that the pins may be
a suitable mold-release material.
embedded'in the shape.’ :For some materials it
.
After the shape 55 has set, it is removed from
the matrix. Its outer surface will have small
70 depressions 12 formed by the protruding ends of
the numeral 5|.
the pin l1, and the bottoms of those depressions
A setting block 54, here shown as an angle
delineate the ?nal outer surface of the shape.
iron, is placed loosely on the face of the drawing
Thus in ?nally ?nishing and polishing the shape,
50 so that it may be freely, manually moved from
the ?nisher will remove the surface material to
a position opposite one pin end'to a position op
posite another pin end. The front face 54a of 75 the depth of the depression, which depressions
adjusted axiallythrough the collars. A contour
line to be followed on the drawing is denoted by
2,410,888
5'.
.
serve as a guide" not only for the ?nal ?nishing
being. followed. In Figs. 20-22 I show a modi?ed
operation, but'also' enable the ?nisher‘ to check
the contouragainst the original contour ‘draw
. ances or variations may be simply made.v I Here,
mg;
instead'of the ?xed contact face on theblock to
.
If no such ?nal ?nishingiwork is to ‘be doneon
the set shape, the pointed ends of thepins should
terminate ?ush with'or short of the top surface of
the matrix sheet 62 so as not to form depressions
on:the
shape.
‘
form of setting block I05 by which such'allow
‘
‘
i
betengaged‘ by the pin being set, as before de
scribed, I employ a .micrometer adjustment
wherein the ,micrometer‘ plunger H16 /may be
moved outwardly or inwardly relative to-the front“
face I01 of the block by the conventional microm
In Fig. 10 I show a modi?ed form of pin I‘! 10 eter mechanisms I08. The plunger I06 is non
which is as before described'except that I here
rotatable and has a line I99 registering with the
employ anvauxiliary spike ‘l5 pivotally mounted
on-a ‘collar 16 secured onithe pin.’ Spike v‘l5 af
fords additional support for the matrix inter
mediate adjacent pins l1.
perpendicular center line H0 on the front face
of the block. -Thus' when line I I0 is registered
with the contour line H I of the flat drawing, the
15 relative setting of the pin I1 may-be Varied to
. In Fig. 11 I show a further variational form
any measured extent by axially moving plung
of-contour-de?ningpin8? having a tubular shank
er I06.
_ I claim:
89a; axially adjustably mounted. on a pin 8|,
which’ latter may be rigidly. attached to the bar
1-. Apparatus forgforming shapes comprising,
t~5qof~a frame element l0. A set screw 82, or 20 in combination, a plurality of pins adapted to
othersuitable locking means, maybe employed
have their adjacent ends adjusted into positions
to. retain the pin in‘ adjusted position.
coordinate with 1a contour line of a drawing
~ In some cases, particularly where the pins are
whereby‘ collectively tode?ne the contour of said,
being coordinated to contour lines of relatively
line, setting means for so adjusting said'pins,
smallradius, to obtain extreme accuracy it may 25 pin-retaining means securing the pins in assem
be necessary to employ objectionably'long tips on
bly in said adjusted position and a matrix made
the‘ spikes. In Figs. 12, 13 and 14 I show a modi
of sheet material formed to a shape substantially
?ed form of pin which overcomes this necessity,
conforming to the contour line de?ned by said
and also‘ may eliminate the stop washers 23.
adjacent ends of the pins, the pin ends being
Here the shank of the spike 85 has a longitudi 30 positioned to project above an upper surface por
nally'flattened portion 85a which prevents rota
tion. of the‘matrix surrounding the pin ends.
tion of the spike relative to the carrying bar
2. Apparatus for forming shapes comprising, in
when ?tted in a hole in the bar which has like
combination, a plurality of rows of pins, the pins
cross-sectional shape. The top, pointed end of V of» each‘ row being adapted to have their adja- .
the spikeisv axially split to provide a flat face 35 cent ends adjusted into positions ‘coordinate with
86 and a spherical portion 81. Thus the tip may
a contour line of a drawing whereby collectively
be-accurately registered with the contour line 88
to define'the contour of said line, a plurality of
of a drawing (see Fig; l4)l-.regardless of the length
separate pin-retaining members, each of said
of the tip end. The relatively increased diameter.
members securing the pins of ‘a row in adjusted
of the'shank portion provides an~annular stop v position, a body providing means supporting'said
shoulder~89 for the matrix.
-
.
separate pin-retaining v‘members in a common‘
In Fig; 151 show a pin or spike mounting which
plane and in assembled position whereby the ad
jacent ends of the pins of the several rows collec
before described. ‘ Here I‘merely ‘employ a set
tively de?ne a composite shape, and a matrix
screw 96‘ thre'adedly mounted in a lateral hole 45 supported on said adjacent ends of the pins‘ of
in the bar‘ 15, the inner'end of the screw being
the several rows and‘ conforming to said de?ned
adapted to engage the pin H to» secure the latter
composite shape, the pin ends projecting from a
against axial movement.
,
'moldingsurface of the matrix.
While‘ I'have'described'the forming of a plastic
3. In a support‘for a molding matrix, a frame
matrix, myapparatus may be'used .to form veneer 60 having sides, a removable cross member having'a
matrices. In Figs. 16-18 Ishow a modi?ed type‘
planiform side support portion, said cross'mem
eliminates the necessity of the clamp collar l8
of contour-de?ning pin 92 axially adjustably dis
her being supported at its respective ends by the
posed in frame members l5, [5a as before de
respective? sides, a plurality of upright pins ax..
scribed. Here,.however, the pin is tubularand
ially adjustably carried by and spaced‘ apart
frustum shaped at its top end. First a hole is 55 along? the cross member, said pins presenting up
drilled in the veneer V by vinsertinga drill 93
per tip portions collectively de?ning a contour,
through the-frustum of the'pin' and rotating the
locking means carried by the cross‘member for
drill‘asby a ?exible shaft 94. The drill has a
locking'engagement with‘ the pins, and a matrix
stop shoulder 95 to limit the depth of the drilled
support element adjacent the upper end‘ of each
hole. After each hole is drilled, the vdrill is re 60 pin whereby the cross member is adapted'to'be
moved and’ a tip member 96 is inserted in the
removed from the frame and supported on its
- axial vholethrough the frustum,-which tip mem
side support parallel to a planiform drawing of ‘a
ber. engages‘ in the hole in the'ven'eer previously
contour line, and the pins adjusted to'have an
made“ by the drill.
. '
.
end portion of each positioned directly above a
In Fig. 19'I show a further modi?ed form of 65 point of the contour line‘. thereby collectively to
pin lllilwhich is like thatxof-Fig's. 16-18 except‘
de?ne a contour line similar to that of the draw
that itrhasimoun'ted'thereon, as by a' bracket llll,
an'auxiliary. pin “32 which is likewise adapted fo
4: Apparatus‘ for-forming shapes, comprising a
mg.
drillingand= to- receive a‘ tip member 96.
>
.
.
'
frame having sides, a cross member supported at
In forming some shapesv it'may be desirablev 70 its‘lrespective ends by the 'respective'sides, a plu
to allow, in the setting of the contour-de?ning
rality‘of pins carried by and spaced apart along
pin's,i'for."a springback of the shape after it is re
the‘cross'member, said pins presenting end por-'
moved from the matrix, or it may be desired to
set the pins to de?ne a contour of a slightly dif
tions collectively de?ning a contour, and a matrix
mounted upon said end portions of the pins and
ferent radius than that of the line of the drawing 75 shaped in conformance with said contour, said
2,410,888:
7
matrix being adaptedto receive an unset plastic‘
material}
'
‘
‘bi-Apparatus for forming a shape, comprising
a ‘frame having sides, a cross member supported
8
set'shape-forming plastic, indicia-forming means
projecting through the matrix vsurface to form
guide indicia on the shape, said means being ad
justable whereby to be positioned coordinate with
l
at 'its‘respective ends'by the respective sides, a U! the contour lines of the drawing. ‘
11. In shape-forming apparatus, a matrix
plurality of pins carried by and spaced apart
shaped coordinate with contour lines of a draw
along‘the cross member, said pins presenting end
ing, ‘said matrix being adapted to receive an unset
shape-forming plastic, indicia-forming means
shaped in conformance with said contour, said 10 projecting from the matrix surface to form guide
depressions in the shape, said means being axially
matrix'being retained by the pins in ?xed posi~
adjustable whereby to' be adapted to be positioned
tion to‘ retain an unset plastic material until the
portionscollectively de?ning a contour, a matrix
mounted upon said end portions of the pins and
material sets to produce a shape conforming to
said contour, and means for retaining a base for
coordinate with the contour lines of the drawing.‘
12. The method of using pins and a matrix to
the shape, consisting of a cross bar and means
form a three-dimensional shape in conformance
with a flat contour line drawing, which com
supporting the cross bar in position spaced above
the form.
prises: assembling the pins with their tip ends
coordinate with the contour line of the drawing,
forming the matrix on and in conformance with
pending longitudinal ?angev having a beveled 20 the contour de?ned by said tip ends of the pins
and applying an unset plastic to the matrix.
outerside surface, a cross member extending be
13. The method of using spikes and a matrix to
tween the sides and having end portions resting
6. In apparatus for forming shapes, a frame
having sides, one of said sides presenting a de
on the top surface of the sides, an eccentric clamp
rotatably carried by the cross member and hav
ing a beveled inner side surface engageable with
the beveled surface of the ?ange.
'7. In a support‘for a molding matrix, 'a body
having sides, a removable cross frame having
spaced upper and lower bars, said cross frame
normally being disposed transversely between the
form a three-dimensional shape in conformance
with‘a flat contour line drawing which comprises:
assembling the spikes with their pointed ends co
ordinate with the contour line of a drawing, plac
ing the matrix onto and in conformance with the
contour de?ned by the pointed ends of the spikes
and applying an unset plastic to the matrix.
- 14. The method of using spikes and a matrix
sides and having a planiform side support por
to form a three-dimensional shape in conform
tion, aligned spaced pairs of registering openings
ance with a ?at contour line drawing which com
_ prises: assembling the spikes with their pointed
‘ends coordinate with the contour line of a draw
through the upper and. lower bars, contour-de
?ning pins adjustably mounted in the respective
pairs of openings, clamp means on the cross 35 ing, placing the matrix onto and in conformance
with the contour de?ned by the pointed ends of
the spikes until the pointed ends of the spikes
project above the surface of the matrix and ap
?ning a contour, means for locking the cross
plying an unset plastic tothe matrix.
frame in adjusted position between the sides, and
15. Apparatus for forming shapes comprising
a matrix support element carried by the pins in 40
aplurality of pins each having a longitudinal
downwardly spaced'relation from the contoured
bore adapted to pass a drill, means for adjustably
tips thereof.
frame releasably lockably engaging the pins, said
pins having pointed upper ends collectively de
8."Apparatus for forming shapes, comprising,
in combination, a plurality of bars, a plurality of
securing the pins in relative axially adjusted posi
tion de?ning a contour, a pointed tip member
contour-de?ning pins carried by and disposed 45 carried by each of the pins, each of the tip mem
bers having a shank portion engaging in the bore
transversely of each bar, the pins of each bar
of the pin by which it is carried, and a matrix
being axially movable relative to said bar where
supported on and retained by the tip members in
by their tips may be moved into adjusted posi
position conforming to the shape de?ned thereby.
tions relative to the bar, means for locking the
pins in such adjusted position, body means sup 50 16. In shape-forming apparatus a plurality of
indicia-forming points arranged to de?ne a con
porting the several bars in a common plane for
toured shape, means supporting the points in
horizontal adjustment relative to each other, and
arranged position, and a matrix shaped substan
a pliant shape-forming matrix supported on and
tially coordinate with the contoured shape de
conforming to the shape de?ned by the tip ends
of the pins, the pin ends penetrating the matrix 55 ?ned by the points, at least some of the points
projecting from a molding surface of the matrix,
to locate a molding surface of the matrix with
said matrix being adapted to receive and mold
respect to the pin ends.
an unset shape-forming plastic with the project
1 '9. Shape-forming apparatus comprising a base
ing indicia-forming points extending into the
providing spaced side members, bars supported in
spaced parallel relationship between the side 60 plastic to form guide indicia in the molded shape.
17. The method of molding a shape by using
members, a plurality of pins carried by and
pins and a deformable molding matrix compris-V
spacedapart longitudinally of each bar, said pins
ing so assembling the pins that their tip ends are
having tapering tip end portions collectively de
relatively disposed to de?ne a contour, providing
?ning-a contour, and a shape-forming matrix
mounted on the tapered end portions of the pins, 65 a matrix support below the contour de?ned by
the pin tip‘ ends, deforming the matrix down
the extreme tip end portions of the pins pro
wardly with respect to the pin tip ends onto the
jecting through the top surface of the matrix
matrix support, with the pin tip ends projecting
whereby to form guide recesses in a shape formed
from a contour de?ned by a molding surface of
10. In shape-forming apparatus, a matrix 70 the matrix, and applying an unset moldable plas
tic to the matrix.
‘
shaped coordinate with contour lines of a draw
OTTO H. LUCY.
ing, said matrix being adapted to receive an un
on the matrix.
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