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Патент USA US3079741

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March 5, 1963
e. o. RAWSTRON ETAL
3,079,731
GENERATION OF SHAPED SURFACES
Filed Feb. 16, 1960
3 Sheets-Sheet 1
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Inventors
6v 0. Ha ws from
H. 5 Reason
By
.
W/
,
Attorneys
March 5, 1963
G. o. RAWSTRON ETAL
3,079,731
GENERATION 0F SHAPED SURFACES
Filed Feb. 16, 1960
s Sheets-Sheet 2
lnveniors
G 0. Ra ws iron
1?. 6'. Reason
$24
A ttorn e ys
March 5, 1963
e. o. RAWSTRON ETAL
3,079,731
GENERATION OF SHAPED SURFACES
Filed Feb. 16, 1960
3 Sheets-Sheet 3
F/G8.
Q2Q3O4
H5 (I
A
Inventors
0. v0. 93 ws {PM
1?. 5 Reason
Attorneys
United States
,,
RC6
1
3,?79,73l
Patented Mar. 5, 1953
2
combined polar and rectangular coordinates generated by
3,079,731
GENERATION 0F SHAPED SURFACES
George Ormerod Rawstron and Richard Edmund Reason,
Leicester, England, assignors to Rank Precision Indus
tries Limited trading as Taylor, Taylor & Hobson,
Leicester, England, a company of Great Britain
Filed Feb. 16, 1960, Ser. No. 9,087
Claims priority, application Great Britain Feb. 18, 1959
14 Claims. (Cl. 51-—58)
rectangular coordinate relative movements.
‘
The relative correcting movement is preferably con
trolled by a cam device shaped in accordance with the
deviations of the desired surface from the basic surface,
whether such basic surface be plane, or spherical. Prefer
ably, the shape of the cam device is determined inv ac
cordance with a chosen large multiple of the deviations,
and the correcting movement is derived therefrom through
a transmission mechanism having a reduction ratio de
This invention relates to apparatus for producing on a
workpiece a surface of revolution which deviates from
pendent on such chosen multiple, means being provided
for effecting relative movement between the cam device
a basic surface by relatively small amounts at different
and the transmission mechanism in accordance with the
radial distances from the axis of symmetry. Although
relative traversing movement.
not limited thereto, the invention is more especially in 15
Whilst other forms of cam device may be used, it is
tended for the generation of what are sometimes known
preferred to employ an optical cam device comprising a
as “?gured” surfaces on optical elements, for such sur
sheet bearing a curved line which contrasts in respect
faces have hitherto been formed by ?rst producing a
of light-transmitting properties with the background con
rough approximation to the desired surface, for example
stituted by the adjacent portions of the sheet, the relative
by moulding or by a lapping process, and then ?nishing
correcting movement being derived from relative move
the surface by a laborious “?guring” process which calls
ment between such cam device and an optical unit for
for highly expert skill and involves repeat-ed optical test
following the curved line on the sheet. Such optical unit
ing between hand rubbing operations until the desired
may act to direct a small beam of light through the
surface has been formed with a su?icient degree of ac
optical cam device on to photoelectric means sensitive
curacy. The basic surface may be a plane surface, and
to lateral displacement between the beam of light and
in such case the invention is suitable, for example, for
the curved line on the sheet, electrical means being pro
the production of the opticalcorrecting plates known as
Schmidt plates. Alternatively, the basic surface may be
a spherical surface, and there arev many known instances
‘in the optical objective art in which use is made of
aspheric lens surfaces which deviate by only small
amounts from a basic spherical surface.
The present invention has for its object to provide a
vided operative in accordance with the output of the
photoelectric means to effect relative movement between
the optical unit and the cam device for correcting such
lateral displacement. The relative movement between
the cam device and the optical unit is preferably effected
by a reversible electric motor whose direction of rotation
is controlled by the photoelectric means, whereby such
simple and efficient apparatus for generating such sur
relative movement consists of small oscillations from one
faces whereby the surface is initially formed with so high 35 side to the other of the correct relative position de
termined by the cam device.
a degree of accuracy as to render unnecessary the expert
?guring process hitherto required.
The invention may be carried into practice in various
In the apparatus according to the present invention, the
ways, but some convenient alternative practical arrange
workpiece is roatated about its axis of symmetry, and
ments according thereto for accurately generating'a sur
interrelated relative movements between the workpiece and 40 face o-f revolution deviating by relatively small amounts
the tool are effected in two coordinate directions respec
from a basic plane or spherical surface, for example the
tively parallel to and at right angles to a ?xed reference
surface of a lens'or other optical element, are illustrated
‘axis, which coincides with the axis of symmetry in at
somewhat diagrammatically in the accompanying draw
least one position of such axis, the relationship between
such coordinate measurements being dependent upon the
shape of the basic surface and being controlled in ac
cordance with the deviations of the desired surface from
such basic surface.
ings, in which
FIGURE 1 is a plan view of one arrangement in which
the basic surface is a plane surface,
'
‘
FIGURE 2 is a front view of the arrangement of FIG
URE 1,
-
,
The basic surface may consist of a plane surface at
FIGURE 3 is a sectional view of the workh'older use
right angles to the axis of symmetry, and in such case, 50 in the arrangement of FIGURES 1 and 2,
'
preferably, a relative traversing movement between the
FIGURES 4 and 5 are partial plan and front views illus
workpiece and the tool is effected in a direction at right
trating apparatus for generating a cam device, for use in
angles to the axis of symmetry, and a relative correcting
an alternative arrangement,
movement controlled in accordance with the deviations
FIGURE 6 illustrates in plan view the alternative ar
of the desired surface from the basic plane surface at 55 rangement employing the cam device of FIGURES'4
the various radial distances from the axis of symmetry is
and 5,
i
effected in a direction parallel to the axis of symmetry.
‘ FIGURE 7 is a front view of the arrangement of FIG
Alternatively, the basic surface may consist of a
URE 6,
spherical surface centered on the axis of symmetry, and
FIGURE 8 is a sectional view on the line 8—8 of
in such case, preferably, a relative movement controlled 60 FIGURE 6,
in accordance with the shape of the basic surface is super
imposed on a relative correcting movement controlled in
accordance with the deviations from the basic surface to
determine the relationship between the coordinate rela
tive movements. Conveniently, the control in accordance 65
with the shape of the basic spherical surface is effected
by relatively guiding the two coordina‘e movements
along a circular path. The relative correcting movement
in accordance with the deviations from the basic spherical
FIGURE 9 is a diagram of an electric circuit used in
the arrangement of FIGURES 6-8,
FIGURE 10 is a fragmentary view illustrating the form
of cam device used in the arrangement of FIGURES 6-8,
and
'
FIGURE 11 illustrates a modi?ed arrangement for use
when the basic surface consists of a spherical surface.
In the arrangement of FIGURES 1 and 2, in which the
basic surface is a plane surface at right angles to the axis
surface may be effected in a direction parallel to the ?xed 70 of symmetry of the desired surface, which may for in
reference axis, whereby the superimposed relative move
stance be the surface of a correcting plate of the Schmidt
ments are interrelated in accordance with a system of
type, the workholder consists of a ?tting A on the end
new
._
.
3
.
.
accurately divided movable [glass scales L1, L3, one of
which L1 extends transversely to the axis of the horizontal
driven through suitable coupling meansA}.3 by an electric
spindle A1 and the other L2, parallel thereto. These scales
L1, L2 each move at right ‘angles tor-their lengths‘and are
guided in their movements by, means of projectionsLa,
L4 sprinO-pressedagainst the accurately polished edges of
a rectangular glass reference plate L5 secured tothe base.
inotor A4. ThespindleAlis so. mounted infits housing as
,togybe substantially wholly. devoid of anyshaKein its rot-a
tion,; for example in one orother of theways described, in
{United StatesPatent No. 2,791,170. It is likewise im
fportan-t to ensure that the workpiece C is accurately cen
tered: on'the axis ofjthe spindleAK: In the case of a
Schmidt plate, the .workpiece C will usually consist of a
fcirculardisc of glass carried in a cell. To ensure accuracy
4
slide E carries a microscope L for viewihg'a'pairuof c
of an accurate spindle A1 journalled horizontally in a
housing A2 secured to a ?xed base B, the spindle being
10
or mounting-on the spindle, the cell C1 is provided (as
shown. in FIGURE. 3)_ with accurately ‘ground. locating
.faces Cj't;which cooperate with complementary faces A5
The transverse scale L1 is moved in the axial direction by
means of a projection E‘? on the cross-slideEcarryinga
pair of rollers E5 between which a rod L6 carried by the
s:ale L1 engages. The axial scale L2 is similarly moved
in the transverse direction by means of ‘a pair of rollers
E6 on the cross-slide E between which arod L'lbcarr‘ied
by thevscaleL2 engages. The microscope L is sejpnst
tioned as'to be sighted won ‘the ‘point of intersection orgnre
provided on theendtof the spindle A71, the cell. being sc
cured on a loose screwthread C3 so .asptorclamp such faces
.inengagement. “The celleCv1 likewise has accurate seating
v‘faces’ C4 for recciving-the-glass disc C which'will usually
two scales L1,_L2., and it will be clear that it will remain
sighted thereon inv allpositions of the cross-slide E, as
be held against such faces by wax in recesses 7C5.
the'scales move relatively to one another.
. ..
The toolholderD is secured to a cross slidelE which can 20~
which the measurements of the deviations ,of the desired
surface from the axis of symmetry. are calculated, the
larly on balls F2 on guide tracks B2 on a ?xed base slab
zero point of the stale being 'so'positioned .thatwhen' it
is in the centre of vthe ?eld of ‘the microscope L, the cross}
slide E. is in the, correct position for the .tool D1 to._.b'e
B1. ;The two sets oi guide'tracks F1 and B2 lie accurately
agrrghtianggs-m one another, those on the base, slab B1 -
beingfaccurately parallel to, the axis of the horizontal
spindle=A1,ca-rryingthe workholder A. The carriage F
accurately aligned on theho'rizontal ~spindle axis.._. The
axial scale Lzis similarly graduated and inQorder ‘to’. get
highly accurate sub-divisions of the scaleldivisions, the
microscope L ‘is provided with an adjustable Vernier
30
tromthei, carriage F having- amicrometer ?tting F4 for
fine adjustment of the-‘axial position of the carriage rela
graticule.
,
.
calculatedv measurements for an individual Schmidt plate,
the connecting rod lfondrivingthe cross¢slide E is ?rst
adjusted alongthe crank arm H‘i'on the vertical spindleH1
to give a'suitable'relationship between the angular rotation
ofthe horizontal table H ‘and the transverse movements
: ‘The lever G is driven atits other end in accordance 35
_;wi.th the deviations of the desired surface from the'basic
driven through worm gearing H2 by .another electric
“motor.
[This spindle _H1_carries aerankarm H4 to
.
mm, for ‘setting inseam Kin acco’r’d'a'né'e with the
tively tothe lever,v a; springiG2 being; provided between
the lever andthe carriage to hold the parts in engagement.
plane surface under the control of a cam device carried
by a horizontal table H mounted on .a vertical‘spindle H1
I. I
spacedgraduations appropriate to the radial positionsrat
slide. for example on three bearing balls E1._ on, guide
tracks F1 on acarriage YF, which-in turn can slide simi
,ismoved. along its-guide tracksjBz by a lever, G through
‘a connecting rod G1 havingltrounded ends abutting re
;spectivelyagainst the-lever G andnagainst a projection F3
. _
The transverse scale L1 is ?nely‘divided into. equally
ofthe cross-slide E for an adequate length of cam in rela
tion to the maximum radius of the desired Schmidt plate,
40 .the total angular, movement vof the crankar'm?lover
the WhoIelength of‘cam K vbeing not greater than about
-which one endof .a connectingrod] is adjustably con
120., degrees, with. the beginning and end. positions, more
‘_ or less equally'spaced on either‘sid'e of a radial; line from
,the vertical spindle axis parallel to the horizontal__'sp_indle
,axis. .The length of 'theconnecting rod J’ isscorrespon'd
,inglyadjust'ed to give the desiredi'vr'elationship‘between
nected, the other end of such connecting rod being em
.ployedto drive the cross-slide, E on its guide tracks F1
{acrossthecarriage
A,micrornetery?tting.J1 is pro
_,.vided for adjusting the effective length ol:'_ the connecting
“rod J. In order to avoid errors in the drive'of the cross
Ith'ejzero points. of the transverse 'scaleLl. and of the
slide E duetovarying inclination of the connecting?rod
crank arm ‘H4. The leverratio is also chosen to suit the
‘I, this rod is nbt connected directly to thercrossfslide, but
‘magnitude, of the, deviation calculationgthe'lever pivot
'to a bar I2 which, extends parallel to'ithe-vaxisof‘the hori
,
s I _
zontal s'pindle'A1 and engages between two pairs of roll 50 (33' being suitably adjusted.
_ The cam striptK, is now, clamped in’ position on the
:ers E? on 'rthecross-slide E, the. bar]? being constrained
against longitudinal movementgbyjmeans of a roller-J3
horizontal Qtable Hstarting with the. zero point, thetable
being rotated and with it the cross-slidegE moved step, by
, engaging in ,a'?xedslot B3 extending at right ‘angles to
v the directionjof the horizontalmspindle axis.
1
The cam device may be arranged in ,vanousways, but
,in one simple form consists ‘of ,aw?exible steel strip K
55
vstep'in accordance with the- g'raduatio'nson the transverse
fjscale’ L1 viewed through the microscope?Lthe cam clamps
‘K1, K2, .. ., . lheing'adju‘st'ed one by one to the correct posi
tionsjrto, suit the chosen, multiple of ‘the. deviations, as de
_termined by, the calculated deviation _mea'sutements
on the axial scale vL2 viewed through the ‘microscope L
; clampedv at alarge vnumber ,of;,close1y spaced points, such’
as K1, K2, along its length to the horizontal table;
_\These clamps K1,
‘are spaced approximately
p with the 'aidof the vernierigraticule, the movements‘ of the
carriage VF corresponding ,to such measurements being
round an arc of a circle centered on the vertical spindle 60
- H1 andcan be accuratel-yjadjusted radially With-respect
‘thereto to give the desired can't shape. These adjustments
_ are made in accordance with calculated measurements de
?ning the deviations of, the'desizred surface from the basic
transmitted to the cam Kthrou‘gh the lever G to deter
L mine the cam positionsforrclamping. v\When the camx
,,has, been, accurately. clamped in its correct, position
. plane surface.- ..When, asWill usually be the case with a 65
,Schmidtbplate, these deviations are very small, the actual
cam shape is preferably determined in accordance-with
. a chosenlarge multiple‘ of the deviations, for example two
hundred timesthe ‘calculated deviations, the lever Grbeing
garrangedlto give a 200:1 reduction ratio,_to provide the
a correct deviations in the actual movement of the carriage
Thelever pivot G3 is preferably adjustableto enable
the reduction ratioto be varied, as. may be; convenient.
For the purpose of setting the camK. in accordance with
"the calculatedmeascrements of the deviations,'the cross 75
throjughouathetool Dlrlis insertedinthe toolholder Din
its ‘correct position. and the cross-slide. Elis moved so that
,rthetooltlies justto? the edge of'thelworkpiece ‘disc C,the
micrometer ?ttingtF4 onltherprojection F3. ‘from the car—
, riageF beingwadju'sted to move; the tool D1._ axially tothe
position ,cor'responding to the desired depth of cut on the
:fdlsg; Whilst a‘ sharply pointed diamond tdoliis usually
> preferable, it‘rnay belpracticable
someviinstanceis to em
__plo_y a driven diamond wheel,~preferably using the rela
tively sharp edgethereofr.
-
The apparatus is now ready‘for‘the'actual 'g'er'iera‘tion
5
3,019,???
of the Schmidt plate surface on the disc C, and the two
6
closely spaced positions accurately determined by ob
electric motors A4, H3 are started vup respectively to drive
the horizontal spindle A1 and to traverse the cross-slide E
at the appropriate speed across the disc C from the edge
to the centre. As this traversing proceeds, the lever G,
serving the graduations on the transverse scale L1 through
the microscope L. In each position, the micrometer
head N6 is operated in accordance with the appropriate
calculated measurement, and when the photographic unit
which engages with the cam K in a substantially radial
N has thus been positioned the shutter N7 is opened to
direction relatively to the vertical spindle H1, is moved
expose the small circular portion of the sensitive photo
by the cam K so as to transmit to the carriage F the cor
graphic plate M on which the light from the aperture
rect deviations, thereby ensuring accurate generation of
N1 is focussed, thus recording one of the desired round
the desired surface on the dis: C.
10 dots on the plate. It should be mentioned that an
This arrangement may be modi?ed by dispensing with
opaque screen (not shown) is provided to minimise risk
the axial scale L2 altogether and providing a micrometer
of fogging the sensitive plate M by the light used for
to measure directly the chosen multiple of the calculated
viewing the scale L1 and setting the micrometer head
deviation measurements for setting the cam K in position,
N6, the plate M itself being slow in order still further
the micrometer measurements being effected in a radial 15 to minimise the risk of fogging.
direction with respect to the vertical spindle H1, in the
When all the dots have been recorded, the sensitive
position in which the end of the lever G engages with the
plate M is removed and developed, to produce a photo
cam K. Such modi?cation will be described below with
reference to FIGURES 4 and 5.
graphic negative on which a curved line of dark or
opaque round dots M8 (FIGURE 10) appears on a
In the foregoing arrangement the cam device is in the 20 translucent background, such line of dots being shaped
form of a thin ?exible steel strip K, but it is usually
in accordance with the calculated deviations of the de
preferable in practice to employ an optical cam device
sired Schmidt plate surface from the basic plane surface.
consisting of a dark or opaque line on a translucent sheet
or a translucent line on a dark or opaque sheet in con
Such photographic negative M is preferably itself used
on a projection H5 from the horizontal table H. such
of light 02 and a lens system 03 for directing a vertical
concentrated beam of light from the source 02 through
the aperture 01. If the photographic negative is used
as the cam device, this aperture 01 is made larger than
to constitute the optical cam device, but it will be c‘ear
junction with an optical follower unit. It is especially 25 that, if it is preferred to use a cam device with translucent
convenient to employ the arrangement forming the sub
dots on a dark or opaque background, the negative may
ject of the present applicants’ copending United States
be photographically printed on to another precisely simi
patent application Serial No. 857,816, now abandoned,
lar plate (likewise provided with the three ground por
wherein such line is made up of a series of small dots at
tions on its edges) to form a photographic positive, which
equal intervals, in the positions de?ned by the calculated 30 can be used as the optical cam device. The plate
measurements, the dots preferably being of such a size
‘(whether negative or positive) is then replaced in posi
in relation to the interva's between dots that they overlap
tion on the projection H5 from the horizontal table H
one another and form a continuous line, the actual cam
against the locating pins M4, M5, M6, so that it will
' line consisting of the line of centres of the dots.
occupy exactly the same position as before. The photo
Such optical cam device can be manufactured in vari 35 graphic unit N is now removed from the long pivoted
ous ways, but it is preferred to make it photographically
arm N5, to be replaced by the optical follower unit,
in the manner forming the subject of the present appli
which cooperates with the optical cam device in prac
cants’ United States patent application Serial No. 857,
tical use.
817. For this purpose, as shown in FIGURES 4 and 5,
Such optical follower unit 0 (see FIGURES 6, 7 and
an unexposed sensitive photographic plate M is mounted 40 8) also includes a small circular aperture 01, a source
‘projection being provided with an arcuate slot H6 (for
a purpose to be described below) over which the plate
M rests. The plate is provided with two accurately
ground surfaces M1, M2 on one of its longer edges and 45 that N1 used during photographing, for example having
a third ground surface M3 on one of its end edges, these
twice the diameter thereof. Although the source of light
three ground surfaces M1, M2, M3 engaging with three
02 and the lens system 03 may be mounted vertically
' locating pins M4, M5, M6 on the projection H5 from the
. above the aperture 01, it is found more convenient, for
table H, whereby it can be positioned with accuracy
reasons of compactness, for the light and lens system
thereon. Clamps M7 are provided to hold the plate M
to have a horizontal axis, a small mirror 04 inclined at
in'the position determined by the locating pins.
45 degrees to such axis being provided to de?ect the
A photographic unit N, comprising a small aperture
beam vertically down through the aperture 01. The fol
N1 within a closed casing N2 which also houses a source
lower unit 0 also includes a beam-splitting device 05,
of light N3. a condensing lens N4 for concentrating the
lying vertically beneath the aperture 01 with the optical
I light on the aperture N1 and an objective N9 for focus
cam device M between them, the arcuate slot H6 in'the
sing the aperture N1 on the photographic plate M. is
projection H5 from the horizontal table H thus serving
movably mounted so that the vertical optical axis of the
to permit the beam of light through the aperture 01 to
beam of light passing through the aperture N1 can move
pass through the optical cam device to the beam-splitting
in a substantially radial direction with respect to the
device 05, which acts to deflect two parts of the beam
vertical axis of the horizontal table H. Since, however, 60 respectively
on to two photoelectric cells 06, 07, also
its total movement is quite small, it will su?ice for it
carried by the follower unit 0. The operative beam
to be mounted on the end of a long pivoted arm N5.
The movements of the unit N are controlled by a
micrometer head N6, whereby such movements can be
effected with a high degree of accuracy in accordance
with calculated measurements. A shutter N7 is pro
vided in the casing of the photographic unit N, so as
splitting plane of the beam-splitting device 05 extends
tangentially with respect to the vertical axis of the hori
zontal table H. Whilst the beam-splitting device 05
may consist of an ordinary beam-splitting prism with its
operative edge tangential with respect to such vertical
axis, so that the two partial beams to the two photocells
normally to shut off the light from the aperture N1, this
shutter being operated, for example by a press button
pass radially, inwards and onwards, with respect to such
N8 on the casing, to permit the light to pass from the 70 axis, it is found more convenient to use a different form
aperture N1, when desired.
of beam-splitting device, which will de?ect the two partial
This device is operated in a manner generally analo
beams in opposite directions parallel to the beam-split
gous to that above described for the setting of the steel
ting plane. This consists (as shown in FIGURE 8) of
strip cam K. Thus the table H bearing the photographic
two similar re?ecting prisms side by side with their in
plate M is rotated step by step through a number of 75 clined re?ecting surfaces facing in opposite directions,
steal
.
beam-splitting plane.
.
,
.
,
current of the valve. The?contacts of the relay Q5,
N,'care being. taken to. ensure that its, small aperture 01
follows the same substantially radial path with respect
and deenergisation of a contactor Q8 controlling revers
ing contacts Q? in the energising circuit of the reversib'e
to the vertical axis of the horizontal table H as the aper
7 .
.i
which open and close in response to variations injt'he
‘anode current of the valve Q, control the energisation
larmNt", which previously carried the photographic unit
‘parts in engagement.
p
vtion by passing [a ,current‘in, opposition to the anode
.
The followerunit O is mounted on the longtpivoted
‘tureNl of the photographic unit N. The followerf unit
vO is'connected to'the'lever G, which operates the tool
.holder D, through a connecting link G4 having ball ends
‘engaging in recesses in the follower unit 0 and in the
lever G, a spring G5 being provided to maintain the
8
Q", for bringingivth'e relay into a criticalioperating pendi
the‘prisfn‘sides in contact with one another lying in the
motor P. _ In this way, highly sensitive control of
direction of rotation of the motor P'by the outputs of the
O7 is ensured, thus causing 'thelf'ollower
to 'photocellsqvOs,
unit 0 to follow the line of dots M8 witha high‘ degree
of accuracy as the traversing proceeds, and thereby‘in
turn causing highly accurate generation of the desired
.
The two photocells O6, 0'7 are connected in a suitable
electrical circuit (which may for‘ instance take the form
described inlthe speci?cation of the copendin'g applica
surface on the workpiece C.
~
I
_.
; r
a n
splitting action, the cam line M8 should not: become too
,steeplyy‘inclinde to the operative beam-splitting plane,
tion" Serial No. 857,816,, now_ abandoned, above‘rnen
and it is found that the angle between the cam line'and
tioned) tov control the. operation of _ a ‘reversible electric
.suchiplane' should, not be greater than aboutjq degrees.
'motor P, the arrangement being 'such that when the out- I _
put-of the ?rst photocell ‘Os’exceeds'that of the second
,O'I'the motor P is driven in one direction, whilst when
;the output of the second‘photocell O7 exceeds that of
the ?rst‘O6 the motor P' is driven in .the‘opposite direc
This‘ motor P drives a worm P1 engaging withi'a
. tion.
worm wheel P2 on'arod P3 which is in screwthreaded
[engagement with a ?xed bracket P4, so that the rodP3
.will move longitudinally in one direction or the other in
,
It should be mentioned that for: satisfactory beam
15
as
In practice, however, this ‘does not present serious di?i
culty, for ajreduced inclination’ can be‘ used if the lever
reduction ratio isnreduced. When generating thevcar‘n
device, therefore, the operator should in?generalhchoose
as large a'reduction ratio (withinwthedavailable range)
as‘ is possible without involving an’ excessive inclina
tion of the, cam line to thetbeam-splitting plane. A
v
H _ .
7 If itgis desired to use the photojgraphicipositive, instead
,ofythe negative, for, the'optical cam device, the'apertuife
vaccordance with the direction of rotation of'the motor
01 in the optical follower unit shouldv preferably be ‘made
.follower
VP. The‘ roundedjend
unitrO itself ofor'(as
this rod
shown)
engages
withthe
either with
leverthe
G 30 of the vsame size as, that ‘used in photographing, and ‘the
.follower unit ‘should also be providedwith a ,graticule
‘having a fairly thick ‘straight line marking indthe path
of the light between the aperture 01 and the beam
splittingdevice 05, such straight line lying in the (beam
‘aperture will pass through a small circular patch of the 35 splitting plane. Thus, as each of the translucent vdotstof
connected thereto.
~
-
,_
.
.
Thus, when the horiZontal table H is rotated to drive
.the optical cam, device slowly past the'small aperture
O1 of the follower unit 0, the beam of light through the .
the cam device comes in its turn beneath the aperture _O_1,
any lateral displacement relatively to the beam-splitting
plane will be revealed by the di?erent amounts _'Of light
‘passing on the two sides of the graticule line respectively
.cam device, across themiddle of which the line of’ dots
M8‘ passes. The light passing through the portion of
'such circular patch ‘on one'side of the line'of dotsMa
passes to, ‘one; photocell Osr'and that through the portion
on the other side of the line of dots passes to the ‘other 40 to Ittheshould
two photocells
be notedO6,that
O7. such
_ I straight
,7 ,7 line
I,
graticule
photocell 07., If the line of "dots Ma'is not exactly
will operate satisfactorily for ‘splitting the beam, even if
the spacing between consecutive dots in the line is such
that thedots- do not overlap one another. This makes
central in the small circular patch, more light will pass
to .one photocell than to, the other, with ‘the result that
the electric, motor P will be caused torotate so ‘as to move
,the followerunit O in the direction to equalise‘the (two 45 it practicable, if desired, to manufacturev an opticalicarn
device by punching small holes through an opaque sheet
‘portions of the. circular patch on the two sides of the line
in the appropriate acculrately'rneasured positionspwith
.of dots M8. The follower unit 0 will in fact move past
out unduly weakening the sheet by overlapping consecu
tive holes and thus producing a continuous‘cam slot. jln
in the opposite sense and'will thereby cause the motor 50 a similar Way, the straight line graticule can be used-with
a row of dark or opaque dots on atransulcent back
.1’ to be reversed, thus bringing the follower unit 0 back
ground, when such dots do not overlap one, another.
_
the position of equality, as- the result of which the out
puts of the .two photocells O6, 0'7 will be caused to’ differ
‘again. The follower unit will therefore be caused to
Again, it is not essential to use round dots to‘makc
oscillate backwards and forwards from one side to the
up
the cam line of the optical cam, device,_and patches
other of its correct position. as determined by the line of
dots M“. I These oscillations can be made very small with 55 of other shape can be‘ employed, if desired, by the use of
an aperture other than circular in the photographic. unit
N. Round dots,>however, are usually preferable, since
.:suitable design of the electric circuit, but they will en
. sure highlysensitive following of the curve of the line
their use will permit satisfactory operation over a great
of dots, and therefore highly accuratejcontrol of the
er range of‘inclinations of .the cam line to the beam
1 movement of'the tool D1 for the generation of the desired
surface.
I
V
,
p
.
_
r
V
A preferred form for such electric circuit is described
in the speci?cation'of the copending application Serial
_/'No. 857,817 above mentioned, buta simpli?ed form of
such'circuit is shown byway of example ‘in FlGURE
'9. This circuit includes an electronic valve Q, thepo
Itential of the‘ grid QI of which is controlled by a circuit
resemb‘ing a bridge circuit, having ‘the 'two photocells
60
sprlittingr plane than patches of other shape.
A
I
The arrangements above described have been. con
cerned withthe generation of a surface deviating by’ small
amounts from a basic plane surface, but they can readily
be modified to deal with the generation of‘ an‘ aspheric
surfacedeviating by small amounts from a basic spherical
surface.
For this purpose, it is necessary to employ a
relative traversing movement which requires‘ cooperation
between the two rectangular coordinate movements to
The other two_'arms
- produce a resultant-equivalent to a rotation about'a pivot
contain resistances Q2, Q3 and a further resistance Q4
is connected across the diagonal of the bridge. The 70 axis at a radius equal to that 'of the basic spherical sur
face.
arrangement is such that, when the photocell outputs
‘ 06A and O7
n I in two'of its arms.
are balanced, su?cient anode current'?ows to close a
sensitive relay ‘Q5 in'the anode circuit of the valve Q.
‘A shunt circuit'is connected across the relay Q5 contain
This can readily'be‘ achieved by modifying the‘fore
going arrangements (as shown in FIGURE 11) to provide
an arcua'te'guide R on the cross-slide E of radius’equal
ing an auxiliary bias supply Q6 and a variable resistance 75 to that of the basic spherical surface, such guide cooper
9
.16
ating with an abutment to which the correcting movement
derived from the lever G is applied. Thus, the pro
justment of the arcuate guide being made to correct
jection from the carriage F against which the connecting
rod abutting against the lever cooperates in the foregoing
stant (to the degree of accuracy required) during the
any error, so that the gauge readings will remain con
traverse. The gauge is now removed from the toolholder
arrangements, is removed and replaced by a member R1
sliding in a ball guide R2 accurately parallel to the axis
of the horizontal spindle A1 and terminating in a roller
R3 engaging with the arcuate guide R provided on the
D and the tool D1 inserted therein, the tool being ad
justed in its holder to the position in which it just tou:hes
the spherical surface. The tool is locked in the tool
holder in this position of adjustment, and the spherical
cross-slide E, the micrometer ?tting used for adjustment
lens is removed from the horizontal spindle.
of the depth of cut still being provided at R4 on this 10
The parts are now ready for setting the cam device,
sliding member R1.
Whether in the form of a steel strip or of an optical
The effect of this modi?cation is that the movement
cam device, in the manner above described, in accord
of the carriage F is no longer con?ned to the correcting
ance with the chosen multiple of the deviations of the
movement derived through the lever G from the cam
desired aspheric surface from the basic spherical surface.
device, but now consists of two superimposed move 15 When the cam device has been set and the lever pivot
ments, ‘one of which is constituted by such correcting
G3 adjusted to suit the chosen ratio, the glass block C
movement while the other is a component movement
on which the aspheric surface is to be generated is mount
which cooperates with the movement of the cross-slide
ed in its cell in position on the horizontal spindle, care
E on the carriage to produce the desired resultant ro
being taken to remove any dirt from the cell seatings
tational traversing movement centered about a vertical 20 to ensure accurate positioning of the glass block there
axis, which intersects the axis of the horizontal sp'ndle
on. The cross-slide E is operated to bring the tool D1
A1 and may be termed the “pivot” axis although no
just off the edge of the glass block C, and the microme
actual. vpivot is provided.
ter ?tting R4 between the lever G and the abutment R3
The arcuate guide R is detachably mounted on the
engaging with the arcuate guide R is operated to move
cross-slide'E, so that itv can be replaced by another ar 25 the carriage F axially to the position corresponding to
cuate guide of different radius, when required, and since
it is important to ensure that the guide is centered with
a high degree of accuracy on a straight line through the
tool D1 parallel to the horizontal spindle axis, it is de
sirable to provide the mounting for the guide R on the
_'_cross-slide E with ?ne adjustmentmeans (not shown)
for tilting the guide to bring its centre into correct align~
the desired depth of cut on the block. The two ecc
tric motors A4 and H3 are now started up and the de
sired aspheric surface is generated on the workpiece in
a manner analogous to that above described.
It should be mentioned that, since the correcting move
ment in accordance with the deviations is applied in _a
direction parallel to the horizontal spind‘e axis, in all
relative positions of the tool and workpiece, the rela
When crossed scales L1, L2 are used, the accuracy of
tive traversing and correcting movements operate ona
: mounting of the arcuate guide R can readily be checked 35 system of combined polar and rectangular coordinates,
directly against correct readings on the two scales in
and of course the deviations must also have been calcu
v ment with such straight line.
accordance with calculated measurements.
lated on this basis. The fact that deviations calcula'ed
In order to check the accuracy of mounting of the
on this basis were applied to the cam device on a truly
arcuate guide R, when the transverse scale L1 alone is
polar coordinate basis is immaterial, since the lever G
used in conjunction with a micrometer head N‘i at the 40 is operated by the cam device in the radial direction and
low magni?cation end of the lever G, a spherical lens
therefore receives the deviation movements from the cam
having a surface accurately corresponding to the basic
device on the same basis as they were applied to the cam
spherical surface is ?rst mounted in a cell on the end
device.
of the horizontal spindle A1 (care being taken to clean
In the foregoing arrangements, the workholder A has
the lens seatings in the cell thoroughly to avoid posi 45 been stationary, except for its rotation about its own
tional errors due to dirt), and a precision gauge is ?tted
axis, and both the traversing movement (whether trans
into the toolholder D in place of the tool D1 with its
lational when the basic surface is plane or e?‘ectively rota
movable gauging element projecting into engagement with
tional when the basic surface is spherical) and the cor
the spherical surface. The cross-slide E is then moved,
recting movement in accordance with the deviations, have
so that the arcuate guide R slides past the abutment
been applied to the toolholder D, such arrangements op
roller R3, with corresponding axial movement of the
erating in the case of a plane basic surface on a rectangu
carriage F, until the gauging element engages with a
lar system of coordinates and in the case of a spherical
marginal point of the spherical surface. With the cross
basic surface on a combined polar and rectangular sys
slide E held stationary in this position, the horizontal
tem of coordinates. It will be appreciated, however, that
spindle A1 is rotated at a slow speed, and the gauge 55 various inversions of such movements'can be used in
readings are watched during this movement. If, as may
stead, if desired.
be the case, for example because of dirt not properly
Thus, for example, the correcting movement could be
I removed from the cell seatings or due to any untru'th
applied to the workholder A, by mounting the support for
in the edging of the lens, the spherical lens has a slight
the horizontal spindle A1 on an axially moving car
tilt in its mounting, so that its centre is not quite accu
riage, whilst the traversing movement remains applied to
rately aligned on the spindle axis, this will be revealed
the toolholder D, the toolholder still being mounted on
by the gauge readings which will vary from a maximum
the cross-slide E on the carriage when the basic surface
to a minimum and back again during one complete
is spherical (a ?xed abutment being provided for the
revolution. The position of maximum error is noted
arcuate guide R), or being mounted on a simple trans
and the spindle A1 is rotated through exactly a right 65 verse carriage when the basic surface is plane.
angle from such position. This will bring the points of
Or again, the traversing movement and the correcting
movement could both be applied to the workholder A, by
mounting the support for the horizontal spindle A1 on the
cross-slide E on the carriage F, the toolholder D being
lens surface through the axis is substantially accurately
circular. The spindle A1 is now locked in this posi 70 ?xed in position on the base.
In another variant, the traversing movement is applied
tion, and the cross-slide E is now operated, so that the
to the workholder A and the correcting movement to the
gauging element is traversed along this circular section
of the surface. The gauge readings during such tra
toolholder D. In the case of a plane basic surface, this
is effected by mounting the toolholder D on an axially
verse will indicate whether the arcuate guide R is accu
rately centered on the spindle axis, the necessary ad 75 moving carriage and the support for the horizontal
maximum and minimum error vertically above and below
the spindle axis, so that the horizontal section of the
semi-s1
11
12
.
'
spindlejAlr on ‘a ‘transversely moving carriage. In the
‘case of a spherical basic-surface, however, the support‘for
.the horizontal spindle A1 is mounted'on the cross-slide
‘transmission means has “a redu'cti'o'nr'atio‘dependentch
of the traversing movement andvappl'y one to the work
with the cam'devic’e ‘and follower mean's'for c'ausi.. g ‘the
such chosen multiple.
,
v
.
.
l
.
5. Apparatus as'clairned in 'claim"4,'in which 'th‘e'cain
jd’evice’consis'ts of an optical cam device'compri'si‘n'g “a
IE on the axially movingjcarriage F (with a ?xed abutment
‘for ‘the arcuate guide‘ R), Whilst the toolholder D is '5 sheet‘be‘aritg a curved'line which contrasts in respect
of light-transmittingproperties.wd-th the background con
‘mounted on another axially moving carriage.
stituted bythe ~adjacent portions of the sheet, and the
v Again, in the case of a spherical basic surface, it is
transmission means includes 'an ‘optical unit cooperating
valso possible to split up'the two coordinate components
’holder 'A and the other to the'toolholder D.
This
can
>
_ '10 optical unit to follow theicurved line on'thelsheet during
'_be achieved, for‘exam‘ple, by mounting the support for the
accurate spindle ‘A1 on an axially moving'carriage, such
the relative traversing movement.
‘
6. Apparatus as claimed in claim 5, in which the optical
‘carriage also carrying the'arcuate guide'R withwhich co
’_ operates an ‘abutment ?xed to a transversely moving car
‘hnit'includesfa source of light, means‘ for directing'a
‘isrn‘all'lieam of light from the source ‘through ‘the opti a1
“slidep‘which is moved by the lever G'in'accordance with‘ the
“correcting movement’ ‘and carries the toolholder 'D.
"line on the sheet, ‘and the follower‘m‘eans compris’és'a
'riage,‘such
latter carriage carrying an‘ axially moving cross- ‘ 15
; “cam device-and"P.hotoelect-ric means res onsi've’to'lateral
.
.7
displacement between the bcam'of light 'and‘ the “ cur ‘d
reversible electric 'm'otonielectrical circuit means? forco‘n
' trolling thedireetion of’rotatio'n ot’s‘uch‘niotor'in‘ acco d
?ed in' other wayswithin ‘the scope'of the‘ invention. For
'_example,'it is not i‘es'sential'to the invention for the hori é'o 'ance: with ‘the output‘iof, the photoelectric means, "and
‘means whereby ‘the electric motor‘causes' relative move
'Z‘ontal table'H, which ‘carries ‘the wca'm'device, to rotate
/ment' between the optical cam devliceand the‘ opticallunit
vabout ' a "pivot : axis,j_and' such ‘table could, if desired, per
‘for correcting the said lateral displacement, such relative
form‘ 2.‘ straight-line"translational movement, appropriate
~ly"interrelated ltor'the relative traversing movement be " movement ico‘nsistin'gof’ small oscillations tram, one" side
"twéémheiool‘Dianathe workpiece C. In such casei?ie "235 :to the‘ other" of the'c'orrect relative" position determined
‘by‘the'optical cam device. 7
_,
I
H
‘cam device (whether in the‘for’m of-a mechanical cam
'7. vApparatus ‘as claimed in claim 1, pwhereinfthie has'ic
‘or ofeanioptical cam‘ device) would take'theform of 'a
v
The various ‘alternativearrangements can also be modi
‘curve ‘differing from a'straight'line (instead of a circle)
in accordance with the‘deviations of'the’de'sired surface
‘i'surface‘ consists ' of ' a spherical “surface centered ‘on ‘the
"V'xis‘of symmetry,v and in whioh‘theime'ans for applying
' "
i ' sing mov merit incln'des‘guidingm ‘s
“from ‘the basic'surfac'e. The step-by-ste'p movement of ‘>30 'i?iéjrag?vetra
‘for linte'ri'rielating the'two'; component rcc'ta?gular'vcbordi
vthe table‘during-generation of the carn'dev'ice ‘would of
‘ nate relative tnu'leising'‘rnciivem'ents'~ toprodu'ce 'a‘ resultant
vcourse take-place along'exactly the same path asv its sub
'_'sequent movement ‘during manufacture of‘ the desired sur
relative ‘traversing movement equivalent ‘to fa rotation
': about ‘apiv'ot axis interséctingtheaxis' Qfsymmetry at
;face.
What we’ claim as our invention and desire to secure 35 right angles at "a" radius equal to that of'the'basiclspher'ical
"by Letters Patent is:
1. Apparatus for producing on a workpiece by means
z'of'a toolga surface of revolution which deviates from'a
basic surface by relatively'small amounts at di?erent
‘radial ‘distances from the 'axis'of symmetry, said appara- ‘40
'tus comprising a ?xed base, a workholder for carrying
the workpiece, means for-‘rotating the workholder about
an axis constituting the said axis of symmetry, ‘a tool
_ 8. Apparatnsas claimedinclaim‘7, inwhich the means
for superimposing the rel-ative'correoting' movement on
‘the relative traversing "movement comprises an'o'ptical
wean device consisting of a' sheet bearing .a gurved lifle
“which "contrasts in ‘respect of light-transmitting prop
"erties with‘ the background constituting the adjacent por
tions of the‘ sheet'an'dlis'shaped in"accordancewith'the
holder for-carrying the tool in operative relationship to the
deviations ‘of the desired "surface from the basic spherical
Workplace on the wmkholder’ mounting means on the71-5"surface,‘an'optical unit'cooperating with the optical cam
base for locating‘the workholder' and toolholder relative
device, means for e?’e'cting relative movement between
ly to a ?xed reference axis which coincides with the axis
the optical unit and the optical cam device in'accordan'ce
" of rotation'of the workholder in at least one position there
with the relative traversing movement between the work
of,‘ superimposed slideways for con?ning component rela
holder and the toolholder, follower means acting during
twe movements Between the Workhold?r and the tool‘ 50 such relative movement to cause the optical unit and the
holder'to two'coordin'ate directions respectively parallel
optical cam device to perform relative working move
to/and:at right angles to the ?xed reference axis, means
‘me‘ts transverse to such relative movement-whereby the
for applying to "the w'orkholder and the'toolholder a re
optical unit is caused to follow the curved line on, the
sultant relative traversing movement in accordance with
sheet, and transmission means through which the said
‘the "shape of: the basic surfac'eun‘der thecontrol of such 55 rrelative working movements are caused 'to'control the
slideways, and means for superimposing on such travers
-relative correcting'movement between‘the vworkholder
ing movement a, relative correcting movement in the'direc
land the 'toolholderl
v
,tion of the; ?xed reference, axis in accordance with the
9. ‘Apparatus as claimed in ‘claim 8, in which the'shape
‘deviations-‘of the ‘desired surface from such basic surface.
‘of the cam device is determined in~accordance*with' a
‘2. Apparatus as claimed in claim 1, wherein the basic (50 - ‘chosen large multiple of the said deviations,'and'the
vsurface consists ‘of a‘ plane surface at right angles to the
'aXiswf‘symm'etry, and in which the relative traversing
movement‘is effected in a direction at right angles to the
transmission means has a reduction ratio'idependention
"such chosen multiple.
10. Apparatus as claimed in claim 8, in which the
optical unit comprises a source of light. means for direct
3‘ Apparatus as claimed ‘in claim 2’ including a cam 65 ing a small beam of light from the source through’ the
‘axis of'symmetry.
device shaped in accordance ‘with the deviations of the
desired surface from the basic plane surface, transmis
"sion means through Q‘which the’cam device controls the
‘relative‘correcting'emovement, andimeans for effecting
optical cam device, and’photoelectric'means'responsive
to lateral displacement between the bea'm'of light and
the curved line~ on the sheet for’ giving- an'eoutput for-the
"con'troli'of the follower means.
_
relative movement between the cam device and the trans- ‘70 ‘ IL'Apparatus as claimed in vclaim 10, in which’ the
follower means‘com‘prises a reversible electric motor,
Vmission means in accordance with therelative traversing
‘electrical circuit means for con-trolling the directionof
rotation of such motor in accordance with the o‘utputof
the photoelectric means, and'means whereby the electric
of‘ the cam device‘ is determined in accordancewith a
chosen“ large multiple of the said deviations, and~the 75 motorvv acts to cause-the-relativeworking-movementsihe
movement between the workholder and the toolholder.
’ 4_. Apparatus as claimedin claim 3, in which the shape
3,079,731
‘i3
tween the optical unit and the optical cam device, such
relative working movements consisting of small oscilla
such element in accordance with the relative traversing
movement between the workholder and the toolholder
tions from one side to the other of the correct position
whereby the said element is caused to perform working
determined by the optical cam device.
12. Apparatus as claimed in claim 7, in which the guid
ing means comprises two cooperating guide members con
sisting respectively of an arcuate guide shaped to suit the
shape of the basic spherical surface and an abutment
cooperating with such arcuate guide, means for mounting
movements transverse to such relative movement de
pendent on the shape of the cam device, and transmission
means through which the working movements of the said
element are transmitted to the one of the two said co
operating guide members to which the correcting move
ment is applied.
one of such two cooperating guide members on the super 10
14. Apparatus as claimed in claim 13, in which the
imposed slideways, and means whereby the correcting
shape of the cam device is determined in accordance with
movement is applied to the other of such cooperating
a chosen large multiple of the said deviations, and the
guide members and is thereby superimposed on the rela
transmission means has a reduction ratio dependent on
tive traversing movement.
such chosen multiple.
13. Apparatus as claimed in claim 12, in which the 15
means for superimposing the relative correcting move
References Qited in the ?le of this patent
ment on the relative traversing movement comprises a
UNITED STATES PATENTS
cam device shaped in accordance with the deviations of
1,485,258
Dzus _______________ __ Feb. 26, 1924
the desired surface from the basic spherical surface, an
element cooperating with such cam device, means for 20
effecting relative movement between the cam device and
2,725,776
2,733,519
Hopkins _____________ __ Dec. 6, 1955
Darogo ______________ __ Feb. 7, 1956
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