This flexible-disk coupling contains at least one disk connected at its outside with one and on its inside with the other of two rotary parts. The side profiles of said disks are true circular arcs whose radius is at least twice the outside diameter of said disks. A very smooth finish is obtainable on the side surfaces of the disks with a rotating tool that has line contact with a portion of the disk profile, by feeding said tool in a principally radial direction over the disk surface as the disk turns. When the tool is a grinding wheel, its grinding surface is preferably part of a sphere whose radius equals the radius of said arcs but whose wheel DIAMETER is smaller than said RADIUS.

Couplings with flexible disks of ample radial extent and slightly concave 
profiles are known. Their radii of profile curvature increase sharply with 
increasing radii of the disks. The grinding wheels used in their 
production have essentially point contact with the side surfaces of the 
disks. They complete the disk sides in a feed motion principally radial of 
the disks. 
The circular arc profiles of the invention permit true line contact. 
Contact is preferably established with a limited portion of the entire 
working profile. Feed motion is used to cover the whole profile. In this 
way each profile point is covered not merely by a point of the grinding 
profile, but by a whole range of points, by a line portion thereof. This 
produces am improved finish. As the stresses are generally largest at the 
outside surfaces, the improved finish permits somewhat larger stresses. 
An asset of circular-arc profiles is the simple motion about a center 
point, to describe it. While this usually makes for higher accuracy, this 
center point is here at such a large distance from the workpiece that it 
is impractical to embody this point with an axis about which to feed the 
grinding wheel. The invention uses a wheel with a spherical grinding 
surface. Its radius equals the radius of said arc profile, but its axis is 
inclined at an acute angle to the plane of said profile and intersects 
said center point. This disposition decreases the grinding-wheel diameter 
to less than the profile radius. It results in a generally face-type wheel 
and provides an exact production of the circular arc profile.

Referring now to the drawings, FIG. 1 shows disk 24 in a section taken 
along its axis 25. A face-type grinding wheel 26 is shown in engagement 
with a portion of circular-arc profile 20 centered at O. The wheel axis 28 
preferably passes through center O. P denotes the mean point of grinding 
engagement. The proportions have been altered to keep center O on the 
drawing sheet. Center O should actually lie at the intersection of lines 
OP and dotted line 28'. The grinding surface is a portion of a spherical 
surface containing circular-arc profile 20. A suitable grinding-wheel 
diameter smaller than the radius of the spherical grinding surface is 
obtained with an axis 28 inclined at an acute angle 29 to the mean contact 
normal OP. It results in wheels of general face type, as shown. 
The spherical grinding surface has line contact with the surface being 
produced on the disk. Preferably only a portion of the rather long disk 
profile is contacted at one time. Feed motion is used to spread the 
grinding contact over the entire length of the active profile. It extends 
between lines 30. The feed motion is about an axis OA, see FIG. 2. In the 
view of FIG. 1 OA coincides with OP. 
This feed motion has the beneficial effect of spreading the contact at each 
profile point over the wheel profile or over part of it. It makes for a 
very smooth finish. The dressed wheel profile is generally not absolutely 
smooth. But whatever departure from smoothness exists is smoothed out by 
the feed. 
This is not possible when grinding with point contact, as is done when the 
disk profile has a curvature varying along its length. 
The spherical grinding surface may be trued with a diamond tool 32 (FIG. 2) 
that is only turned about an axis (OB) that intersects the sphere center 
O. In FIG. 1 OB coincides with OP. It is a simple and accurate dressing 
operation, with a dresser of moderate radius much smaller than the sphere 
radius. 
Dresser 32 may be placed in any convenient position about the axis 28 of 
the grinding wheel. Disk 24 is omitted in FIG. 2. 
Machines to achieve the required settings are in existence. Axis OA would 
be the horizontal cradle axis. The workpiece axis 25 would be turned about 
OA into a horizontal plane. 
While disk-type grinding wheels with circular-arc profiles might also be 
used in place of face-type wheels 26, with an axis offset from O in the 
plane of FIG. 1, the more complicated dressing operation would be somewhat 
less accurate, as the arc center is at such a large distance from the disk 
being ground that it cannot be used as a pivot for dressing. 
If desired, a circular-arc profile can be used also to approximate a 
desired profile of varying curvature, for instance one where the x-value 
parallel to the disk axis, defining half the varying thickness, is 
inversely proportional to the disk radius. A first approximation may 
consist of using an arc radius equal to the curvature radius at mean point 
P of the profile. 
FIG. 3 shows the profiles in proper proportion at a large scale. Circular 
arc 20, shown in full lines, has the same curvature radius at mean point P 
as the profile 21 of varying radius, shown dotted. Arc 20 reaches slightly 
outside of curve 21 at the larger disk radii, and slightly inside thereof 
at the smaller radii. The departures are shown exaggerated in FIG. 3. If a 
still closer match is desired, the arc may be shifted along its tangent at 
P, cutting the maximum departures to about one third. However close 
matching is generally unnecessary. 
To better show up the slightly concave disk profile, dotted curve 20i is 
drawn with its horizontal coordinates five times these of arc 20. 
FIG. 4 is an axial section of a disk. It differs from known designs only by 
having true circular-arc profiles 20 that lend themselves to grinding with 
line contact, and to feed that overlaps the minute irregularities. The 
concavity of the shown profiles are hardly visible. They are shown in FIG. 
3 at a larger scale. 
Disk 60 shown in FIG. 5 also contains the circular-arc profiles, but lacks 
the heavy portion 51 at the outside. It connects two rotary parts 52, 53 
with axes 54, 55 shown here in alignment without angularity. The coupling 
may be used conventionally in pairs. The outmost portion of disk 60 is 
clamped to part 52 by screws 56 with recessed heads, that thread into a 
cover 57 and reach through holes in said portion. The inmost portion of 
disk 60 may be welded or otherwise secured to a hollow shaft that is a 
portion of rotary part 53. 
In the embodiment of FIGS. 6 and 7 disk 70 with circular arcuate profiles 
contains thin ring-shaped sheets of rubber-like material 71 bonded thereto 
on both sides adjacent their outside rim. Said sheets are indicated by 
heavy lines. The disk is pressed to part 72 by screws 66 with recessed 
heads. The screws extend through holes near the outside of disk 70, shown 
in FIG. 7, and thread into cover 67. 
FIG. 8 shows a disposition with multiple equal disks 80 of circular arcuate 
profile. Except for these profiles it corresponds to the design shown in 
my patent application "Flexing-Disk Coupling", Ser. No. 695,205, filed 
June 11, 1976. The disks 80 are rigidly secured to rotary part 83 with 
axis 85, as by welding. At their outside rubber-like sheets 81 are bonded 
to them on both sides, and may also be bonded to intermediate ringlike 
disks 86 reaching between them. Disks 86 engage teeth internally provided 
on an element 88 rigid with rotary part 82. The disks 80 and 86 are 
pressed against a shoulder of element 88 by screws 87. 
The use of multiple disks 80 permits to reduce the diameter and weight of 
the coupling. And the rubber connection nearly equalizes the stresses in 
the several disks. It permits also a slight offset between the axes 84, 
85. In some cases a single coupling may be used in place of a coupling 
pair.