Note: Descriptions are shown in the official language in which they were submitted.
DFSCRI:°TiON
TITLE OF INVENTION
TERTIARY NEGATIVE-DEVIATION FLEXING CONTACT TYPE GE:AH DRIVE
OF NON-PROFILE-SHIFTED TOOTH PROFI1,F
Technical FiEld
The present invention relates to 3 flexing~contact-
type gear drive, pnd particularly to tooth profiles of a
ri~r,id internal gear and a flexible external gear employed in
this type of gear drive.
Background Art
A flexing-contact-type gear drive typically consists
of a rigid circuinr~ intarnal gear, a flexible exterwal gear
which has 2n (n being a positive integer) less teeth than the
internal gear and which is disposed inside the internal gear
and flexed into an elliptical shape so as to mesh with the
internal gear at ~Cwo places, and wave generator fitted inaic9e
t;~~e external gear for flexing it. The basic tooth profile
for the guars of a flexing contact gear drive is linear (see
U.S. Patent No. 2,906,1t~3), On ~,tle other hard, an i.nvolc,te
tooth profile has also been proposed (see Japanese Patent
Publication No. S~IO 4~-111171). However, where the linear or
the involute tooth profile is adapted as that o'f° each of the
inr,ernal and external gears, the addendum faces of the gears
1
ran ,~__ ~r"~Y(r44~ ,., c~ 'y~.i~ la ~7;
~:~.~~ i~<'
cannot be Continuously meshed with each other.
For increasing load capacity the inventor of the
present invention proposed in Japanese Patent Laid Opcn No.
SHO 6g-11593 a system using as the basis for the tooth face
profile the curve obtained by similarity transfor~rninR the
locus of motion at a reduction ratio of 1/2 over a prescribe
range from the meshing limit point on the locus of motion
basod on the rack approximation of the tooth of the external
gees relative to Lloe internal gear determined by the shape o:'
the wave generator. With the tooth profile disclosed ~.n this,
publication, the addendum faces of the internal and external
gears can be continuously meshed with each other.
In the meantime, as a flexing-contact-type gear drive,
one having a cup-shaped flexible external gear has been
known. If the internal and external gears of this type gear
drive are designed to have the same tooth profiles as
disclosed in the above Japanese Patent Laid Open No. SHO 53-w
115943, it cannot be realized to Form a continuous meshing
between the teeth of the gears all along the tooth trace
direction.
More specifically, in a cup°shaped, flexing-contact-
type gear drive, the eup~shaped flexible external gear is
subjected to deflection called honing, in which the deflection
value of the external gear increases gradually in the
direction from its diaphragm side to its opening side and :in
proportional to a distance from the diaphragm (the deflection
E/:~ r/:E~~.~ y~r~~G ~~GE ~7u'~ ny
. ~ Y~O~~ fi~~00 h~~~U _ Yo
~~2~3~~~
being a difference .in the length between tho ma,~or axis and
the minor axis of the el'iiptical shape of the external gear).
The change in the deflection along the axis of the external
gear due to the coning is not considered in determination cf
the tooth profiles disclosed in Japanese Patent Laid Open No.
SNO 63-1159~43~
Accordingly, where a cup--shaped, flexing-contact--type
gear drive is provided with the internal and external gears of
the tooth profiles as disclosed in the above publication,
both gears can be meshed continuously with each~other only at
a specific sectional portion along the tooth trace direction
(for exanple, at such a sectional portion of non-deviation
where a normal deflection occurs), while they may be
improperly meshed to cause tooth interference or the like at
the other sectional portions.
Measures to avoid the defect are disclosed, for
example, in .lapanese Patent Laid Open Nos. SHO 62--75153 and
HEl 2-62u61. rn these measures, however, it is required i;o
apply special additional processings such as crowning,
relieving and the like to t:he tenth of gears.
Tn order to achieve a wider range of meshing of the
external and internal gears atang the tooth trace direction of
the cup-shapod flexible external gear without tooth
interference between the external and internal gears, the
inventor of the present invention proposes a tooth profile
disclosed in Japanese Patent Application No. II~I--3-357036.
3
~~d '! r ..~'Ef~~d Y~4~G ,4Gr ~0~'' ~G
~~~8~~%.
The invention diqclosed in this patent application was
made based on the recognition that, in a flexing, contact type
gear drive, moving lcci cf teeth of the cup-shaped flexible
external gear at respective sections of rotation along tooth
trace direction thereof are found to be changed and decreased
in deflection along the tooth trace direction viewed Prom the
opening side of the flexible external gear, and that th~se
moving loci are found to form a single envelope when these
moving loci are overlapped on a same plane. In this patent
application, a rack approximation method is introduced to
simplify the analysis in finding a formula of the obtained
envelope. Moreover, a moving locus of the flexible external
ge2r is obtained at a section of rotation near and outside the
diaphragm--side end of the flexible external gear, and is
Connected to the envelope to thereby form a composite curve.
Then, a portion of the composite curve which starts from a
selected meshing limit point and corresponds to two times the
working depth in the tooth depth direction is,sub,)ected to
the simllarit-,y transformation at a reduction ratio of 1/2 to
obtain a curve which is employed as convex tooth profiles of
tooth faces of tho external and internal gears.
The present inventor also proposed in Japanese Patent
Application iJo. HMI 3-357037 that a moving locus based on
which tooth profiles are introduced is defined only by the
above-mentioned envelope. The invention disclosed in this
Japanese Patent Application eras made based on the recognition
n
01d s,~~,~E~.~:.~Y~r4GG.kGE INOdd v~~00 ~~~~'~~Oi'0
~~.2~ ~~~'
that the envelope is similar to a curve obtained by sub,~ecting
to the similarity transformation at a reduction ratio of 1/2
a moving locus of teeth of t:he flexible external gear at a
rotational section of a non-deviated state. With this
envelope, tooth profiles are determl.ned which are applicable
to tooth profiles of both gears of a cup-shaped, flexing-
contact-type gear drive wherein the difference in tooth number
between the rigid internal gear and tha flexible external
gear is four.
However, in the inventions disclosed~in Japanese
Patent Application Nos. HEI 3-357036 and HEI ~-357p37, an
opening of the cup-shaped flexible external gear is regarded
as in a non-deviated state. Further, setting of a pressure
angle at a datum point of tooth profiles is not specified.
While, recently there has been increased more and
morea demand for enhanced performance of flexing contact type
gear drives. In order Lo satisfy the demand, it is necessr,ry
to further Pnhance strength and rigidity of the flexing
Contact type gear drive, and at the same time it is necessary
to further improve wear-resisting capability. For these
purposes, the actual load distribution appeared on the teeth
along the tooth traco direction must be equalized.
Disclosure of Tnvent:ion
The present invention is directed to an improvement of ,
tooth profi2es disclosed in Japanese Patent AppJ.icatzon Nos.
~~2~~~
HFI 3-35703b and HEI 3°357037. The present invention is
characterized by setting the deflection of an opening of a ,
cup-shaped flexible external gear of a flexing contact type
gear drive to be a negative-deviated state wherein the amaunt
of deflection is set smaller than that of a normal deflection.
Concept of positive and negative with resp~ct to deviation
of teeth are described in Japanese Publication No. SHO u5-
U1171 by the same inventor of the present invention.
Further, according to the present invention, tooth
profiles are determined based on a composite curve formed by
an envelope of moving loci of teeth of a flexibly external
'~d gear and a moving locus pf teeth at a section of rotation
which is located on an end of the diaphragm-side of the
external gear along the tooth trace direction or located
adjacent to the outside of the end portion thereof. This
concept is similar to that disclosed in Japanese Patent
Application Nos. HEI 3-357036 and HEI g-357037, except that
the moving locus of teeth at the section of rotation located
on the end of the oxternal gear is employed.
According to the present invention, different from the
inventions disclosed in the above-cited Japanese Patent
Application Nos. HFI ~-357036 and H~z ~-357037 in which the
envelope employed includes the moving locus or. the section of
non-deviated state, a clearly limited portion of the envelope
is employed Which corresponds to an amount of negative
deviation of teeth of each of rsSpect sections of rotation of
6
..«. ....~,~.:~.y~y.Ha:~.y:yaYlililuE;cYL518:i5;;kBfdbma~5~tueu°.a.~xt
~C;tiiFtiSs
~~.~~'J~ d
the flexible external guar along its tooth trace direction.
In addition, the present; invention is characterized in that
an pressure angle at a datum point of tooth is d!~fin~d in
accordance with an amount. of negative deviation occurred on
an opening of a flexible extornal gear,
MorE specifically, according to the present invention,
in a flexing contact type gear drive having a rigid internal
gear, a cup-shaped flexible external gear disposed inside the
internal gear, and a wave generator for deflecting the
external gear into an elliptical shape such that the value of
deflection is proportional to a distance from a diaphragm
o,~ along the direction from the diaphragm to an opening of the
external gear and for rotating the elliptica? shape of the
external gear, whereby a relative rotation between the both
gears IS generated by rotating the wave gear, tooth profiles
of the rigid internal gear and the flexible external gear are
defined as follows.
Firstly, both the rigid internal gear and the flexible
external gear are made to be non-profile-shifted spar gears,
'~J and an opening of the flexible external gear is set to be a
negative-deviated state in which a deflection occurred is
lower in volume than a normal deflection, Then, a moving
locus is obtained through rack approximation of teeth of the
external gear to the internal gear at respective sections of
rotation along the tooth trace direction of ,the flexible
external gear, and the obtained moving locus is overlapped on
7
~~~~'~~t~
one of sections of rotation, whereby an envelope i:a obtained.
Another moving locus in a section of rotation at an end
portion of tooth trace on the side of a diaphragm or in the
vicinity of the outside of the end portion is smoothly
connected to the envelope so that a composite curve is
obtained. A curve is obtained by subjecting to the similarity
transformation at a reduction ratio of 1/2 a portion from a
starting point of the envelope to a terminating point.
c~rresponditlg to two times the working depth in the direction
of depth from an ape~c of a moving locus when the deviation is
0, using the terminating point as an original point. The
curve thus obtained is made to be each of main portion:; of
convex tooth profiles at the tooth faces of the both gears.
Furthermore, a composite curve is obtained which includes a
straight line having a limited pressure angle associated with
a deflection value of an opening and inserted in the vicinity
of a datum point of tooth profile, and a transient curve
smoothly connecting the above straight lina to the main
portion of the convex tooth profile. This composite curve or
its similar curves is made to be each of tooth profiles at the
tooth faces of the both gears. While, tooth flanks of the
both gears are defined by a composite tooth profile including
a straight line and a concave curve which is symmetrical to
the tooth proff:~e of each ef the tooth faces of the gears with
respect to each of the datum points of tooth profiles of the
gears, or are defined by a tooth profile which is obtained by
8
212 ~0~'
\ providing the composite tooth profile with some amount of
escape.
Brief' Description of Drawings
Figure 1 is N perspective view of a cup-Shaped flexing
coritaet type gear dr.ivo.
Figure 2 is a front view of~ the goat drive of Figure
1.
Figure 3 illustrates a state of a flexible external
gear before deflection due to coning.
Figure ~1 illustrates a state of the flexible external
gear on a major axis of elliptical shape after deflection due
to contng.
Figure 5 illustrates a state of the flexible external
gear on a minor axis of elliptical shape after deflection due
to coning.
Figures 6, 7 and 8 show a locus of one of teeth of the
flexible external gear when moving with respect to a tooth
groove of a rigid internal gear, wherein Figure 6 shows a
moving locus thereof at, a seotion of rotation on an opening of
the flexible external gear, Figure 7 shows a moving locus
thereof at a central section of rotation of tooth trace of
the external gear, and Figure 8 shows a moving loons thereof
at a section of rotation on an end portion of the diaphragm
of the external gear.
Figure 9 is a composite curve by which a tooth profile
9
SId s~;~ ~s~.r,.~4f~,~~,,~~G
. Y'a0~a ~5~00 BO"~_~;~o
of the present invention is defined.
Figure 10 illustrates how to obtain the tooth profile
of the present invention from the cornposite curve of Figure 9.
rJ
Figures 11, 12 and 13 show meshing condl.ti0ns of the
tooth profiles of the present invention, respectively,
whar~ein Figuro 11 shows a s'~ate of moshing at a section of
rotatipn on the opening of the external gear, Figure 12 shows
a state thereof at a central section of rotation of tooth ,
trace of the external gear, and Figure l~ shows a State
thereof at a soetiori of rotation on an end of the diaphragm
of tooth trace of the external gear.
E3est Mode for Carrying Out the Invention
An example of the present invention will now be
described with reference to the drawangs.
Figures 1 and 2 is a perspective view and a front view
of a known cup-shaped fle5ting con'~aet type gear drive. The
fleXing contact typo gear drive 1 comprises a circular rigid
internal gear 2, a cup~shaped flexible external gear 3
disposed inside the internal gear, and an elliptically-shaped
wave generator 4 fitted into the external gear. The cup-
shaped flexible external gear 3 is in a state flexed into an
elliptical shape by the elliptically-shaped wavy generator 1~.
~i8ures 3, ~t and 5 show a state of deflection of the
fl.ext~ble external gear caused by coning, respectively, by
1 0
9Id s~7 ~s~.r"~y~4~G.~~.~ ~0~~ ~~~00 ~u?~~0~76
~:~~~3~~)'
means of a section taken along an axis of the flexible
external gear, Figure 3 shows a state of deflection of the
external gear before flexed by the wave generator ,1 (before
def~,ection). Figure it is a sectional view taken along the
ax is pf the external gear and along a major axis of the wave
generator, showing a state flex~d by the wave generator U.
Whereas, Figure 6 .is a sectional view taken along the axis of
the external gear and along a minor axis of the wave
generator, showing a state flexed by the wave generator u.
As can be seen from these figures, the Cup~sraped
flexible external gear 3 is deflected Owing to coning, so that
the deflection in value is maximum on its openin 3a and
$ . is
gradually decreased toward the side of its diaphragm 3b,
Figures 6, 7 and 8 show & moving locus. of one of
teeth of the cup-shaped flexible external gear with respect
to a tooth groove of the rigid internal gear 2 of the flexing
contact type gear drive 1, the moving locus being obtained by
the reek approximation provided that the numbers of the both
gears 2 and 3 become infinite without changing the difference
in number of teeth between the both gears, Each of the
obtained moving loci is in a state of n~gative deviation.
Note that in these.figures, the teeth of the internal and
external gears are provided with same tooth profiles
provisionally<
In these figures, the moving locus of, Figuro C ~.s
obtained at a section of rotation of a point 31 on the opening
1 1
2~~8~~~~~
3a of the teeth 30 of the cup-shaped flexible external gear
3. The moving locus of rigure 7 is obtained on a sQetion of
rotation at a center of tooth trace of the~external gear,
while that of Figure 8 is obtained at a section of r~otat:ior, of
a point 33 on an end portion of the diaphragm 3b of tooth
trace of the external gear.
As is apparent from these figures, a degree of tooth
Interference of the both gears increases gradually toward the
side of the diaphragm 3b From the opening 3a. To avoid the
tooth interference, it, is necessary to apply an additiona.t
processing such as cell~ving to the teeth of the gears,
The moving locus on a desired section of rotation can
be expressed by
x = 0.5 mn( n - ,~ sin n )
(1)
Y - mn(1 - ~ pOs
wherein x is an orthogonal coordinate along a pitch line of a
rack, y is an orthogonal coordin&te along a depth of the rack,
m is a module of the tooth, n is 1/2 of the number of tooth
difference between the rigid internal gear and the flexible
external goar~, r~ is an angular parameter, ~; is a deflection
ooofficient (,~ - 1 represents a state of non deviation,
whereas ~ ~ 1 represents that of negative deviation).
The following expression (2) can be derived by
eliminating tha term
g ~n from the expression (1).
1 ?.
pe
k.D ~J
x - 0.5mn [COS ~' ( ( ~ 'Y/m/n)/,~ f - ~c J- 1- ( ( 1~y/m/n)/ ~c } 4 7.
(2)
Further, the following expression (3) can be obtained by
solving x through a partial differential of the expression
in terms of
- ~ 1 -y/m/n
(3)
elimination of the term x from the expressipns (2) and (3)
makes an expression defining an envelope a obtained by
overlapping a moving locus with respect to each value
of
on an plane. That is, the following expression (4) can be
obtained.
x - 0 . 5mn ~ cps - ~ f' 1 -y/m/n - ,r y/m/n ( 1 -y/m/n ) } _ 0
The definition of the above envelope leads t,o the
following facts. If the constant ,~ is :;et to r,e a certain
value, this means to select a section of rote.
>rion having a
deflection in value corresponding to the value of x . On Lhis
section of r4tation, the envelope is meant to contact; with
the moving locus of teeth at the point of y obtained b
Y
substituting the above value in the equation (3),for the
co~fficient~ is . In other words, a portion of the envelope
on or ad,~acent to this point of y represents a part of the
13
r~
moving locus of teeth.
As mentioned before, the Inventor of the present
tnvention found that the above envelope is not but a similar
curve obtained by reducing a moving locus at a ratio of 1/2,
the waving locus being obtained wYren x - 1 (non deviation)
in the equation (2). However, it is insufficient to provide
an effective tooth depth by.using only this envelope. This is
especially apparent when n = 1, that is,.when the number of
tooth difference between the rigid internal gear' and the
flexible external gear is 2.
Therefore, according to the present invention, based
on the inventions disclosed in the above-cited Japanese
Patent Application Np. HEI 3 357036, a moving locus of teeth
of the flexible external gear is obtained on a section of
rotation of an erid portion of the diaphragm side of tooth
trace or on a section of rotation in the vicinity of outside
of the end portion (wherein the section of rotation is
referred to hereinafter as the limit section), a'nd is smoothly
connected to the envelope to form a composite Curve, so that
the composite curve is made to a basis of deriving tooth
profiles of the gears.
Figure 9 illi.istrates the thus formed composite curve
L~ In this figure, there are illustrated five moving loci in
total including a movipg locus Q a of teeth on a section
corresponding to the state of non deviation and a moving locus
.~ g of teeth on the section of rotation In the vicinity of
1 ~l
outside of the end portion Of tooth tr&ce of the diaphragm
(the fihove-mentioned 7.imit section), in ndditi.on t:o the
respective moving loci ,P. a, ~ b and .~ c shown in Figures 6,
'1 and g. Further, the respective points A, 5, C and D of
Figure 9 represent th~ places where the moving loci .B a, a b
and ,g c ~,re contacted with the envelope e, respectively.
Where the limit Section is selected on the ~nd portion of
tooth trace of the diaphragm, the moving locus. g is in
accordance with the uioving locus
Figure 70 shows how to derive the tooth profiles of _
the present invention from the composite curve L. Now, a
prescribed portion of this curve is selected from a
point A to
a point E. The starting point A is a point where the moving
locus Q a of teeth on the section of rotation of the opening
3a of the flexible exter~nsl gear 3 is contacted with t;he
envelope e. The terminating point E is a point where the
value in y-ordinate is equal to the two times of working tooth
depth, this pint being usually located on the moving locus
~ g of teEth on the limit section as mentioned above.
While, it was not specified in the inventions
disclosed in Japanese Patent Application Nos. HEI 3-357036 and
HEf 3-350737 how to settle the point p.
In contrast to this, according to the present
invention, the point A can be Bottled as follows. Where the
deafleetion constant of the opening 3a of the flexible
external gear is ,~ , t?1e value of rc , < 1 , and therefore in
1 5
~d
2ceordance with the expression (~)~
Y = mn(1 - ~ ~ z)
(5)
can be obtained, gy applying this equation into the equation
(2), the x and y coordinates of the point A cen be settled.
Further, for the purpose of latQr necessity, a value of ~ ,
corresponding to the point A is obtained at this point from
the equations (1) and (5),
r~ . - cos
w, a straight line is drawn passing through the origin of
the Coordinate axes and the point A. Then, a composite curve
MFE is obtained by similarity transforming a composite curve
OAE at a reduction ratio of 1 J2. ThP th"c "h,-~ ~ ~.,a __~_ . .
curve MFE is rounded at the point F so as. to smoothly connect
the curve and the straight portions thereof, which in turn is
madE to be convex tooth profiles at the tooth faces of the
rigid internal gear 2. Thereafter, a curve MO which is
sym~tetrical to the convex tooth profile with respect to the
poitlt M (datum point) is obtained and is made to be convex
tooth profiles at the tooth Faces of the flexible external
gear 3. Accordingly, the tooth profiles of the present
intention become linear tooth profiles on and near the datum
points through the rack approximation. Then, the pressure
1 6
'~ 2~2~~~;~
angl a a ~, is obtained of the straight .line, 'The value of a ,~
can be obtained by the following equ~ction, using the
expressions (1) and (6).
a ~ - tan '' { 0.5( ~J 4 ' ~t , S1n r~ . )l( 1 -- rc
The tooth profiles at the tooth faces of the gears are
assured to contact with each other properly at sections
corresponding to the values of ,~ associated with the values
of y through which the teeth of the external, gear mpve in the _
tooth grooves of the internal gear. 'This is based on the
facts that the tooth apex P of the flexible external gear is
on the point obtained by extending two times the straight
line EQ beyond the point Q from the point ~, and the
inclinations of the tangents at the point Q of the both tooth
profiJ,es are equal, which facts are derived from the fact l,het
the tooth profiles of the both gears contacting with Each
othsr~, for example, at the paint Q i.n the drawing are
symmetrical with respect to the point Q when viewed through
the rack approximation, and by the process of defining the
tooth profiles at the tooth faces as mentioned 4bove.
Figures 11, 12 and 13 show the meshing of the tooth
profiles of teeth when the limit sectzon ig selected on the
end portion of tooth trace of the diaphragm. Figure 11 shows
th'e meshing'thereof on the section of rotation at the opening,
Figure 12 shows the meshing on the central section of
1 7
,. ~~.~Fv°~~
rotation of tooth trace, and F~jgur~e t3 shows thsa.t on the
section of the end of tooth trace of the diaphragm. When
viewed along t:he tooth trace direction, the portion of the
composite curve defined by the envelope from the apex thereof
corresponds to the meshing or contact oi' the teeth form the
opening of the flexible external gear to the end portion of
the diaphragm side or to the limit section in the vicinity of
outsido of the end portion, while the remaining portion of
the Composite Curve corresponds to a continuous contact of the
tooth profiles within the limit section. l~Iowever, if th@
limit section is settled in the vicinity of outside of the
end portion of the diaphragm side, no actual tcc~th exist. on
this section and therEfore the meshing or contact: of the teeth
within this limit section is a imaginary one. Although, the
meshing of the tooth portions located on the end portion of
th~ diaphragm sido can be regarded as like as that on the
limit section. As seen from the drawings, according to th~
example of the present invention, in the sections shown in
Figures 11 and 12, a part of the continuous contact of the
'~
teeth can be reali2ed in accordance wl.th a degree of Contact
between the envelope and the moving locus of the shown
Section, and in Figure 13, a continuous contact of the toot
profiles within the section can be realized.
Tndustria7 Applicabflity
According to the present invention, a composite curve
is
--. ~~~8 ~~«
is obtained by an envelope of a moving locus of the teeth of
the flexible external gear obtainod when the deflection of
the Opening of t:he flexible external gear is set to be a stetc
of negative deviation which is lower in value than a normal
deflection, and a moving locus at; a section of rotation at an
end portion of tooth trace on the side of a diaphragm or in
the vicinity of the outside of the and portion, and the thus
obtained composite curve is employed for def:(ning the tooth
profiles of the both gears, Hence, it is possible to use a
limited part of the envelope for the basis of the formation of
the tooth profiles of teeth, the limited part of the envelope
corresponding to the values of negative deviation of the
respective sections of rotation of tooth trace of the flexible
external gear. Furthermore, the pressure angle at the datum
.point can be decided in connection with the value of the
negative deviation of the opening of the flexible external
gear.
~y employing the tooth profiles of the prQSent
invention, in the cup-shaped flexing contact type gear drive,
a smooth meshing of the teeth can be realized all along the
tooth trace direction toward the end portion of the diaphragm
side without need of additional processing such as crowning,
relieving and the like applied on the exterhaa gear and with
maintaining the thickness of tooth rim, whereby a natural or
proper tooth contact can be realized along the tooth trace
direction. Zn addition, if the limit section is selected on
1 9
r-.
~~~~'1~~D
the end portion of tooth trace of the diaphragm side, the
continuous meshing of tootp~ profiles within th~ s~ction can
also be utilized. Tris produces an effect of~reducing sr,ress
of tooth surface, and at the same 'time produces an effect of
enhancing a rigidity of teeth. $Spocially where n = 2, in
other words, the number of tooth dj.fference between the rigid
internal gear and the flexible external gear is 4, a radius of
Curvature of the tooth profile becomes larger in accordance
with the increase of the tooth depth, and therefore a
remarkable effect of reducing the stress of tooth surface can
be obtained.
Moreovor, since the flexing contact type gear drive is
driven in a state or negative deviation, the tooth rim
bending stress caused by elliptical. deformati.0I1 Of t:he
external gear can be greatly reduced. For instance, the
bending stress occurred when ~c , - 1 (non deviation) can be
reduced by 20 ~ by setting ,~ , .- O,g (negative deviation).
With the reasons mentioned above, according to the
present invention, a tertiary flexing contact gear drive of
the type having high strength, rigidity and precision can be
reali2Qd. Further, the present invention can be applied
Lrrespective of the value of the coning angle, and therefore
it can be applied directly to a cup-shaped flexible external
gear of the short. barrel type.
2 0
