Note: Descriptions are shown in the official language in which they were submitted.
lZ~6~2
Title
Differential Rotary-to-Rotary Cam System
to Achieve Long Dwell Peiods With Continuous Rotary
Input.
Field of Invention
Mechanisms utilizing a rotary prime mover
input to produce a controlled output with a dwell
pattern.
Background of Invention
There arise applications in which it is de-
sired to create a non-uniform angular velocity in the
rotation of a shaft, and, more particularly, to have
any such predetermined variation repeat itself with
each revolution of the shaft.
It is one object of this invention to provide
a cam system which can create a variation in the output
angular velocity of a shaft, which repeats itself with
each revolution of the shaft,and,further, that such
variation be created as a differential motion, as opposed
to a system in which a cam is the sole connection between
the input and output.
~L2~6~
There have been disclosed in my U. S. Pat-
ents, Nos. 3,730,014 and 4,018,090, and certain em-
bodiments of my U. S. Patents, Nos. 3,789,676 and
4,075,911, acceleration-decleration systems involving
gears or chainsandsprockets in which, among other
objectives, a momentary stop, a near stop, or a slight
displacement reversal could be created in an output
shaft for some portion of the overall cycle.
It is another objct of this invention to pro-
vide a cam mechanism which can be coupled to the outputshaft of these basic mechanisms of the aforesaid patents,
which can create a true dwell or motionless condition of
the system output shaft for a relatively larger portion of
an overall cycle, or to accomplish other kinematic varia-
tions or objectives beyond the capabilities of the basicmechanisms. This is again accomplished by a differential
action of a cam, as opposed to having the entire work
pass through the cam system.
Other objectivesand features of the invention
will be apparent in the following description and claims
in which the invention is described and details of the
manner and process of using the invention are presented
directed to persons skilled in the art, all in connec-
tion with the best mode presently contemplated for the
practice of the invention.
lZ~ Z
DRA~INGS accompany the disclosure and the
various views thereof may be briefly described as:
FIG. 1, a plan view of a conventional prior
art plate cam system;
FIG. 2, a transverse section taken on line
2--2 of FIG. l;
FIG. 3, a plan view of a conventional prior
art barrel cam and follower index system;
FIG. 4, a transverse section taken on line
4--4 of FIG. 3;
FIG. 5, a longitudinal section of a mechanism
forming a part of this invention and described as a
differential cam system;
FIG. 6, a transverse section of the mechanism
of FIG. 5 taken on line 6--6;
FIG. 7, a transverse section of the mechanism
of FIG. 5 taken on line 7--7;
FIG. 8, a transverse section of the mechanism
of FIG. 5 taken on line 8--8;
FIG. 9, a section taken on line 9--9 of FIG. 7;
FIG. 10, a schematic representation of the
mechanism of FIG. 5 showing it in a base position and
three additional displaced positions;
FIG. 11, an illustrative drive system utilizing
the differential cam mechansm of FIG. 5;
FIG. 12, a graph of the displacement character-
istics of an illustrative differential cam mechanism, and
o a combined mechanism comprised of a cycloidal output
mechanism disclosed in my U. S. Patent No. 3,789,676 and a
differential cam mechanism;
~2~ LZ
FIG. 13, a side view of one embodiment of
the mechanism disclosed in my U. S. Patent No.
3,789,676 for generating an approximate cycloidal output;
FIG. 14, a plan view of the mechanism of FIG. 13;
FIGS. 15-18, schematic drawings of principal
elements of the mechanism of FIG. 13 shown in five
positionsduringan index cycle;
FIG. 19, an illustrative drive system utiliz-
ing the differential cam mechanism driven by one or
the other of illustrative indexing mechanisms includ-
ing the mechanism of FIG. 13;
FIG. 20, a side view of one embodiment of the
mechanisms disclosed in my U. S. Patent No. 4,075,911
for generating intermittent long dwell index cycles;
FIG. 21, a plan view of the mechanism of
FIG. 20;
FIGS. 22-25, schematic drawings of principal
elements of the mechanism of FIG. 20 shown in three
positions during the dwell portion of a cycle;
FIG. 26, a graph of the dwell characteristics
of the specific but illustrative mechanism of FIG. 20;
FIG. 27, a graph of the displacement charac-
teristics of the differential cam mechanism combined
with two different indexing mechanisms;
FIG. 28, a longitudinal section of the mecha-
nism disclosed in my U. S. Patent No. 4,018,090;
FIG. 29, a transverse section taken on line
29--29 of FIG. 28;
6~Z
FIG. 30, a transverse section taken on line
30--30 of FIG. 28;
FIG. 31, a longitudinal section of one of
the mechanisms disclosed in my U. S. Patent No.
3,730,014;
FIG. 32, a transverse section taken on line
32--32 of FIG. 31;
FIG. 33, a transverse section taken on line
33-33 of FIG. 31;
FIG. 34, a graph of the displacement charac-
teristics of the differential cam mechanism combined
with two additional indexing mechanisms;
FIG. 35, a longitudinal section of a mecha-
nism similar to the mechanism of FIGS. 31-33 but having
no input eccentricity;
FIG. 36, a section, analogous to FIG~ 7, show-
ing an alternate bell crank link coupling utilizing
sector gears;
FIG. 37, a section, analogous to FIG. 7, show-
ing an alternative inverted bell crank link connection;
FIG. 38, a section taken on line 38--38 of
FIG~ 37; and
FIG. 39, a section, analogous to FIG. 7, show-
ing an alternative reversed bell crank link connection.
--5--
~2~6~2
Cam systems as a general class, and viewed
as work transfer systems, or as means of transferring
work according to a predetermined variable movement
ratio, have the entire work being .transferred from
the input to the output pass through the cam and
follower elements. The term "work" is used in the
accepted classical sense in which:
Work = Force x Distance
or
Work = Torque x Angular Displacement (Radians)
FIGS. l and 2 illustrate a widely used plate
cam and roller follower system comprised of an input
shaft 2 rotatable in external bearings (not shown) on
which is mounted a plate cam 4 in which is cut a con-
toured cam groove 6, whose variation from a base circle
is a function of the output motion desired. A cam
follower arm 8 is mounted on an output shaft 10 substan-
tially parallel to input shaft 2 and also rotatable in
external bearings, not shown. A cam follower roller 12
is mounted in the arm 8 and operates in the cam groove 6.
It can be seen that, as the input shaft 2 is rotated by
an external power source at a given angular velocity, the
output shaft 8 will oscillate according to the movement
characteristics designed into the cam groove 6.
lZ~6~
Moreover, it can be seen that, neglecting
friction, the output work over any arbitrarily small
time interval, must equal the input work; that is,
Output Torque x Output Angular Increment must equal
Input Torque x Input Angular Increment. This work
must also be equal to the force on the cam roller
multiplied by the distance through which it is moved
by the cam groove, in any given small cam rotation
increment.
Another widely used cam system employing a
cylindrical or barrel cam is shown in FIGS. 3 and 4.
An input shaft 14, supported in external bearings, has
mounted on it a cylindrical cam 16 in which is cut a
contoured circumferential cam groove 18. An output
shaft 20, also operating in external bearings, has
mounted on it a follower plate 22, on which are mounted
a series of cam follower rollers 24, which operate in
the cam groove 18. As shown, when one roller 24
exits the cam groove 18, another roller 24 enters the
other end of the same groove. This type of system can
be used to provide a constant indexing of the shaft 20,
or, if the groove 18 closes on itself and only a single
roller 24 is employed, it can be used to provide a pre-
determined oscillation of the shaft 20. In either case,
the output work, as previously described, e~uals the
input work, neglecting friction, and this work is again
63L2
equal to the forceon the cam follower multiplied by the
distance through which the follower is moved by the cam
groove, in any given small cam increment. In other
words, all of the work is transferred through the cam and
follower in these typical systems.
The cam and cam followers briefly described in
FIGS. 1-4 are illustrative only. There are known in the
art many other types of cam systems using male bands as
well as female grooves, and flat or contoured followers
in place of the rollers shown. But in each instance, the
work supplied by the input shaft is transmitted to the
output system through the cam and follower elements.
A different type of cam system is shown in FIGS.
5-9. Referring to these figures, an input shaft 30 is
mounted in bearings 32 and 34 supported in a housing 36,
and held in place by a nut 38. A crank arm 40 is made
integral with the input shaft 30 or rigidly fastened
thereon; at its outer end the crank arm 40 carries a crank-
pin 42 on an axis substantially parallel to the axis of the
input shaft 30.
A cover plate 44 is bolted to the housing 36 to
complete the mechanism enclosure; a cam groove 46 is cut
into the plate 44 and forms a closed curve around the input
shaft axis. An output shaft 48 is mounted in a bearing 50
mounted in the cover plate 44 and in a bearing 52 in the
input shaft 30. The bearing 50 is retained in the cover
~z~
plate 44 by a retainer ring 54 which also carries a
seal 56 operating on the output shaft 48. An output
arm 58 is splined to the output shaft 48 and axially
positioned thereon through a spacer 60 and nut 62. The
output arm 58 has formed in it a slot 64 (FIG. 7) into
which is closely fitted a slider block 66 which can slide
therein along a substantially radial line.
A bellcrank link 68, triangular in outline, and
U shaped in section to straddle the output arm 58 and
slider block 66, is used to connect the input crank arm
40 to the output arm 58 as follows. At its apex, the
bellcrank link 68 is pivoted on the crankpin 42 through a
bushing 70. At the end of one leg, the bellcrank link 68
is connected to the slider block 66 through pivot pin 72
and bushing 74; and at the end of the other leg, the bell-
crank link 68 carries a cam follower roller 76 and this
roller operates in the cam groove 46 in the cover plate 44.
The entire mechanism enclosed in the housing 36 and cover
plate 44 will be referred to as the differential cam mecha-
nism 78.
It can be seen that if it is presumed that thebellcrank link 68 is stationary with respect to the crank
arm 40 that there is no relative motion between the crank
arm 40 and the output arm 58, and if it is further presumed
that the input shaft 30 is rotated at some given angular
121~ 6~LZ
velocity, that the output shaft 48 will rotate in exact
synchronism with the input shaft, and that under these
presumptions, the path traced by the cam follower roller
76 will be a true circle concentric about the axis of
the input shaft. Conversely, it can also be seen that
if the cam groove 46 is a true circle about the axis of
the input shaft, there is no relative motion of the bell-
crank link 68 with respect to the crank arm 40, and there-
fore no relative motion is generated between the input and
output shafts, and the output shaft rotates in exact syn-
chronism with the input shaft. If, under these hypothetical
conditions, torque and work is required by an external load
on the output shaft, this torque and work must be supplied
by the input shaft, but the work will be transmitted di-
rectly from the input shaft to the output shaft withoutpassing through the cam and cam follower. This must be so
since it was shown that the bellcrank link does not move
relative to the input arm and hence can contribute no work.
The conditions of movement and work transfer with
an illustrative contoured cam groove can be visualized
through FIG. 1-0 which shows the essential system elements
schematically at several representative angles in a one-
revolution cycle. Only the centerline of the cam groove 46
is shown, together with a circular "basel' circle 80 from
which the actual cam follower position can be judged. The
cam groove centerline 46 in FIG. 10 corresponds to the cam
--10--
12i~`6:~L2
groove 46 illustrated in FIG. 8, and the position of the
essential elements, shown in solid lines and without suf-
fix, correspond to their positions in FIGS. 5-9; this is
the arbitrary starting position of the mechanism.
The position reached by the mechanism after the
input shaft and crank arm 40 have rotated approximately 12
counterclockwise from the starting position is shown by the
elements in dotted schematic having the suffix letter ~.
The crank arm has reached the position 4OA and the bell-
crank link has reached the position 68A as driven by the
cam follower 76A in cam groove 46. It will be noted that
the output arm 58 has not moved, since the positions 58
and 58A are coincident. This situation is created by the
fact that the illustrative cam groove 46 was designed
to achieve exactly this result; i.e., that a portion of
the movement of the crank arm 40 on either side of its
starting position would result in no output movement of the
output arm 58.
As the crank arm 40 rotates furthercounterclock-
wise, with the cam roller 76 confined to follow the cam
groove 46, the relative rotation of the bellcrank link with
respect to the crank arm slows down causing the output arm
58 to accelerate counterclockwise. At the maximum radius of
the cam groove 46, this relative rotation ceases and the out-
put arm rotates at the same angular velocity as the crank
arm, though it is still lagging`in displacement.
~Zl~`612
After the crank arm has rotated approximately 80
from the starting position, a position is reached as shown
by the elements having the suffix letter B. Since the cam
groove 46 when engaged by the cam follower roller 76B has
a greater radius than the base circle 80, the output arm
58B still lags the crank arm 40B, but, since the radius of
the cam groove 46 is decreasing, the output arm 58B is now
moving at a greater angular velocity than the crank arm 40B.
It should also be noted that where the cam groove
46 recrosses the base circle 80~ the bellcrank link has the
~ same relative position with respect to the crank arm as it
:: : had at the starting position and hence the output arm has
"caught up" with the crank arm.
:
After the crank arm has rotated approximately 280
:~15 from the starting position, a position is reached as shown
by the elements having the suffix letter C. Here the cam
groove 46, where engaged by the cam follower roller 76C, has
a small~er radius than the base circle 80, and it can be seen
that the bellcrank link has forced the output arm 58C ahead
of the crank arm 40C. Furthermore, since the cam groove 46
: is still becoming smaller in radius, the output arm 58C is
still moving ahead of the crank arm 40C. This continues
until the minimum radius of the cam groove is reached by
the cam follower roller 76C at which point the output arm
and the crank arm rotate at the same angular velocity.
- -12-
~Zl6~L2
From the foregoing qualitative description of
the operation of the mechanism, the following broad de-
ductions may be reached:
1. In the absence of any movement input from
the cam, work is transferred directly from the crank arm
to the output arm, without an~ work contribution from the
cam system. This situation exists whenever the cam groove
has a portion of constant radius.
2. In those areas where the cam groove has an
increasing radius, the output arm is moving more slowly
than the crank arm, and the cam system is absorbing work
from the crank arm.
3. In those areas where the cam groove has a
decreasing radius, the output arm is moving faster than
the crank arm, and the cam system is adding work to the
output, but the proportion of work provided by the crank
arm is equal to the ratio of the angular velocity of the
crank arm to the anglular velocity of the output arm.
4. Over any 360 interval of rotation of the
crank arm, the output arm also rotates 360 because the cam
follower roller starts and finishes at the same point on the
cam, hence the crank arm and output arm have the same rela-
tive positions at the beginning and end of one revolution.
5. In a general sense, the cam system provides
differential movement and work between the input and out-
put, rather than being the sole means of transferring
movement and work from the input to the output. It adds
and subtracts from the input to achieve the output and
therefore in many applications, the amount of work it
must absorb or deliver is very small compared to the
total amount being transferred from the input to the out-
put over any given revolution. Practically, this means
that the cam will be physically smaller and less expensive
than a cam system such as shown in the prior art section
through which the total work must pass.
This cam system can be utilized in a variety of
ways, as will be illustrated. ~IG. 11 shows a simple
arrangement in which the input shaft is rotated at constant
velocity. The cam mechanism 78 is mounted to a base 84
through a cradle bracket 86. A worm gear reducer 88 is
also mounted on the base 84; its output shaft 90 is coupled
to the input shaft 30 of the cam mechanism through a coup-
ling 91. An electric motor 92 is also mounted on the base84 and drives the gear reducer 88 through pulleys 94 and 96
and belt 98.
The performance of this differential cam system,
with the input shaft 30 rotating at constant velocity, is
shown in FIG. 12. The curve A represents the rotation of
~ZlC~6~2
the input shaft 30 and is drawn as a reference only.
Curve B represents the rotation of the output shaft 48,
and is based on the cam groove contour shown in FIGS.
8 and 10. In essence, the differential cam system pro-
vides a dwell of the output for about 12 on either sideof the stàrting position with a smooth transition to an
approximatley constant velocity extending from approxi-
mately 70 to 290 where this approximately constant
velocity is slightly greater than the constant velocity
of the input shaft.
While this differential cam system is shown with
a cam groove configured to provide a short dwell of the
output shaft once during each revolution, it can also be
configured to provide a wide variety of kinematic func-
tions within its angular displacement capacity range, andwithin the limits of good cam rise and cam follower pressure
angles. In the scale of the embodiment of FIGS. 5 to 9, it
is possible for the output shaft to lag or lead the input
shaft by approximately 21 although this can be altered by
changing the proportions of the bellcrank link.
This differential cam system can be utilized by
itself as described in connection with FIG. 11; but it has
special merit when used in conjunction with other already
existing mechanical systems as will be illustrated.
-15-
lZl~ 2
FIGS. 13 and 14 are simplified schematic draw-
ings of one embodiment of an approximate cycloidal motion
generating mechanism 100 from my U. S. Patent No. 3,789,676.
An input gear 102 is mounted on an input shaft 104 which
is journalled in a suitable housing or frame on axis A1
and driven by an appropriate external drive system. Also
journalled on the input shaft 104 ~is a tangential link
106 which oscillates thereon as will be described. A
driving gear 108'is mouhted on a shaft 110 journalled in
the outboard end of the link 106 on axis A2, and an inter-
mediate gear 112, also journalled in the link 106, is formed
to mesh with the input gear 102 and driving gear1`08. An
eccentric gear 114 is mounted on the shaft 110 with an
eccentricity,approx~imatelyequalto its pitch radius. This
eccentric gear 114, rotating on a moving axis A3, meshes
with an output gear 116 mounted on a shaft 118 also journalled
in the housing or frame on axis A4. A radial link 120 is
also journalled on the output shaft 118 at its one end; at
its other end, the radial link 120 is journalled to a stub
shaft 122 on axis A3 mounted concentrically on the eccen-
tric gear 114. It is the purpose of this radial link 120
to keep the eccentric gear 114 in mesh with the output
gear 116 as the eccentric gear 114 moves through its rota-
tional and translational path.
When the mechanism is in the position shown in
FIG.13, it is in a natural dwell position, i.e., a small
rotation of the input gear 102 causes a corresponding rota-
tion of the driving gear 108 and the eccentric gear 114.
-16-
lZ~ 2
This rotation of the eccentric gear 114 is accompanied
by a corresponding movement of the shaft 122 about the
output shaft 118, such that the gear 114 literally rolls
about the output gear 116 which remains stationary or in
dwell.
A qualatitive schematic representation of the
motion of the output gear 116 during a complete 360 ro-
tation of the driving gear 108 and eccentric gear 114, at
90 intervals, is shown in FIGS. 15-18. An arbitrary
radial marker line Z has been added to the output gear
116 to show its position change at these intervals.
FIG. 15 shows the position of all gears at the center of
the dwell, which is the same configuration as shown in
FIG. 13. Additionally, a second position is shown in which
the driving gear 108 and eccentric gear 114 have been ro-
tated 10 counterclockwise (as driven by intermediate gear
112 and input gear 102). The rolling action o~ the gear 114
on the output gear 116 which remains substantially stationary
during this 10 interval can therefore be visualized. In
this second position, the components are redesignated by
the callout suffix letter a.
As the gears 108 and 114 continue to rotate
counterclockwise, the output gear 116 is accelerated and
moves in the clockwise direction. After 90 of this rota-
tion of gears 114 and 108, the position shown in FIG. 16
~2~ 2
is reached. At this point, the acceleration of gear 116
in the clockwise direction has reached its approximate
maximum, and the velocity of the gear 116 in the clock-
wise direction is approximately equal to its average velo-
city.
As the gears 108 and 114 continue their rotation
counterclockwise from their position shown in FIG. 16, the
output gear 116 continues to accelerate, at a decreasing
rate, in the clockwise direction. After an additional 90
of rotation of gears 114 and 118, the positions shown in
FIG. 17 is reached. At this point, the acceleration of
the gear 116 has substantially returned to zero, and its
velocity in the clockwise direction has reached an approxi-
mate maximum which is approximately double the average
velocity.
As the gears 108 and 114 continue to rotate
counterclockwiæe from the position shown in FIG. 17, the
outpu$ gear 116 continues to rotate clockwise but is de-
celerating. After an additional 90 of rotation of gears
108 and 114, or a total of 270 from the start of the cy-
cle, the position shown in FIG. 18 is reached. At this
point, the decleration of the output gear 116 is at or
near maximum, while the velocity of the output gear 116,
still in the clockwise direction, has slowed down to
approximately its average velocity.
-18-
12~¢~i~2
As the gears 108 and 114 continue to rotate
counterclockwise from the position shown in FIG. 18, the
output gear 116 continues to rotate clockwise, but is
still decelerating, though now at a decreasin~ rate.
After an additional 90 of rotation of gears 108 and 114,
or a total of 360 from the start of the cycle~ the posi-
tion shown in FIG. 15 is again reached, with the output
gear 116 having completed one revolution and is now again
in dwell.
It can be seen, therefore, that as the input
gear 102 is driven by some external power means at a
substantially constant angular velocity, the gears 108
and 114 are driven by the intermediate gear 112. Gears
108 and 114 have an angular velocity which is determined
by the superposition of the effect of the oscillation of
link 106 about shaft 104 on the velocity created by the
input gear 102 so gears 108 and 114 do not rotate at a
constant angular velocity. And the oscillation of the
gear 114 along the arcuate path controlled by radial link
120 and created by its eccentric mounting on shaft 110
creates another superposition on the velocity of the out-
put gear 116. With the proportions shown in FIGS. 13-18,
the output gear 116 will come to a complete stop or dwell
once in each revolution, since the pitch diameters of gears
114 and 116 are shown as being equal.
--19--
~21C6~2
With the mechanism shown in FIG. 13, the out-
put motion of gear 116 has the broad characteristics of
cycloidal motion, but slight distortions exist which
are caused by the short length of link 106 and the ar-
cuate rather than linear path of shaft 122. To somedegree, these distortions can be compensated for by the
proper choice of gear ratio between input gear 102 and
driving gear 108 and the ratio of the length of link 106
to the center distance between input shaft 104 and output
shaft 118.
In order to determine the exact quantitative
kinematic characteristics of the mechanism shown in FIG.
13, it is necessary to use numerical methods for which a
programmable calculator or computer is a great convenience,
but not a necessity. Setting up classical equations of
motion and then differentiating to find velocity and
acceleration is excessively laborious and time consuming.
But numerical calculation for the exact determination of
the output shaft position for a series of discrete positions
of the input shaft can be accomplished using straightforward
geometry and trigonometry. By ma~ing these calculations at
sufficiently small intervals, it becomes possible, by
numerical differentiation, to obtain the velocity, and then
by numerically differentiating a second time, to obtain the
accelerations. These calculations can be repeated as required
for different values of the geometrical parameters to very
closely approximate the conditons to be described below.
-20-
~.21~ 2
Pure cycloidal motion displacement in unitized
coordinates and using radian angular notation is given by:
S = 21 (2~t - sin2~t~ (1)
where t i.s the input variable having a range of 0 to 1 for
one cycle of cycloidal motion, and S is the output dis-
placement, also having a range of 0 to 1.
If degree notation is used and for an input angle
and output angle range through one revolution of 360,
equation (1) may be rewritten:
1~ o = i 23~ 6in~i (2)
where
0O = output angle in degrees (shaft 118)
~ i = input angle in degrees (shaft 104)
The relationship of equation (2) is plotted as
curve C of FIG. 12; and represents the functional output
of the mechanism 100 of FIGS. 13 and 14. It will be
noted that there is a very slow initial rise of the output
from the starting point of both input and output, which
can be more easily discerned from the following table:
Input AngleOutput Angle
00 o
10 .05
20 .40
30O 1.35
40 3.17
50 6.11
60 10.38
70 16.16
-21-
~2~ Z
This relatively slow initial rotation of the
output of mechanism 100 can be converted to a long true
dwell with no output movement, by connecting the input
shaft 30 of the differential cam mechanism 78 to the
output shaft 118 of the mechanism 100. This is schem-
atically shown in FIG. 19.
A base 130 supports a motor 132, gear reducer
133, accelerating-decelerating mechanism 100, and diff-
erential cam mechanism 78. The motor 132 drives the gear
reducer 133 through pulleys 134 and 136 and belt 138.
The output shaft 140 of the gear reducer 133 is coupled
to the inpùt shaft 104 of the accelerating-decelerating
mechanism 100 through coupling 142; and the output shaft
118 of the accelerating-decelerating mechanism 100 is
coupled to the input shaft 30 of the differential cam
mechanism 78 through coupling 144. The effect of the
differential cam mechanism 78 is therefore superimposed
on the normal output of the accelerating-decelerating
mechanism 100. If the input shaft of the overall system
is considered to be the shaft 104, and its rotation
"scaled" so that a full cycle of the mechanism equals 360
and the output shaft is 48, the input to output characteris-
tics are shown by curve D in FIG. 12. It will be noted that
an overall true dwell in excess of ~ 60 has been achieved on
either side of the starting point. This, of course, presumes
that the connection of the two mechanisms is made with both
mechanisms at their starting or zero position, i.e., that they
are properly phased. Dwells of this magnitude are vexy useful
in various mechanically interrelated operating systems.
-22-
~Zl~L2
Another example of a combination system will be
based on one embodiment of a flexible motion generating
mechanism utilizing higher harmonics as disclosed in my
~. S. Patent No. 4,075,911. FIGS. 20 and 21 are simpli-
fied schematic drawings of this embodiment which is again
proportioned to provide a 360 output for one acceleration-
deceleration cycle of its output shaft. Referring to FIGS,
20 and 21, an input shaft 150 rotates on axis Ao in station-
ary bearings in a case which is not shown. An eccentric
segment 152, on the shaft 150, is concentric about an axis
Al displaced a small amount from the axis Ao. An input
gear 154, fastened on the eccentric segment 152, is also
concentric about axis Al. Tangential links 156 are
journalled on the eccentric segment 152. A driving gear
158 is mounted on a shaft 160 journalled in the tangential
links 156 and rotates on a moving axis A2; it is driven by
the input gear 154 through an intermediate gear 162 also
journalled in the tangential links 156. In this instance
the ratio between the inp~t gear 154 and the driving gear
158 is exactly 3:1; i.e., the inp~t gear 154 rotates three
times for every revolution of driving gear 158.
An eccentric plate 164 is mounted on the shaft
160 and in turn supports an eccentric gear 166 concentric
about a moving axis A3. This eccentric gear 166 meshes
25 - with an output gear 168 mounted on an output shaft 170
rotating on a stationary axis A4 in bearings mounted in
the case not shown. The eccentric gear 166 and the output
gear 168 are equal in size to provide the 360 output cycle.
-23-
¢~L2
The eccentric gear 166 is held in mesh with the output
gear 168 by a radial link 172 which is journalled on
the output shaft 170 and on a stub shaft 174 mounted on
the eccentric gear 166 concentric about axis A3.
It can be seen that the mechanism of FIGS. 20
and 21 is simlar to the mechanism of FIGS. 13 and 14,
differing only in the addition of an eccentricity between
the input shaft 150 on axis Ao and the input gear 154 to-
gether with the journal supports for the tangential link
on axis Al. The distance from axis Ao to axis Al will be
defined as eccentricity E2, while the eccentricity between
axis A2 and axis A~ is defined as eccentricity El. The
addition of this second eccentricity E2, which rotates at
an integral multiple number of times for each rotation of
15- the eccentricity El, makes it possible to :achieve a wide
variety of kinematic effects on the rotation of the output
shaft 170. This is disclosed in considerable mathematical
detail in my existing U. S. Patent No. 4,075,911.
The mechanism of FIGS. 20 and 21, designated
mechanism 176, is configured to create a relatively long
dwell in terms of input angle rotation, in which the dwell
is not a true stationary condition of the output shaft,
but rather, muItiple small amplitude oscillation of the
output shaft about the center of these oscillations, which
is defined as the zero point for output angle measurement.
For clarity, the eccentricity E2 between axis Ao and Al has
been exaggerated several fold in the scale o.f the FIGS. 20
and 21.
-24-
~Z1~612
The qualitative behavior of the system near
dwell is shown in FIGS. 22-24. At the starting point,
or center of dwell, the primary elements are shown in
solid lines in FIG. 22 and are labeled without subscript.
Since the axes Ao and Al are so close when drawn to
scale, FIG. 23 shows their relationship when the scale
is expanded 20 times. If, from this starting position,
the input shaft is rotated 90 clockwise, the relative
position of the elements is shown by dotted lines and the
suffix label "A"; here the position of E2A is shown in
expanded scale in FIG. 24. Similarly, if the input shaft
is rotated 90 counterclockwise, the relative position of
the elements is shown by dashed lines and the suffix let-
ter "B"; and here the position of E2B is shown in expanded
scale in FIG. 25. Throughout this movement range of the
input shaft the movement of the output gear is too small
to be shown diagrammatically. In effect the eccentric
gear 166 rolls on a nearly stationary output gear 168.
Quantitatively, the movement of the output gear
168 is shown graphically by the curve of FIG. 26. The
data for this curve were obtained by the methods and
formulas disclosed in my U. S. Patent No. 4,075,911. The
clock angle is the true input angle divided by three since
the gear ratio between gears 154 and 158 is 3:1 and there-
fore it takes three revolutions of the input gear 154 to
complete one cycle which is represented by360"clock" degrees.
-25-
~2~6~2
The output displacement of the output gear 168
and output shaft 170 is shown for a complete cycle by
the curve E in FIG. 27. Since this curve is very flat
on either side of the starting point, the following table
enumerates the output movements in these areas.
Input Angle Output Angle
Degrees Clock Degrees
O O
.005
-.004
.020
.246
~ .994
2.739
6.072
11.604
280 (-80) 347.933 (-12.067)
290 (-70) 353.753 (- 6.247)
300 (-60) 357.211 (- 2.789)
310 (-50) 358.997 (- 1.003)
320 (-40) 359.753 ~- .247)
330 l-30) 359.980 (- .020)
340 (-20) 360.004 (+ .004)
350 (-10) 359.995 (- .005)
360 0 360. 0
-26-
` lZl~
From these data, it is clear that the mecha-
nism 176 is inherently capable of being configured to
provide a long dwell with little output movement for
a wide range of input angle, which is of great value
for many applications. Other applications arise in
which an even longer dwell is required or whexe it is
desirable that no oscillation of the output occur during
the dwell.
Both these objectives can be met by combining
the mechanism 176, utilizing the higher harmonic addi-
tions with the differential cam mechanism 78 previously
described. This is accomplished by directly coupling
the output shaft 170 of mechanism 176 to the input shaft
30 of mechanism 78 and can also be represented by FIG. 19
by substituting mechanism 176 for mechanism 100. With
output shaft 170 connected to input shaft 30, the behavior
of the entire system, as represented by the movement of
output shaft 48, is shown by curve F in FIG. 27. It will
be noted that a true dwell in excess of +75 has been
achieved, which is much greater than the sum of the dwells
of the two mechanisms operating independently. In effect,
it only takes a relatively small modification to the E
curve to achieve the F curve.
-27-
~21(~6~Z
The dwell behavior of other types of motion
generating mechanisms having an intermittent dwell can
also be considerably enhanced by adding the differential
cam mechanism 78 to their outputs. ~everal more examples
will be shown.
The mechanism 200 (FIGS. 28-30) which also has
a natural dwell, has been disclosed in my U. S. Patent
No. 4,018,090 and will be briefly described as follows.
A case 202 supports a stationary shaft 204 on which in
turn is mounted a stationary sun gear 206. A planetary
carrier assembly is made up of a plate 208 and a housing-
210 bolted thereto. The planetary carrier 208, 210 is
mounted to the stationary shaft 204 through bearings 2I2
and 214 and rotates about the axis Ao. The periphery of
the plate 208 is formed into a gear suitable for meshing
with an input gear 216 mounted on a shaft 218 which ro-
tates in bearings 220 and 222 mounted in the case 202.
A planetary gear 226 suitably formed to mesh with
sun gear 206 is mounted on a planetary shaft 228 which in
turn is carried in the planetary carrier 208, 210 through
bearings 230 and 232. The planetary gear 206 rotates on the
moving axis Al as the planetary carrier 208, 210 rotates
about axis Ao as driven by the input gear 216.
-28-
~Z~ 2
An eccentric support plate 234 is mounted to the
planetary shaft 228 and has projecting therefrom an eccen-
tric shaft 236 on an axis A2 displaced from the axis Al.
A slide block 238 is rotatably mounted on the eccentric
shaft 236; this slide bloc~ 238 in turn is slidably mov-
able in a slot 240 of an output spider 242 IFIG. 30)-
This output spider 242 is mounted on an output shaft 244
which rotates in bearings 246 and 248 mounted in a case
cover 250 fastened by bolts (not shown) to the case 202.
The shaft 244 and output spider 242 rotate about an axis
A3 displaced from the primary axis Ao~
It can be seen that as the planetary carrier
208,210 rotates about the axis Ao, and the planetary shaft
228 is driven about the moving axis Al, the eccentric shaft
lS 236 and its axis A2 move in an epitrochoidal or epicycloidal
motion, dependingon the amount of displacement of the axis
A2 from the axis Al~ Provided only that the axis A3 lies
within the path of the axis A2, the eccentric shaft 236 and
the slide block 238 cause the output spider 242 and output
shaft 244 to rotate about the axis A3. The mathematical
development of the kinematics of this system is covered in
my U. 5. Patent No. 4,018,090, with specific reference to
the effects created through the displacement of the axis
A3 from axis Al.
-29-
~21~6~
In the specific configuration shown in FIGS.
28-30, and applicable to a combination mechanism, the pitch
diameter of the planetary gear 226 is equal to the pitch
diameter of the sun gear, (R=l), and an output cycle re-
peats for every 360 rotation of the output shaft 244 and
planetary carrier 208, 210. Further, if the eccentricity
of axis A2 to Al (K) approximates the pitch radius of the
planetary gear 226 (K~l),the output spider 242 and output
shaft 244 will come to a stop or near stop once every 360.
The specific configuration of FIG. 28 arbitrarily
shows the eccentricity of axis A2 to ~1 equal to the pitch
radius of the planetary gear 226, (K=l) and arbitrarily
shows the eccentricity of the axis A3 to axis Ao to be
equal to one-half of the pitch radius of the planetary gear
226, along the master center line (El = .5, E2 = ) Under
these conditions, the displacement characteristic of the out-
put shaft 244 relative to the displacement of the input,
planetary carrier 208, 210, is shown by curve G of FIG. 27.
It can be seen that there exists a momentary stop or dwell
of the output once for each revolution. Here again this
dwell can be significantly enhanced by combining the mecha-
nism 200 with the differential cam mechanism 78 by directly
coupling the output shaft 244 to the input shaft 30 as is
again illustrated through FIG. l9. In this combination,
the output shaft (48) displacement relative to the input
displacement (planetary carrier 208, 210) is shown by curve
H of FIG. 27.
-30-
~2~6~2
The mechanism 260 shown in FIGS. 31, 32 and 33
is one embodiment of the mechanisms disclosed in my U. S.
Patent No. 3,730,014 and may also be used to advantage in
combination with the differential cam mechanism 78. This
mechanism 260 is configured to provide a 360~ output cy-
cle as is appropriate for this combination. A case 262
supports a stationary shaft 264 on which is mounted an
input assembly, comprised of gear 266 and input spider 268
journalled on the shaft 264 through bearings 270 and 272.
The gear 266 is driven by an input gear 274 mounted on an
input shaft 276 journalled in the case 262 through bear-
ings 278 and 280.
The stationary sun gear 282 is directly mounted
to the shaft 264 which also supports a planetary carrier
assembly, made up of plates 284 and 286 connected by
spacers 288, through bearings 290 and 292. The planetary
carrier assembly 284-288 carries one or more planetary
gears 294, each of which is mounted on a planetary shaft
296, journalled in the planetary carrier assembly 284-288
through bearings 298 and 300. Three such planetary gears
; are utilized although only one is shown in FIGS; 31-33,
and each gear meshes with the stationary sun gear. At one
end of each of the planetary shafts 296 is mounted an input
eccentric 302 on an axis displaced from the axis of the asso-
~5 ciated planetary shaft. Each input eccentric 302 can rotate
in a slide block 304 (FIG. 33) closely fitted in a corres-
ponding slot 306 of the input spider 268.
-31-
J6~2
At the other end of each planetary shaft 296
is mounted an eccentric support pla~e 308, a portion of
which isformed into an output eccentric 310. A slide
block 312 (FIG. 32) is rotatably mounted on each output
eccentric 310 and is closely fitted into a correspond-
ing slot 314 in an output spider 316. This output spider
316 is mounted on an output shaft 318 which rotates in
bearings 320 and 322 mounted-in a case cover 324 fastened
by bolts (not shown) to the case 262. The output shaft
318 and output spider 316 rotate about the same axis as
the axis of the sun gear 282 and on which the input spider
268 and planetary carrier assembly 284-288 also rotate,
as must be when multiple planetary gears 294 are employed.
It can be seen that as the input spider 258 is
driven by the gear 266 from input gear 274, the input spider
drives the planetary gears 294 through the slide blocks 304
and input eccentrics 302~ If it is assumed that the input
spider rotates at constant angular velocity, the planets
and planetary carrier assembly will rotate at a variable
angular velocity due to the eccentricity of the drive point,
i.e., the input eccentric. This is covered in mathematical
detail in my U. S. Patent No. 3,730,014. The planet gears
294 in turn drive the output spider through the output
eccentrics 310.
-32-
~L2~612
In the specific configuration shown, the planet
gears 294 are equal in size to the sun gear 282, and the
axis of the output eccentric lies on the pitch diameter
of the planet gears 2g4 (Rl=l). Therefore, the output
spider and output shaft will come to a momentary stop or
dwell once for each revolution of the output shaft and
planetary carrier assembly. Furthermore, in the specific
configuration shown, the input eccentric is on a radiai
line diametrically opposite from the radial line on which
the output eccentric is located, and the input eccentric
axis is displaced from the axis of the planetary gear a
distance equal to 0.3 times the pitch radius of the planetary
gear (R2= -3). Under these conditions, the planetary
carrier assembly is rotating more slowly than the input
spider, at the time in the cycle that the output eccentric
axis lies on or near the pitch line of the sun gear. This
has the effect of lenthening, in terms of time or input
angle, the portion of the cycle that the output spider is
stopped and in dwell, or on either side of this point near
dwell.
Under these conditions, the displacement character-
istics of the output shaft 313 relative to the displacement
of the input spider 268 is shown by curve J of FIG. 34. Once
again, the dwell of the natural mechanism 260 of FIGS. 31 to 33
-33-
can be significantly improved by combining it with the
previously described differential cam mechanism 78, by
coupling the output shaft 318 directy to the input shaft
30 as is again illustrated through FIG. 19. With this
combination, the displacement of the system output shaft
48 relative to the input spider 268 is shown by curve X
of FIG. 34. It will be noted that the curves of FIG. 34
are plotted only for one-half cycle (180) for both the
input and output; this is done because the movements are
symmetrical about 180.
If the input eccentricity is reduced to zero by
moving the input eccentric 302 to.the axis of the planet
gear 294, there will exist no relative movement of the
input spider relative to the planetary carrrier assembly
284-288. In a design of this type the input spider may be
eliminated and the mechanism simplified as shown in mecha-
nism 330, FIG. 35.
Referring to FIG. 35, a case 332 supports a sta-
tionary shaft 334 on which is mounted the sun gear 282 and
the planetary carrier assembly is again made up of plates
284 and 286 and spacers 288. In this case a gear 336 is
directly bolted to the planetary carrier assembly for driv-
ing; the gear 336 is driven by the input gear 274 mounted on
the input shaft 276 journalled in the case as before.
-34-
12~t~6~2
The remainder of mechanism 330, FIG. 35, is
identical with the mechanism 260, FIG. 31, except that
the input eccentric 302 is deleted on the planetary
shaft 296, since the planetary carrier assembly is now
driven directly by the gear 336. In the configuration
shown, the planet gear is again equal in size to the sun
gear, and the axis of the output eccentric lies on the
pitch diameter of the sun gear. Therefore, the output
spider and output shaft will come to a momentary stop or
dwell once for each revolution of the output shaft and
planetary carrier assembly.
Under these conditions, the displacement charac-
teristics of the output shaft 318 relative to the displace-
ment of the planetary carrier assembly as the input is shown
by curve L of FIG. 34. Recalling that curve J indicates
the input output characteristics of the mechanism 260 with
an input eccentric, it is clear that the difference between
J and L is caused by effect of the input eccentric. Even
though the dwell of the mechanism 330 is somewhat less than
the dwell of the mechanism 260, it too can be significantly
improved by again combining it with the differential cam
mechanism 78. As before, and as is illustrated in FIG. 19,
the output shaft 318 is directy coupled to the input shaft
30. With this combination, the displacement of the system
output shaft 48 relative to the planetary carrier assembly
is shown by curve M of FIG. 34.
. -35-
Z
In the mechanisms 200, 260 and 330 of FIGS. 28,
31 and 35, respectively, the nature of the natural dwell
is controlled by the eccentricity of the output eccentric
relative to the pitch line of its associated planetary
gear. If this eccentricity is exactly equal to the pitch
radius of its planetary gear, the output shaft will come to
a momentary stop once each revolution. If this eccentricity
is slightly less than the pitch radius of the planetary gear,
the output will come to a near stop, the minimum velocity
being related to the difference of the eccentricity from
the planetary gear pitch radius. And if this eccentricity
is slightly greater than the pitch radius of the planetary
gear, the output wi11 go through a slight displacement re-
versal at the dwell. In all three cases, the addition of
the differential cam mechanism, in the configuration shown,
will significantly improve the dwell in terms of its length
as measured by the input angle, and in converting the near
stop, momentary stop, or displacement reversal into an exact
non-reversing true dwell.
Similarly, the mechanism 100 of FIGS. 13 and 14 can
be configured to provide a near stop, a momentary stop, or
displacement reversal once each revolution, and the mecha-
nism 176 of FIGS. 20 and 21 can be configured to provide a
near stop, a momentary stop, or one or two displacement
reversals once each revolution. In all cases, the addition
of the differential cam mechanism can convert these various
situations into a true dwell of significant length.
-36-
6~Z
While the primary intent and application of the
addition of the differential cam mechanism to these
natural cyclic mechanisms is to improve their dwell charac-
teristics, it is also trué that this addition can also be
utilized to modify othex kinematic characteristics of the
natural cyclic mechanisms, such as reducing peak accelera-
tions, creating a long constant velocity portion, or other
desiredeffect, within the modifying capabilities of the
differential cam mechanism.
In the basic differential cam mechanism 78,
FIGS. 5-9, the input shaft and the output shaft were shown
as operating on the same axis. In some cases, in which it
is desiredto change the effective leverage through the bell-
crank from the cam to the output arm, as when the output
load varies with position in the cycle, it can be ad-
vantageous to introduce an offset between the input shaft
and output shaft axes. This requires a mechanical modifi-
cation by eliminating the bearing 52 and adding another
bearing between the output shaft 48 and the cover plate 44.
Referring to FIG. 7, the slot 64 in the output
arm 58 was shown as being on a radial centerline. This also
need not be. Inclining this slot relative to a true radial
line may be employed to introduce a non-symmetrical response
in the differential angle relative to the cam generated dis-
placement of thebellcrank link 68;where the differential angle
is defined as the angle between the input shaft and the output
shaft away from their base relationship.
-37-
~Zl¢6~1 2
When larger differential angle ranges are re-
quired, and lower torques are a~ceptable relative to cam
loading, the bellcrank link to output arm connection may
be revised as shown in FIG. 36 which is analogous to FIG.
7 of the first embodiment. The input arm 40 and crank pin
42 are utilized as in the original embodiment, FIGS. 5-9.
A revised bellcrank link 340 is pivoted on ~he crank pin 42
through bushing 70; at its outboard end the bellcrank link
340 again supports the cam followers 76 as before, and is
driven through it by the cam groove. The bellcrank link
340 further supports a gear sector 342 having its center of
curvature coincident with the axis of the crankpin 42. In
place of a slotted output arm 58 previously employed, an
output sector gear 344 is splined on the output shaft 48
for driving. Gears 342 and 344 are formed and positioned
for a driving relationship; it can be seen, therefore, that,
as the cam follower 76 is driven by the cam groove, the ro-
tation of the bellcrank link 340 about crankpin 42 causes a
change in the differential angle between the input and out-
put s~afts. It can further be seen that for a given angular
movement of the bellcrank link 340 about the crankpin 42
caused by a given cam radius difference, a larger differential
angle is generated than with the embodiment of FIGS. 5-9.
-38-
~2~6:~2
If, on the other hand, smaller differential angle
ranges are acceptable and higher torques are desired rela-
tive to the cam loading, the bellcrank link to output arm
connection may be inverted relative to the embodiment of
FIGS. 5-9. Such an inversion is shown in FIGS. 37 and 38.
In this case, the slider block to output arm connection is
made on a radius from the centerline of rotation which is
larger than the radius of the crankpin from that same axis.
Referring to FIGS. 37 and 38, a revised bellcrank link 350
is again pivoted on a crankpin 42; the crankpin again being
mounted on the crank arm 40A which is altered only to provide
more clearance for the bellcrank xelative movement. At its
one end the bell~rank link 350 carries the cam follower
roller 76 which engages the cam groove 46, as before. At
its other end, the bellcrank link 350 has mounted in it a
pin 352 on which is pivotally mounted a slider block 354
through a bushing 356. This slider block 354 is closely
fitted in a slot 358 in the output arm 360 which is again
splined on the output shaft 48. It will be noted that in
this embodiment the slider block to output arm driving con-
nection is at a much greater relative radius than was the
case in the embodiment of FIGS. 5-9. Therefore, for a given
angular movement of the bellcrank link about the crank pin,
as caused by a given cam groove radius difference, the
dlfferential angle generated between the input crank arm and
the output arm is less than in the embodiment of FIGS. 5-9.
-39-
~LZ~6~2
Another reversal of the bellcrank connection be-
tween the input arm (formerly the crank arm) and the out-
put arm is shown in the embodiment of FIG. 39. In this
instance the bellcrank link 370 is pivotally connected to
the output arm 372 through a pin 374 at its one end and
carries the cam follower roller 76 at its other end. This
bellcrank link is driven through a slider block 376 and pin
378 by a slotted input arm 380.
In all of the embodiments shown, it can be seen
that when there is no variation induced by the cam, the in-
put arm and output arm operate in unison or synchronously,
and that any movement caused by the cam through a relative
rotation of the bellcrank link causes a differential move-
ment of the output shaft relative to the input shaft as
opposed to the more conventional system in which the cam
must generate the entire output movement.
-40-
