Note: Descriptions are shown in the official language in which they were submitted.
1~7~J~
Related Applications
The subject matter of this application is related to
that included in my United States Patent No. 4,490,091 which
issued on December 25, 1984.
Title
!
Reciprocating Long Dwell Mechanism
Field of Invention
Mechanism which in combination can produce, with a
constant speed rotary input, a long dwell output which can be
utilized, for example, in gantry type transfer systems with
mechanical hands for work parts.
Backaround and Obiects of the Invention
In the field of mechanically generated motions, many
applications arise in which it is desired to create a
reciprocating motion from a rotary motion. These requirements
are generally met with the well-known crank and slider mechanism
or the related Scotch type yoke mechanism. However, these have
a relatively short dwell which is inadequate for some
applications.
Itisan object of this inventiontoprovidea mechanism
which generates a reciprocating motion from a rotary motion and
in which the output remains substantially stationary, that is,
- 1~71055
in dwell for an appreciable fraction of the overall cycle at
each end of the reciprocating output stroke.
Motions of this type can also be generated by cam
mechanisms, but these are limited practically to strokes of a
few feet or less before becoming very expensive.
It is another object of this invention to provide a
mechanism which, by its nature, can be economically constructed
to achieve strokes of 6 feet or more.
Another object of this invention is to provide a
reversing mechanism having a dwell at each end of its stroke
and having an additional dwell at a predetermined point along
its stroke along one direction of travel and another such
additional dwell at anotherpredeterminedpoint alongthe reverse
direction of travel, where such dwells may be instantaneous
stops or significant reductions of velocity.
This invention is directed to a reciprocating
mechanical drive system capable of providing a wide variety of
kinematic objectives including long dwells at the ends of a
stroke,intermediate slowdowns, stops, or short reversals during
a stroke, and non-symmetrical movement when moving in one
direction as compared to the movement in the other direction.
The structure involves the use of a rotary output drive system
~27~05~
, .
which is comprised of a frame, an output shaft member mounted
for rotation in said frame, a rotary output member mounted on
said output shaft member, a drive surface on said rotary output
member, an eccentric drive member rotatable about a moving
center to engage said drive surface in a tangential driving
relationship, means mounting said eccentric drive member for
rotational motion about its moving center and in driving
engagement with said drive surface of said rotary output member,
a rotative drive member, means mounting said rotative drive
member for movement in a path generally transverse of said drive
surface of said rotary output member, means mounting said
eccentric drive member in non-rotational relation to said
rotative drive member with the axes of said eccentric drive
member and said rotative drive member parallel but spaced from
each other wherein rotation of said rotative drive member causes
it to rotate about the moving center of said eccentric drive
member, and power drive means to impart a rotation to one of
said drive members, whereby upon such a rotation of one of said
drive members said output shaft member rotates at a cyclically
varying velocity including cyclically slowing down, stopping,
and undergoing a slight reversal, dependent upon the distance
between the axes of said eccentric drive member and said rotative
drive member, and the number of such cyclic variations per
revolution of said output shaft is the ratio of the pitch radius
of said output member to the pitch radius of said eccentric
member. The invention also utilizes a reciprocating output
.~
~271055
drive system which includes a crank member mounted at its one
end to said output shaft member, connecting rod means journalled
at its one end tothe other end of said crank member,reciprocating
output means mounted for reciprocation in said frame, and
pivotally connectedto the other end of saidconnecting rodmeans.
Other features of the invention will be apparent in
the following description and claims in which the principle of
the invention is disclosed together with details directed to
persons skilled in the art to enable the invention to be utilized
all in connection with the best modes presently contemplated
for the invention.
Brief Description of the Drawinqs
DRAWINGS accompany the disclosure and the various
views thereof may be briefly described as:
-2b-
A
`"-" 1~7105S
FIG. 1, a semi-schematic front view of a mechanism
which is one embodiment of the mechanisms disclosed in my U.S.
Patent No. 3,789,676, dated February 5, 1974.
FIG. 2, a plan view of the mechanism of FIG. 1.
FIG. 3, a schematic representation of the mechanism
of FIG. 1, shown at the starting and stopping point of an index
cycle.
FIGS. 4, 5 and 6, schematic representations of the
mechanism of FIG. 1 after rotation of the input shaft through
angles of 90, 180 and 270, respectively.
FIG. 7, a front view of a crank and connecting rod
mechanism.
FIG. 8, a section taken on line 8--8 of FIG. 7.
FIG. 9, a schematic diagram for determining the output
motion of the crank and connecting rod mechanism of FIG. 7.
FIG. 10, an illustrative diagram used to define the
terms dwell amplitude and dwell length of any dwell producing
mechanism.
FIG. 11, a front view of an embodiment of my U.S.
Patent No.4,490,091, dated Dec. 25, 1984, showing an application
of this invention to rotate a mechanical hand during the lift,
transfer, and rotate motion of a gantry type transfer mechanism.
FIG. 12, a section taken on line 12--12 of FIG. 11.
FIG. 13, a graph showing the output characteristics
of the mechanism of FIG. 1 and the output characteristics of
the mechanism of FIG. 11.
FIG. 14, a plan view of another embodiment of this
invention.
FIG. 15, a front view of the mechanism of FIG. 14.
FIG. 16, a graph showing the dwell characteristics
of: the crank and connecting rod mechanism; the mechanism of
~27~0r,5
FIG. 1 with ~= 1; the mechanism of FIGS, 14 and 15 with ~ = 1; and
the mechanism of FIGS. 14 and 15 with ~ = 1.1.
FIG. 17, a graph showing the angular dwell charac-
teristics of the crank only of the mechanism of FIGS. 14 and 15
for various values of ~.
FIG. 18, a graph showing the dwell characteristics
of the mechanism of FIGS. 14 and 15 for various values of ~.
FIG. 19, a graph showing the displacement
characteristics of the mechanism of FIGS. 14 and 15 with a phase
angle of 90; and a second graph showing the characteristics
with a phase angle of 60.
FIG. 20, a graph showing the displacement charac-
teristics of the mechanism of FIGS. 14 and 15, in which the
output index angle of the mechanism 20 is 360.
FIG. 21, a graph showing the displacement charac-
teristics of the mechanism of FIGS. 14 and 15, in which the
output index angle of the mechanism 20 is 90.
First Dwell ~echanism - Backaround
In my existing U. S. Patent No. 3,789,676, a family
of mechanisms are disclosed which are capable of generating an
intermittent output motion, either linear or rotary, from an
input motion rotating at a given constant angular velocity.
Subsequently, in this disclosure, the Patent 3,789,676 wiil be
referred to as the background patent. A review of this background
patent will indicate that there are several embodiments, e.g.,
FIGS. 14, 15, 16; 22, 23, 24; 25, 26, 27; and 33, 34, 35, which
all provide a rotary output. Specifically referring to FIGS.
14, 15 and 16 of the background patent, and FIGS. 17 to 21,
--4--
i~7~55
which illustrate the sequential position and motion
characteristics of that system during an index cycle, it can
be seen that the output gear 330 rotates through an angle of
90 during a given index cycle. This is a result of the gear
328 having a pitch diameter which is ~ the pitch diameter of
the output gear 330. In this present invention which will
subsequently be described, that portion of the mechanism arising
from the background patent will utilize an index angle of
approximately 180. Such a mechanism is described in FIGS. 1 to
6 of the present disclosure.
These FIGS. 1 to 6 have also previously been shown
as Figs. 9 to 14 in my U. S. Patent No. 4,490,091.
Referring to FIGS. 1 and 2, a mechanism 20 includes
an input gear 22 mounted on an input shaft 24 which is journalled
in a housing or frame 25 on axis Al and driven by an appropriate
external drive system. The housing 25 is shown in phantom for
application reference. Also journalled on the input shaft 24 is
a tangential link 26 which oscillates thereon as will be
described. A driving gear 28 is mounted on a shaft 30 journalled
in the outboard end of the link26 onaxisA2, and, anintermediate
gear 32, also journalled in the link 26, is formed to mesh with
the input gear 22 and driving gear 28. An eccentric gear 34
is mounted on the shaft 30 through a cheekplate 35 with an
eccentricity approximately equal to its pitch radius. This
eccentric gear 34, rotating on a moving axis A3, meshes with
an output gear 36 mounted on an output shaft 38 also journalled
in the housing 25 on axis A4. A radial link 40 is also journalled
on the output shaft 38 at its one end; at its other end, the
--5--
~27~()55
.
radial link 40 is journalled to a stub shaft 42 on axis A3
mounted concentrically on the eccentric gear 34. It is the
purpose of this radial link 40 to keep the eccentric ~ear 34
in mesh with the output gear 36 as the eccentric gear 34 moves
through its rotational and translational path.
When the mechanism is in the position shown in FIG. 1,
it is in a natural dwell position, i.e., a small rotation of
the input gear 22 causes a corresponding rotation of the driving
gear 28 and the eccentric gear 34, but this rotation of the
eccentric gear 34 is accompanied by a corresponding movement
of the shaft 42 about the output shaft 38, such that the gear
34 literally rolls about the output gear 36 which remains nearly
stationary or in dwell.
A qualitative schematic representatiOn of the motion
of the output gear 36 during a complete 360 rotation of the
driving gear 28 and eccentric gear 34, at 90 intervals, is
shown in FIGS. 3-6. An arbitrary radial marker line Z has been
added to the output gear 36 to show its position change at these
intervals. FIG. 3 shows the position of all gears at the center
of the dwell, which is the same configuration as shown in FIG. 1.
After 90 of clockwise rotation of gears 34 and 28,
the position shown in FIG. 4 is reached. At this point, the
acceleration of gear 36 in the counterclockwise direction has
reached its approximate maximum, and the velocity of the gear
36 in the counterclockwise direction is approximately equal to
its average velocity.
-~ ` 1271055
As the gears 28 and 34 continue their rotation clock-
wise, the output gear 36 continues to accelerate, at a decreasing
rate, in the counterclockwise direction from the position shown
in FIG. 4. After an additional 90 of rotation of gears 34 and
28, the positions shown in FIG. 5 is reached. At this point,
the acceleration of the gear 36 has substantially returned to
zero, and its velocity in the counterclockwise direction has
reached an approximate maximum which is approximately double
the average velocity.
As the gears 28 and 34 continue to rotate clockwise,
the output gear 36 continues .to rotate counterclockwise from
the position shown in FIG. 5- but is decelerating. After an
additional 90 of rotation of gears 28 and 34, or a total of
270 from the start of the cycle, the position shown in FIG. 6
is reached. As this point, the deceleration of the output gear
36 is at or near maximum, while the velocity of the output gear
36, still in the counterclockwise direction, has slowed down
to approximately its average velocity.
As the gears 28 and 34 continue to rotate clockwise,
the output gear 36 continues to rotate counterclockwise from
its position shown in FIG. 6, but is still decelerating, though
now at a decreasing rate. After an additional 90 of rotation
of gears 28 and 34, or a total of 360 from the start of the
cycle, the position shown in FIG. 3 is again reached, with the
output gear 36 having completed 180 of rotation and is now
again in dwell. The position of the marker Z has now reached
the position Zl
~7~(355
It can be seen, thereEore, that as the input ~ear 22
is driven by some external power means, at a substantially
constant angular velocity, the gears 28 and 34 are driven by
the intermediate gear 32. Gears 28 and 34 have an angular
velocity which is determined by the superposition of the effect
of the oscillation of link 26 about shaft 24 on the velocity
created by the input gear 22 so gears 28 and 34 do not rotate at
a constant angular velocity. And the oscillation of the gear
34 along the arcuate path controlled by radial link 40 and
created by its eccentric mounting on shaft 30 creates another
superposition on the velocity of the output gear 36. With the
proportions shown in FIGS. 2 to 6, the output gear 36 will come to
a complete stop or dwell once every 180, since the pitch
diameter of gear 34 is shown as being one-half the pitch diameter
of gear 36.
Whereas the rotary output embodiment of thebackground
patent shown in FIGS. 14 to 21 therein produced an output index
angle of 90, due to the proportions of gears 328 and 330, the
output index angle of the embodiment shown in FIGS. 1 to 6
herein produces an output index angle of 180 as previously
described. Furthermore, in the background patent, the mechanism
of FIGS. 14 to 16 shows a chain connection 320 from the member,
sproc~et 322, on axis Al to the member, sprocket 318, on axis
A2, whereas in the embodiment, FIGS. 1-6, shown herein, this
equivalent drive connection is shown as being through gears 22,
32 and 28. This minor structural modification was made to
achieve greater drive stiffness.
~ ~27~055
Second Dwell Mechanism - Back~round
The second background mechanism utilized in the
invention of the present disclosure i8 comprised of a crank and
connecting rod mechanism described in many books on fundamental
kinematics. It is illustrated here schematically in FIGS. 7,
8 and 9.
Referring to FIGS. 7 and 8, a shaft 50 rotates on
axis As, and is journalled in a frame 52 through a bushing 54;
this shaft 56 can be driven by any suitable prime mover. ~ crank
56 is fastened to the shaft 50, and at its outer end supports
a crankpin 58 concentric about an axis A6. A connecting rod 60
is journalled at its one end on the crankpin 58; at its other end
it is pivot connected to a slide block 62 through a pivot pin 64
on axis A7. The slide block 62 is supported by the frame 52
in which it is free to slide along an axis Ag, which, as shown
in FIG. 8, intersects the axis A5.
In FIG. 9 is shown a schematic diagram useful to
analyze the kinematic characteristics of the system. The
distance on the crank 56 between axis As and A6 is defined as R
and the length of the connecting rod between pins 58 and 64 is
defined as L. The mechanism is shown in two positions: a base
position shown in solid lines (which is the top dead center
position) and a position shown in dotted lines after the crank R
has rotated from its base position by some arbitrary angle ~ .
From this diagram, it is easily seen that the amount the slider
block 62 has moved from its base position as the crank R moves
through the angle ~ from its base position is given by
t _9_
7~055
D = R - L - R cos~ + L cos a ( 1 )
where ~ = sin~l (~ sin~) (2)
If it is assumed that L is large compared to R and
therefore the angle N iS small, even when it is at a maximum,
then cos a is very closely approximated by 1, whereupon:
D - R - R cos~ ~ R (1 - cos~) ~3)
This approximate equation is for the kinematic
displacement characteristics of the crank and slider block
motion.
Dwell
The term "dwell", in the generally accepted kinematic
sense and as applied to any mechanism, is taken to mean that
the output of that mechanism is stationary while its input
continues to move. In the theoretical sense, the output is zero;
cam generated output movements oftentimes incorporate such a
dwell as is well known. However, many practical applications
arise in which a true zero movement dwell is not required, but
in which some very slight oscillatory motion of the output is
acceptable. Such a situation will be defined, for the purposes
of this disclosure as a "near dwell"; and furthermore, it will
be characterized by a numerical value which gives the maximum
peak-to-peak amplitude of the output oscillation, expressed as
a fraction of the total output stroke of the mechanism. For
example,a near dwell ~.OOl)would meanthat the outputoscillates
during the defined near dwell through a total amplitude of .001
--10--
i271055
times the total stroke of the mechanism. This is shown
schematically in FIG. 10 which further schematically de~ines
the term "dwell length". If it is assumed that a mechanism is
driven by an input shaft which rotates at a constant angular
velocity, and that the time required for a given index cycle
is divided into 360 units, then each of those units is defined as
1 degree of clock angle. A dwell length of 90 clock angle,
for example, would represent a cycle in which the output would
be in near dwell for 90/360 or for one quarter of the cycle.
Clearly, if the input shaft rotates through one revolution
during an index cycle, then one degree of input shaft rotation
equals one degree of clock angle; or, if, for example, the input
shaft rotates through three revolutions during an index cycle,
then every three degrees of input shaft rotation equals one
degree of clock angle. Stated another way, the number of degrees
of input shaft rotation equal to one degree of clock angle may
be determined by dividing the total number of input shaft
rotation degrees required for an index cycle by 360.
Description of the Invention
The invention to be described herein is a combination
or tandem mechanism employing two drive stages, the first stage
of which is comprised of a rotary output indexing mechanism of
the type disclosed in the background patent and in FIGS. 1 to
6 herein and having an output index angle of approximately 180;
and the second stage of which is comprised of the crank and
connecting rod mechanism described above. This combination of
mechanisms is both unique and useful and yields results which
can be determined only by detailed analysis which must be made
to ascertain the various system characteristics achievable.
)S~
A first embodiment of this invention is shown in my
U. S.Patent No.4,490,091andis redescribedhereininconnection
with FIGS. 11 and 12.
The embodiment of this invention as shown in FIGS. 11
and 12 is used as an auxiliary mechanism to rotate a workpiece
100 during the lift, transfer and lower motion of a gantry type
transfer system. The workpiece 100 is located and clamped by
a cylinder actuated mechanical hand 102 mounted on a shaft 110
suitably journalled in a bracket 112; the shaft 110 is driven by
an actuator arm 114 as will be described. The bracket 112 is
mounted on one end of a transfer beam 116 which comprises the
element of the gantry type transfer system which moves through
the lift, transfer, and lower motion. This transfer beam 116
is supported by multiple crank arms from a horizontally moving
overhead carriage. One such crank arm 118 is shown and rotates
360 clockwise with respect to the transfer beam 116 during a
typical transfer motion as is completely explained in my patent
4,490,091. The crank arm 118 supports the transfer beam 116
through a crankpin 120, which is ~ournalled in the transfer
beam 116 and is used as the power and synchronizing source for
the hand rotation mechanism to be described. The mechanism 20
in housing 25 is mounted to the transfer beam 116 and positioned
such that the input shaft 24 is coaxial with the crankpin 120,
to which it is directly coupled; or the input shaft 24 may be
made integral with the crankpin 120. Within the housing 25,
the gear system previously described in FIGS. 1 to 6 herein
drives the output gear 36 and output shaft 38; the housing 25
is further oriented on the transfer beam such that the output
-12-
1271(~55
shaft 38 lies approximately in the plane of the actuator arm
114. A drive crank 122 is mounted on the output shaft 38 and on
it is mounted a spherical headed crankpin 124 to which is
journalled a connecting rod 126. The other end of thisconnecting
rod 126 is pivotally connected to the actuator arm 114, again
through a spherical headed pin 128 (FIG. 12).
In FIGS. 11 and 12, the drive crank 122, connecting
rod 126, and actuator arm 114 are shown in their position
corresponding to the position of the carriage in the starting
position prior to a forward transfer stroke. As the carriage
is moved forward through its stroke, the crank arm 118 is rotated
360 clockwise with respect to the transfer beam 116 as described
in Patent 4,490,091. This rotates the input shaft 24 360
clockwise causing the output shaft 38 to rotate 180
counterclockwise with anaccelerated-decelerated motionas shown
by curve A of FIG. 13, and by arrow M in FIG. 11. It will be
noted that curves A and B of FIG. 13 are also identical with
the curves A and C respectively of FIG. 15, Patent 4,490,091.
This in turn drives the actuator arm 114, through the connecting
rod 126, in the direction shown by arrow N in FIG. 12. At the
completion of the forward stroke the drive crank 122, connecting
rod 126 and actuator arm 114 reach the positions shown in dotted
lines and respectively noted as 122A, 126A and 114A.
It can be seen that the crank arm 122 and actuator
arm 114 rotate in different planes; hence, the requirement for
the spherical pins at each end of the connecting rod 126. Since
the crank arm and connecting rod in themselves comprise a second
accelerating-decelerating mechanism, having its own dwell at
each end of the stroke (approximately harmonic motion), this
` ` ~"27~0~;~
effect is superimposed on the dwell of the mechanism of FIG. 1.
This increases the dwell in the movement of the actuator arm
114 relative to the rotation of the crank arm 118. This movement
relationship is shown by curve B of FIG. 13 and approximates
the characteristics of a cam mechanism.
The rotation angle of the actuator arm 114 is shown
as 60 in FIG. 12. This is variable by changing the length of
the drive crank 122 and/or changing the length of the actuator
arm 114.
The description in connection with FIGS. 11, 12 and
13 presents a specific and very useful application of this
invention in which it is used to provide a coordinated rotation
of a workpiece synchronously with a primary lift, transfer and
lower motion of the gantry mechanism. In this application, the
very long dwell is of particular importance in delaying rotation
of the workpiece during the lift portion of the transfer stroke.
However, this mechanism's usefulness is not limited
to such auxiliary roles. A more generalized application is
described below.
Referring to FIGS. 14 and 15, the mechanism 20,
previously described in connection with FIGS. 1 to 6, is enclosed
in the housing 25 and mounted on a base 140. Its input shaft 24
i8 driven through a coupling 142 by the output shaft 144 of a
gear reducer 146 also mounted on the base 140. The input shaft
148 of this gear reducer is in turn driven by a motor 150 through
a coupling 152. Depending on the application the motor may run
continuously, or it may be stopped during the mechanism dwell
` 1271()55
with suitable conventional limit switches and electrical
circuits. The crank 56 (FIGS. 7, 8 and 9) is directly mounted
on the output shaft 38 of the mechanism 20, whereupon axes A4
and A5 become coincident. Clearly the shaft 50 and frame 52
(FIGS. 7 and 8) could be retained and a coupling used to connect
shafts 38 and 50 if this were more convenient. The crankpin 58
on crank 56 is used to drive the connecting rod 60 in a
reciprocating motion. The other end of the connecting rod 60
is connected to a reciprocating output member, which may be a
slider block, such as shown in FIG. 8, from which the load is
driven, or the connecting rod 60 may be directly connected to
an input member of the load to be driven. Such an input member
may be a link, a bellcrank, or a sliding member. In any case,
the output movement will be as given by the approximate equation
(3) derived above, where the angle ~ is now the output angle of
the mechanism 20.
Referring to the background patent, the velocity was
shown to be:
da = 1 - ~cosO [I + (a2 ~ 1 + sin2~
It will be noted that a is the ratio of the distance
from axis Al to A2 to the distance from the axis A2 to A3
~FIG. 1) and is generally a large number. Therefore, as a first
order approximation, the denominator ~a2 - 1 + sin2~)~ will be
large, and the entire fraction negligibly small. Equation (4)
will therefore reduce to:
12710~5
d~ cos~ (5)
This equation may be integrated to give the
displacement:
u -- a - ~sin~ + Cl (6)
This is a general approximate equation for the
displacement, properly dimensioned and scaled, for any of the
embodiments of the background patent.
Unitized Output
For comparative purposes in comparing the dwells, and
other characteristics, of the mechanism of FIGS. 1-6, the crank
mechanism of FIGS. 7-9, and the combination mechanism of FIGS.
14 and 15, it i3 conver.ient to scale the output of each system
such that the index stroke is arbitrarily set to equal 1.
Similarly, the input angle is defined in terms of the clock
angle which has a range of 360 to create the output stroke of
1. Under these arbitrary scaling procedures, equation ~3)
becomes
DU a .5 [1 - cos (~Pc)] (7)
where
DU = "unitized" output
~ C = "clock" angle
This rescaling is dependent on the following reasoning
relative to equation (3). The minimum position occurs when ~ =
-16-
lX7~
0, and D = O independent of the value of R. The maximum position
occurs when ~= 180 and D is equal to 2R. Therefore, by setting
R = ~and ~ C) the maximum reaches 1 when~c = 360 and it is
by substituting these values for R and ~ into equation t3) that
equation (7) is obtained.
The output displacement rom equation (7~, in the
near dwell area, is tabulated in Table I and shown graphically
by curve Ref A in FIG. 16.
TABLE I
Unitized Displacement of a
Simple Crank Mechanism Near Dwell
Clock Anqle Unitized Displacement
-20 .007596
-15 .004278
-10 .001903
_ 5 .000476
O O
.000476
.001903
.004278
.007596
By following a comparable process, the generalized
displacement equation (6), which represents the mechanism 20,
may be scaled to provide
-17-
~2~0~5
Du 2~ [180 ~C ~ Asin~c)] 1 t8~
The factor ~/180 is used as a multiplier Of ~C
to convert the "clock angle" to radians, as required by the
basic theory of the background patent; and the factor 1/2~ is
a required scale factor on the bracketed quantity, since, when
the clock angle reaches 360, the value of that bracketed
quantity is 2~ . The constant of integration Cl is in effect
a phase angle and will be set to 0 for the initial comparative
purposes. Equation t8) therefore reduces to:
,,
U ~C A sin (~C)
360 2~
By referring to equation (4), it can be shown that
for the velocity to be zero when ~ = 0, A must be 1, i.e., the
distance from axis A2 to axis A3 of the mechanism of FIGS. 1-6
must be equal to the pitch radius of the gear 34, whereupon
equation (9) further reduces to:
DU = ~C ~ 12 sin (~C) (10)
The output displacement, from equation (10), in the
near dwell area, is tabulated in the following Table II and
shown graphically by curve Ref B in FIG. 16.
-18-
1~ 71() '~
Table II
Unitized Displacement of a
Mechanism of Patent 3,789,676 Near Dwell
Clock Anqle Unitized Displacement
-20 -.001121
-15 -.000474
-10 -.0001~1
- 5 -~000018
O O
.000018
.000141
.000474
~001121
Two observations may be made relevant to Tables I and
II and their graphical representation in curves Ref A and Ref B
of FIG. 16. The first concerns the relative shortness of their
individual dwells. If, for example, the dwell amplitude is
arbitrarily defined as .001 ~in unitized displacement), the
dwell length of the connecting rod mechanism is approximately
+8 for a total length of approximately 16; this is obtained
from curve Ref A. For the mechanism 20, the intersection of
the curve Ref B with the +.0005 and -.0005 lines (for a total
of .001) is found to be approximately +16 for a total of
approximately 32.
The second observation concerns the directional
behavior of the displacement in the vicinity of the dwell.
Relative to the crank and connecting rod mechanism, it can be
seen that the displacement on either side of the center of
dwell, where the clock angle is 0, is unidirectional as would
--19--
12710~:;5
be expected with an inherently reversing mechanism such as a
crank and connecting rod. On the other hand, it can be seen
that, relative to the mechanism 20, the displacement on either
side of the center of dwell is bidirectional; this is again as
would be expected for an indexing mechanism of this type; i.e.,
for unidirectional input shaft rotation, the output will
momentarily stop after a given index, but then reaccelerate in
the same direction it had before stopping.
The foregoing data on the near dwell characteristics
of each of the mechanisms operating independently are provided
as reference data for the new data to be shown.
In the present invention, as illustrated in the
mechanism of FIGS. 11 and 12 and 14 and 15, it is necessary to
rescale equation (6), representing the mechanism of FIGS. 1-6
and equation (3) representing the crank mechanism of FIGS. 7-
9. By a process similar to the one described above, equation
(6) is rescaled to:
~ = 180 12~ [180 ~C ~sin (~C~ + Cl (11)
which reduces to
~ ~C 90~ sin (~C) + Cl (12)
where ~ is the true output angle, in degrees, of the shaft 38
(FIG. 2).
-20-
~ " i271055
Equation (3) is rescaled to:
D = 5 [1 - cos(~)~ (13)
where ~ is again the true angle in degrees of the shaft 38 which
is the input shaft of the crank mechanism. The displacement
characteristics of the combined mechanism of FIGS. 14 and 15
is therefore obtained by combining equations (12 and (13) as
follows:
D = 5 { 1 - cos [ 2 ~ 90~ sin(~C) 1~ (14)
which simplifies to:
[ 2 ~ ( ) ] (15)
The arbitrary quantity Cl ~which was the constant of
integration)representsa phase angle between the twomechanisms.
If it is set to 0, it means physically that the mechanism 20 is
at the center of its dwell when the crank is at its top dead
center or bottom dead center position. For the first analysis,
it is set to 0; other values will be subsequently analyzed.
Similarly, the factor ~ i3 initially set equal to 1
as was done for the analysis of the individual mechanism 20;
subsequent analyses will be made with values of ~ other than 1.
The unitized displacement for the combined mechanism, which
comprises this invention, as calculated from equation ~15) with
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127~(~55
Cl = 0 and ~= 1 is given in Table III and shown as curve C in
FIG. 16.
Table III
United Displacement of One
Embodiment of This Invention
Clock Anqle Unitized Displacement
-60 .002050
-50 7.10 x 10-4
-40 1.91 x 10-4
-30 3.48 x 10-5
-20 3.10 x 10-6
-10 Less than 1 x 10-7
O O
Less than 1 x 10-7
3.10 x 10-6
3.48 x 10-5
1.91 x 10-4
7.10 x 10-4
2.050 x 10-3
Two observations may also be made with respect to
curve C, FIG. 16 representing the dwell behavior of the combined
mechanism. The first concerns the width of the dwell, again
for the arbitrarily set value of dwell amplitude of .001. The
magnitude of the dwell length is seen to be approximately -53
for a total dwell length of 106 which is more than double the
sum of the dwells of the individual mechanisms.
Next the importance of the ~ factor will be shown.
If ~ , in equation (15) is arbitrarily set equal to 1.1, while
1271~55
the phase angle Cl is still set equal to 0, a further increase
in the dwell length is found as shown in Table IV and curve D
in FIG. 16.
Table_IV
Unitized Displacement On An
Embodiment of this Invention
~ = 1.1
Clock Anqle Unitized Displacement
-70 2.21 x 10-3
-60 5.59 x 10-4
-50 -5.63 x 10-5
-40 4.99 x 10-6
-30 4.36 x 10-5
-20 4.61 x 10-5
-10 1.70 x 10-5
~ o O
1.70 x 10-5
4.61 x 10-5
4.36 x 10-5
4.99 x 10-6
5.63 x 10-5
5.59 x 10-4
2.21 x 10-3
This highly desirable lengthening of the dwell may
be explained as follows. The setting of ~ to 1.1 means that
the distance between axes A2 and A3 of the mechanism 20, FIGS. 1-
6, is 1.1 times the pitch radius of the eccentric gear 34. In
turn, this condition causes the output gear 36 to experience a
slight "overshoot" before it reaches the center of the dwell,
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127~055
and then a reversal to the 0 point at the center of the dwell.
This reversal continues through the 0 point, and "undershoots"
with continued input shaft rotation, before the output gear
continues its next forward index. Since the crank 56, FIGS. 7,
8, 14 and 15, and crank 122 of FIGS. 11 and 12, rotates in
unison with the output shaft 38 and the output gear 36, this
results in a slight oscillation of the crank 56 (FIGS. 7 and
8). This is quantitatively shown by curve D' in FIG. 17 which
shows the true crank angle, in degrees, plotted against clock
angle, where 0 degrees on the crank angle scale represents a
top dead center or bottom dead center position. For curve D',
which represents the condition for ~ 1.1, it can be seen that
the oscillation amplitude of the output gear 36 and crank 56
is +0.82; this in turn creates a significant increase in dwell
length for the overall system as shown by curve D (~ = 1.1)
relative to curve C (~ =1.0) in FIG. 16. Indeed, for the
arbitrary previously chosen dwell amplitude of .001, the dwell
length for ~ = 1.1 is seen to be +64 for a total dwell length
of 128, which is some 20% more than for curve C ( ~= 1.0).
A still further improvement of the dwell length can
be made by increasing ~ still more. With ~ set equal to 1.2,
the dwell characteristics of the total system are shown by curve
E of FIG. 18 which is plotted to the same scale as FIG. 16.
The corresponding curve showing the overshoot, reversal and
undershoot of the crank 56, and output gear 36, as plotted in
true crank angle, is shown by curve E' of FIG. 17, from which it
can be seen that the crank oscillates through an angle of +2.2.
The magnitude of this oscillation is now sufficiently great to
manifest itself in the overall ~ystem dwell curve E of FIG. 18.
Clearly the "lobes" of the curve E from -58 to 0 and from 0
-24-
1;~71V55
to 58 are caused by the crank oscillation shown by curve E',
FIG. 17. It will also be noted that the dwell length, for an
amplitude of .001 and ~ 1.2, curve E, is now + 74 for a total
dwell length of 148.
It follows, therefore, that for the dwell length to
be maximized for some arbitrary but knowledgably set value of
the dwell amplitude, a A can be found in which the height of
the lobes on either side of the center of dwell are equal in
amplitude to the set dwell amplitude. With respect to the
previously set dwell amplitude of .001, a value of ~was found
which creates this condition. For a ~ of 1.2829, the system
displacement curve F, FIG. 18 was calculated, in which it will
be noted, the lobes on either side of the center of dwell just
touch the .001 displacement line at + 40. The corresponding
crank angle oscillation is shown by curve F', FIG. 17 and is
3.624, which values are reached at approximately + 40 clock
angle. The dwell length, as shown by curve F, FIG. 18 is +79 for
a total dwell length of 158. This is some 49~ longer than the
total dwell length of curve C, FIG. 16 (~- 1) and over three
times greater than the sum of the dwells of the individual
mechanisms.
The value of A = 1.2829 used to calculate curve F and
F' was found by a process of successive approximation. With a
programmable calculator or computer, it is a relatively simple
process to iterate the value of A either by a manual or automatic
loop process to achieve a maximum lobe amplitude equal to the
set .001.
-25-
~L~7~5
By a similar process of successive approximation,
values of were found which give other dwell amplitudes, in
which the lobes approximate the set values thereof. These,
together with the resultant dwell lengths, are tabulated below:
Set Value Dwell
Dwell Amplitude ~Lenqth
.00001 1.058 74
.0001 1.13 114
.001 1.283 148
The selection of dwell amplitude is determined by the
application intended. Once this is known, it is a simple process
to find the ~ that gives the longest dwell, or conversely, if
the dwell length required is known and the smallest dwell
amplitude for that given dwell length is sought, ~ may be
iterated again to the new objective.
The curves of FIGS. 16, 17 and 18, and the descriptions
thereof addressed themselves to achieving the longest dwell
length possible for a given dwell amplitude. This was
accomplished by setting the phase angle equal to 0, where the
phase angle mathematically is represented by the value Cl in
equation (15), and is mechanically represented by the angle of
the crank 56 away from its top dead center or bottom dead center
position when the mechanism 20 is at the center of its dwell.
The maximum systems dwell is reached when the phase angle is 0.
However, other useful objectives can be achieved when
the phase angle is set to some value other than 0. For example,
if the phase angle is set equal to 90, a dwell or near dwell of
the crank rotation, and its output motion can be reached midway
-26-
~27~0~
during its stroke, dependent on the value of ~. Physicallythis means that when the mechanism 20 is at the center of its
dwell, the angle ~ , FIG. 9, is equal to 90. This is merely
a matter of assembly positioning of the crank 56 on the shaft
38, for example, in FIG. 15.
The unitizeddisplacement curve Gof FIG.19represents
the output of this invention for a given phase angle of 90
with ~ set equal to 0.9. The clock angle is shown as moving
through 720 which is two indexes of the mechanism 20 but only
one revolution of the crank 56. The momentary stops at the ends
of the strokes are evident at clock angles of 180 and 540.
A significant slowdown to a near stop at clock angles of 0, 360
and 720 (720 is the same position as 0) is also evident.
The slowdown, as differentiated from a complete stop, is a
result of the arbitrarily illustrated ~ = 0.9; if ~ were set
equal to 1, the output would come to an instantaneous stop at
0 and 360. Furthermore, if ~ were made slightly larger than
1, there would be a slight output reversal at these angles.
This midstroke slowdown is useful in many applications such as
lifting or lowering of transfer bars which pick up or deposit
workpieces at or near midstroke.
Another illustrative output displacement graph is
shown in curve H, FIG. 19. In this example, the phase angle was
set to 60 and ~ set equal to 0.8. Again the momentary stops
and reversals can be seen at 215 and 575 clock angle. A
significant slowdown is evident at 0 and 360 clock angle.
Here again, the slowdown can be greater if ~ is increased, and
a momentary stop achieved at ~ = 1, or a slight reversal
obtained by making ~ slightly more than 1. It is further
-27-
evident that the slowdown occurs at different positions of the
output on forward stroke than on the return stroke, if the
forward stroke is defined as 575 to 215 clock angle and the
return stroke defined as 215 to 575. On the forward stroke,
the slowdown occurs at a displacement of .25 and on the return
stroke the slowdown occurs at a displacement of .75. A property
such as this is useful, for example, in operating a lift system
such as in my U. S. Patent No. 4,750,605, where it is desired
to slow down at one level moving up and at another level moving
down.
The foregoing performance descriptions are
illustrative only. Clearly there exist many combinations, which
are mathematically represented by the factors ~ and Cl in
equation (15) which provide useful results and as previously
noted these factors ~ and Cl are controlled in the total
mechanical system by the design of the distance from axis A2
to axis A3 and by the assembly positioning of the crank 56 on
the shaft 38 (FIGS. 14, 15).
All the performance curves shown in FIGS. 16-19 were
derived onthe basis of equation (15), which, it will be recalled,
was derived after making some approximating simplifications.
However, in rigorously calculating the performance of these
systems without approximations by numerical computer
calculations (classical math non-approximating calculations
become hopelessly complex), it has been found that a very high
degree of correlation can be found between the characteristics
described herein and the exact characteristics numerically
calculated. This has involved adjusting, by successive
A
710S5
approximations, such factors as the distance between axes A
and A2 and between axes A4 and Al of mechanism 20.
In all of the combination mechanisms shown above,
independent of the values of ~ and the phase angle Cl, the
mechanism 20 was scaled to generate a 180 output rotation
during a given index cycle, as previously explained. However,
this invention has still further applications when the output
index angle of mechanism 20 is other than 180. As noted
earlier, and as shown in the reference patent, the output angle
index angle is determined by the ratio of the pitch diameter of
the output gear 36 to the pitch diameter of the eccentric gear
34. If this ratio is.defined as M, the output index angle is
360/M. Stated anotheE way, there are M indexes per revolution.
If equation (6) which, it will be recalled, is the equation for
calculating the output angle of mechanism 20, is rescaled in
the general form, it becomes:
~ M 2~ [180 C (~C)~ + Cl (16)
which simplifies to:
5 MC - 180~ sin (~C) + Cl (17)
When M is 2, the index angle is 180 and equation
(17) reduces to the already stated equation (12). If equation
(17) is substituted into equation (13) and simplified, the total
combinationmechanism output, in unitlzed displacement, is found
to be:
-29-
`- 12710S5
D ~ 5 - .5 cos[~c ~ 18M ( C) ] (18)
Again, it can be seen that when M = 2, equation t18)
reduces to the form, previously derived for the 180 index
angle, of equation (15). Using equation (18), the unitized
displacement characteristics of other embodiments of this
invention have been calculated.
The first of the illustrative examples is shown in
FIG. 20. In this instance, M was set equal to 1 representing a
360 output index angle of the mechanism 20, ~ was set equal to
1.1 and Cl set equal to 0. The curve of FIG. 20 shows a
reciprocating output having a very long dwell at one end of the
stroke, and a relatively short dwell at the other end of the
stroke; this is useful in applications in which the service is
such that the prime mover, e.g., motor 150, FIG. 14, is stopped
after each reciprocation, and it is required that a very accurate
output position be maintained over a wide range of stopping
positions of the prime mover.
Another illustrative example is shown in FIG. 21. In
this instance M was set equal to 4, representing a 90 output
index angle of the mechanism 20, A was set equal to 1 and Cl
set equal to 0. The curve of FIG. 21 again shows a reciprocating
output having a relatively long dwell at each end of the stroke,
together with a significant dwell at the midpoint of each stroke.
This duplicates the performance, in principle, of the conditions
of curve G of FIG. 19, except that by using the conditions of
FIG. 21, both the dwells at the ends of the strokes are longer,
providing more stopping leeway for motor stoppage when that
mode is being used in the application.
-30-
i.~710~;5
From the descriptions of the above illustrative
combinations, it is clear that a wide variety of kinemati~
characteristics can be achieved through a proper selection of
the various parameters involved, which may be summarized as
follows:
A. The ~ factor controls the cyclic behavior of the
mechanism 20; with ~ = 1, this output shaft will come to a
momentary stop once for each revolution of the eccentric gear;
with ~ slightly less than 1, the output shaft will come to a
near stop after each revolution of the eccentric gear; and,
with ~ slightly more than 1, the output shaft will slightly
reverse after each revolution of the eccentric gear.
B. The M factor controls the number of stops, near
stops, or reversals of the output shaft made during one total
revolution of the output shaft.
C. The phaseangle~ controls the angular relationship
of the output crank angular position from its top dead center
position when the driving mechanism 20 is at the center of its
dwell or near dwell.
The disclosure made above related to the rotary output
indexing system typified by FIGS. 14, 15 and 16 of the background
patent, No. 3,789,676, as earlier noted, except that the chain
320 was replaced by an equivalent gear train in the mechanism
of FIGS. 1-6 herein. It should be noted, however, that the
chain drive system of FIGS. 14, 15 and 16 of the background
patent is usable for many applicationq in which extreme accuracy
or rigidity are not required. Indeed, the double chain system
illustrated in FIGS. 33, 34 and 35 of the background patent is
1.;~7~055
. .
also usable subject to chain load and rigidity limitations.
Furthermore, the rotary output systems illustrated in FIGS. 22,
23 and 24 and by FIGS. 25, 26 and 27 in the backgraund patent
are also usable subject to the limitation that these embodiments
are limited to maximum output index angles of 120.
-32-
