CA1266190A - Reversing mechanism having great kinematic versatility - Google Patents

Abstract

ABSTRACT OF THE DISCLOSURE
Mechanisms which can produce, with a constant speed rotary input member, a reciprocating motion capable of producing very long dwells at each end of the stroke of the reciprocating motion, unequally long dwells at opposite ends of a stroke, and/or momentary stops intermediate the ends of the stroke. The mechanism can generate a dwell at each end of the stroke and an additional dwell at a predetermined point along the stroke in one direction of travel and another additional dwell at another predetermined point along the reverse direction of travel. The mechanism is further capable of creating high degrees of kinematic versatility between the ends of the stroke of the reciprocating mechanism.

Description

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Title Reversing Mechanism Having Great Kinematic Versatility Field of Invention An inherently reversing mechanism combination which can produce, with a constant speed rotary input, extremely long dwells, and/or an extremely wide variety of predetermined kinematic characteristics between the ends of a stroke, including different characteristics on the reverse stroke as compared with those of the forward stroke.

Backqround and Objects of the Invention In the field of mechanically generated motions, many applications arise in which it is desired to create a reciprocating motionfrom a rotary motion. Theserequirements 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.

It is an object of this invention to provide a mechanism which generates a reciprocating motion from a rotary moticn and in which the output remains substantially stationary, that is, in dwell for an appreciable fraction of the overall cycle at each end oE 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.

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It is another object of this invention to provide a mechanism which, by its nature, can be economically constructed to achieve strokes of 6 ~eet 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 another predetermined pointalong the reverse direction of travel, where such dwells may be instantaneous stops or significant reductions of velocity.

In my copending Canadian application, Serial No.
515,790, filed ~ugust 12, 1986, entitled "Reciprocating Long ~well Mechanism," there is disclosed a mechanism also capable of meeting the aforesaid objectives but whose kinematic versatility, while being very large, i5 not as great as that of the invention to be described herein. This new invention is capable of creating still longer dwells and/or greater kinematic versatility between the ends of the stroke than that of the aforesaid copending application.

The invention consists of a reciprocating mechanical drive system capable of providing an extremely wide variety of kinematic objectives, including very long dwells at the ends of the stroke, unequal dwells at opposite ends o~ the stroke 6~

intermediate dwells between the ends of a stroke, and non-symmetrical movement when moving in one direction, as compared to the movement in the other direction. This is accomplished by a combination mechanism comprising a rotary drive means which drives a reciprocating output drive system. The rotary drive means includes a frame, an output shaft member mounted for rotation in said frame, an output member mounted on said output shaft member and adapted for tangential driving and ha~ing a given pitch raaius, a first rotating pair supported in said frame comprising a first rotating member mounted for rotation in said frame, a first eccentric member mounted eccentrically, in non-rotational relation to, and on said first rotating member, a second rotating pair mounted in fi~ed spatial relationship with said first rotating pair comprising a second rotating member, a second eccentric member, having a given pitch radius, mounted eccentrically in non-rotational relation to, and on said second rotating member, means connecting for rotation said first rotating pair and said second rotating pair for sub-stantially an integral angular velocity ratio, means connecting said output member and said second eccentric member in a driving relationship, and power means connected to one of said rotating pairs to impart a rotary motion to that of said rotating pair, whereby rotation of said rotary pair by said power means at a presumed substantially constant angular velocity causes said output shaft member to undergo a series of acceleration-deceleration cycles and the angular distance traversed by said output shaft member during one such cycle is known as the index -2a-A.

angle. Also, the reciprocating output drive system includes a crank member mounted at one end to said output shaft member, connecting rod means journalled at one end to the other end of said ~rank member, reciprocating output means mounted for reciprocation in said frame, and pivotally connected to the other end of said connecting rod means.

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.

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Brie~ Description of the Drawinqs DRA~I~GS accompany the disclosure and the various views thereof may be briefly described as:
FIG. 1, a side semi-schematic view oEone embodiment of my existing U. S. Patent No~ 4,075,911.
FIG~ 2, a top view of FIG. 1.
FIG. 3, a side view oE the well-known crank and connecting rod mechanism.
FIG. 4, a section taken on line 4--4 of FIG. 3.
FI&. 5, a schematlc diagram of the mechanism of FIG. 3 useful for determining the equations of motion of that mechanism.
FIG. 6, a schematic diagram illustrating the definitions of dwell length and dwell amplitude.
FIG. 7, a plan view of the mechanical combination com~rising this invention.
FIG. 8, a side view of FIG. 7.
FIG. 9, an illustrative graphical presentation of the dwell characteristics of the crank and connecting rod mechanism; the mechanism o FIGS. 1 and 2 operating in the second and third harmonic arrangements with very long dwells;
and the combined mechanism of FIGS. 7 and 8.
FIG. 10, a generic dwell characteristic curve showing the behavior of the mechanism of FIGS. 1 and 2 operating in a five point dwell configuration.
FIG. 11, a generic dwell characteristic curve, showing the output of this invention when the crank is positioned on the mechanism of FIGS. 1 and 2, such that the crank is at a dead center position when the mechanism oE FIGS.
1 and 2 is in the center of dwell and configured to create a five point dwell.

FI~ , specific dwell characteristics curves of this invention configured to provide a dwell amplitude of .001 using a second and a third harmonic.
FIG. 13, a graph showing the velocity charac-teristics of this invention for the configurations whose dwell charact~ristics were shown in FIGS. 9 and 12.
FIG~ 14, an illustrative graph showing the dis-placement characteristics of this invention when the crank is positioned on the mechanism of FIG5. 1 and 2 with phase angles of 90 and 60.
FIG. 15, an illustrative graph showing the displacement characteristics of this invention when the ~mechanism of FIGS. 1 and 2 is configured to produce a 90 ~~index angle, with 0 phase angle.
FIG. 16, an illustxative graph showing the dis-placement characteristics of this invention when the mecha-nism of FIGS. 1 and 2 is configured to produce a 360 index angle, with 0 phase angle~ and using a second and third harmonic.
FIG. 17, a generic dwell characteristics curve showing the behavior of the mechanism of FIS. 1 and 2 operating in a three point dwell configura-tion.
FIG~ 18, a generic dwell characteristic curve, showing the output of this inventiOn when the crank is positioned on the mechanism of FIGS. 1 and ~, such that the crank is at a dead center position when the mechanism of FIGS.
1 and 2 is in the center of dwell and configured to create a three point dwell.
FIG. 19, an illustrative graphical presentation of the dwell characteristics of this invention when the mechanism of FIGS. l and 2 is configured to produce a three point dwell and the phase angle is 0; for both the second and third harmonic arran~ements.

F~G~ 20, ~ graph showing the velocity characteristics of this invention for the configurations whose dwell character-istics were presented in FIG. 19.

First Dwell _echanism - B~ckqround In my existing U.S. Patent No. 4,075,911~ 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 ~,075,911 will be referred to as the background patent. A reviewof this background patent will indicate that there are several embodiments, e.g., FIGS. 51, 52, 53; 54, 55, 56; 57, 58, 59; 60, 61, 62; 63, 64 and 65, which all provide a rotary output. Specifically referring to FIGS. 51, 52, and 53 of the background patent, it can be seen that the output gear 332 rotates through an angle of 90 during a given index cycle. This is a result of the gear 330 having a pitch diameter which is ~ the pitch diameter of the output gear 332. In this present invention which will subsequently be described, that portion of the mechanism arising from the background patent will initially utilize an index angle of approximately 180. Such a mechanism is described in FIG5.
1 and 2 of the present disclosure.

FIGS. 1 and 2 are simplified schematic drawing~
of this embodiment which is proportioned to provide a 180 output for one acceleration-deceleration cycle of its output shaft. Referring to FIGS. 1 and 2, this mechanism 30 is compri~ed o~ an input shaft 3~ which rotates on axis Ao in stationary bearin~s in a housing which is not shown. An eccentric segmen-t 34, on the shaft 32, is concentric about an axis Al displaced a small amount from the axis Ao~ An input gear 36, fastened on the eccentric segment 34, is also concentric about a~is Al. Tangential links 38 are journalled on the ecc~ntric segment 34. A driving gear 40 is mounted on a shaft 42 journalled in the tangential links 38 and rotates on a moving axis A2; it is driven by the input gear 36 through an intermediate gear 4~ also journalled in the tangential links 38. In this instance, the ratio between the input gear 36 and the driving gear 40 i5 e~actly-2:1, iOe., the input gear 36 rotates two times for every revolut.ion of driving gear 40.

An eccentric plate 46 is mounted on the shaft 42 and in turn supports an eccentric gear 48 concentric about a moving axis A3. This eccentric gear 48 meshes with an output gear 50 mounted on an output shaft 52 rotating on a stationary axis A4 in bearings mounted in the housi.ng not sho~n. The eccentric gear 48 is shown as being one-half the pitch diameter of the output gear 50 creating one index cycle for each 180 of rotation of the output gear 50, as will be described. The eccentric gear 48 is held in mesh with the output qear 50 by a radial link 54 which is journalled on the output shaft 52 and on a stub shaft 56 mounted on the eccentric gear 48 concentric about axis A3.

The operation of the mechanism 30, which is analyzed in the reference patent, may be qualitatively and briefl~
described as fol~ows. The total motion of the output gear is a superposition of a group of individual componen-ts, each of which will be individually analyzed as if it were the only component creating a motion of the output gear 50.

Assuming temporarily tha-t the axes Ao and Al are coincident, and further that the axes ~2 and A3 are coincident, it can be seen that the mechanism 30 would, in effect, be a simple gear reducer with the output gear 50 rotating at one-fourth the angular velocity of the input gear 36. The ratio from the output gear 50 to its driving "eccentric" gear 4~
is 2:1; this gear 40 is coupled to and rotates with the drivi-ng gear 48, whose ratio relative to the input gear 36 is aiso 2:1; hence the 4:1 ratio. Assuming the input shaft 32 rotates at a constant angular velocity, the output shaft 52 would also rotate at a constant angula. velocity albeit one-fourth that of the input shaft~

If it is now assumed that the axes A2 and A3 are separated by some distance, it can be seen that the gears 40 and 48 rotate about each other with the centerline A3 of gear 48 oscillating about the axis A~, since the distance between axes A3 and A4 is fixed by link 54; and with axis A2oscillating the coincident axes Ao Al since the distance between axes A2 and A1 is fixed by links 38. The magnitude of these oscillations is determined by the magnitude of the distance between axes A2 and A3, and this would impart an oscillation on the output gear caused by the oscillation of the axis A3 and the eccentric gear 48 about the axis A4.

Similarly, when the axi~ A1 is displaced from the axis Ao~ and still assuming that the input shat 32 is ~7--rotating at some constant angular velocity, it can be seen that the axis Al rotates about the axis ~0 creating a circular motion at the right end of the link 38. This in turn superimposes another oscillation on the gear 50 whose amplitude is determined by the spacing of axis Al from Ao~
Furthermore, this latter oscillation has a fre~uency that is double the frequency of the oscillation of the output gear ereated by the displacement of axis A3 from axis A2 since the input gear 36 rotates at twice the angular velocity as the average angular velocity of the driving gear 40 due to their 2:1 pitch diameter ratios.

The final component of motion of the output gear 50 is ereated by the angular oseillation of the links 38~
As these links move through spaee with their right ends moving in the cireular path ereated by axis Al rotating about axis Ao~ their left ends oseillate up and down about the moving axis Al as driven by the axes A2 and A3 rotating about eaeh other. This complex motion also creates a slight eomponent of motion in the output gear, which becomes increasingly smaller as the length of the links 38 is inereased. The angular oscillation of the links 38 creates a slight change in the projeeted length of these links on a base line passing through axis Ao and tangential to the output gear 50, and it is this ehange in projeeted length whieh ereates the motion eomponent in gear 50. Sinee the lengthening o~ the links 3a reduces their angular excursions for given motions of the axes Al and A2, the projected length variations deerease rapidly with inerease in link length.

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~ he total motion of the output gear 50, is thereby created by the superposition of the three primary design components summarized as follows:

1. A constant velocity determined by the gear ratios described.

2. A first oscillating component created by the rotation o axes A2 and A3 about each other.

3. A second oscillating component created by the rotation of axis Al about axis Ao Additionally, a fourtb incidental component is created inevitably by the angular excursion of the links 38, which can be made very small as their length is increased.

The four components described above create a cyclical variation in the motion of the output gear 50, and a given cycle repeats once or every revolution of the eccentric gear 40. Therefore, for a given cycle, the output gear 50 rotates through an angle represented by the ratio of the pitch diameter of the eccentric gear 48 to the pitch diameter of the output gear 50. For example, and to the scale shown in FIGS. 1 and 2, in which gear 48 is half as large as gear 50, the output will complete a given cycle in 180 o motion of the output gear 50. If gear 48 were the same size as gear 50, clearly a cycle would take place during a 360 rotation of the output gear 50.

_g_ The distance from axis Ao to axis Al is defined as eccentricity E2, while the eccentricity bet~een axis A2 and axis A3 is defined as eccentricity Bl. The addi-tion of this second eccentricity E2, which rotates at an integral multiple number of times for each rotation oE the eccentricity El, makes it possible to achieve a wide variety o-f kinematic effects on the rotation of the output shaft 52. This is disclosed in considerable mathematical detail in my existing U. S. Patent No. 4,075~911.

Themechanism of FIGS. 1 and 2, designa-ted mechanism 30, 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, a small amplitude oscillation of the output shaft about the center of this oscillation, which is defined as the zero point for output angle measurement.

Whereas the rotary output embodiment of the background patent shown in FIGS. 51, 52, 53 therein produced an output index angle oE 90, due to the proportions of gears 330 and 332, the output index angle of the embodiment shown in FIGS. 1 and 2 herein produces an output index angle of 180 as previously described. Furthermore, in the background patent, the mechanism of FIGSo 51, 52, 53 shows a chain connection 322 from the member, sprocket 324, on axis Al to the member, sprocket 321, on axis A2, whereas in the embodiment, FIGS. 1 and 2, shown herein, this e~uivalent drive connection is shown as being through gears 36, 44 and 40. This minor structural modiEication was made to achieve greater drive stiffness.

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Second Dwell Mechanism - Back ~ound The second background mechanism utilized in the invention of the present disclosure is comprised of a crank and connecting rod mechanism described in many books on fundamental kinematics. It is illustrated here schema-tically in FIGS. 3, 4 and 5.

Referring to FIGS. 3 and 4, a shaft 60 rotates on axis A5, and is journalled in a ~rame 62 through a bushing 64; this shaft 60 can be driven by any suitable prime mover.
A crank 66 is fastened to the shaft 60, and at its outer end supports a crankpin 68 concentric about an axis A6.~ A
connecting rod 70 is journalled at its one end on the crankpin 68; at its other end it is pivot connected to a slide block 72 through a pivot pin 74 on axis A7. The slide block 72 is supported by the frame ~2 in which it is free to slide along an axis Ag, which, as shown in FIG. 3, intersects the axis A5.

In FIG. 5 is shown a schematic diagram useful to analyze the kinematic characteristics oE the system. The distance on the crank 66 between axis A5 and A6 is defined as R and the length of the connecting rod between pins 68 and 74 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 ~. Fxom this diagram, it is easily seen that the amount the slider block 72 has moved from its base position as the crank R moves through the angle ~ from its base position is given by D = R - L - R cos~ + L cos~ (1) where ~ = sin~l (R sin(p) (2) L

If it is assumed that L is large compared to R and therefore the angle ~ is small, even when it is at a maximum, then cos ~ 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 ar.d slider block motion.

Dwell and Clock An~le 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 often times 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 s;tuation 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 (.001) would mean that the output oscillates during the defined near dwell through a total amplitude of .001 times the total stroke of the mechanism This is shown schematically in FIG. 6 which further schematically defines the term ~Idwell length". If it is assumed tha-t 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 o~ those uni-ts is defined as 1 degree of clock angle. A dwell length of 90 clock angle, for example, would represent a eycle in which the output would be in near dwell for 90/360 or for one quar-ter of the eycle.
~learly, if the input shaft rotates through one revolution during an index eyele, then one degree of input shaft rotation equals one degree of elock angle; or, if, for example, the input shaft rotates through three revolutions during an index cycle, then every three degrees o~ input shaft rotation equals one degree of elock angle. Stated another way, the number of degrees of input shaft rotation equal to one degree of elock angle may be determined by dividing the total number o~ input shaft rotation degrees required for an index cycle by 360.

Description of the Invention The invention to be described herein is a eombination or tandem mechanism employing two drive stages, the first stage of whieh is eompr~sed of a rotary output indexing meehanism of the type diselosed in the baekground patent and in FIGS. 1 and 2 herein and having an output index angle of 180 (initially);
and the seeond stage of which is eomprised of the erank and eonnecting rod mechanism deseribed above. This combination of meehanisms is both unique and useful and yields results whieh ean be determined only by detailed analysis whieh must be made to aseertain the numerous system eharaeteristies achie~able.

Referring to FIGS. 7 and 8, the mechanism 30, previously described in connection with FIGS. 1 and 2, is enclosed in the housing 33 and mounted on a base 82. Its input shaft 32 is driven through a coupling 84 by the output shaft ~6 of a gear reducer 88 also mounted on the base ~2. The input shaft 90 of this gear reducer is in turn driven by a motor 92 through a coupling 94. Depending on the application the motor may run continuously, or it may be stopped during the mechanism dwell with suitable conventional limit switches and electrical circuits. The crank 66 (FIGS. 3, 4 and 5) is directly mounted on the output shaft 52 of the mechanism 30, whereupon axes A4 and As become coincident. Clearly the shaft 60 and frame 62 (FIGS. 3 and 4) could be retained and a coupling used to connect shafts 52 and 60 if this were more convenient. The crankpin ~8 on crank 66 is used to drive the connecting rod 70 in a reciprocating motion. ~he other end of the connecting rod 70 is connected to a reciprocating output member, which may be a slider block, such as shown in FIG. 3, from which the load is driven, or the connecting rod 70 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 30.

A

Fu~ction~l D~scripti~n of the Invention As described in connection with FIGS. 1 and 2, and as more fully described in the background patent, the kinematic behavior of the output shaft 52 can be varied over a very wide range; with the specific arrangemen~ shown in FIGS. 1 and 2 and assuming that the input shaft 32 is driven at some constant angular velocity, the output shaft 52 will repeat a given kinematic cycle for each 180 of output movement since the eccentric gear 48 has a pitch radius equal to one-half of the pitch radius of the output gear 50. Furthermore, with the eccentricity shown between axes A~ and A3 and between axes Ao and Al, a given kinematic cycle is comprised of a stopped position of the output shaft 52, when the various elements are positioned as shown in FIGS. 1 and 2. During two revolutions of the input shaft 3~, the eccentric gear 40 will make one revolution smoothly accelerating the output gear 50 and output shaft 52 to a maximum velocity during the first approximate 90 of their rotation and then smoothly decelerating the output gear and shaft to a stopped position during the second 90 of their rotation. Stated another way, during a given kinematic cycle of the mechanism of FIGS. 1 and 2, the input shaft will make two revolutions at a presumed constant angular velocity, the eccentric gear 40 will make one revolution at a varying angular velocity, and the output gear and shaft will move through an angle of 180 from a first stopped position to a second stopped position, at each of which the various elements are positioned as shown in FIGS. 1 and 2.

-14a-~ 3 ~

Given this behavior of the output shaft 52, the resultant behavior of the crank ou~pu-t system can be varied over a wide range depending on the orientation of the crank on the output shaft 52 when the output shaft is in a stopped position.
For example, if the crank is positioned on the output shaft 52 in a top or bottom dead center position when the shaft 52 is also in a stopped position, it will be found that the dwell length at each end of the stroke of the total system is very long. This situation will be described in considerable quantitative detail.

On the other hand, it is possible to position the crank on the output shaft 52 such that the crank is in a top or bottom dead center position when the shaft 52 is at some in~ermediate position between two adjacent stopped or dwell positions. This arrangement gives rise to a variety of kinematic output characteristics, several of which will be subsequently quantitatively analyzed and illustrated.

Furthermore, it is possible to configure the mechanism of FIGS~ 1 and 2 such that the output index angle of the shaft 52 between stopped positions is other than the 180 index angle that is generated by the specific mechanism shown (since the eccentric gear 48 has a pitch radius equal to one-half the pitch radius of the output gear 50). For example, if the pitch radius of the eccentric gear 48 is the same as the pitch radius of the output gear 50~ the index angle of the output shaft 52 between -14b-.~

3~3 stops or dwells is 360. It is, ~herefore, possible to position the crank 66 on the shaft 52 in a stopped position only with the crank 66 in a top dead cen~er position or bottom dead center position, but not both, as was the case when -the mechanism of FIGS. 1 and 2, which is configured to provide a 180 output index angle.

Clearly, the mechanism of FIGS. 1 and 2 can be configured to provide index angles of 90, ~0 or any other useful angle and for each of these angles it is possible to position the crank 6~ on the shaft 52, such that the crank 66 is in a top or bottom dead center position when the shaft 52 is in a stopped or dwell position, or at some specified angle a~ay from the stopped position which will be defined as a phase angle. The number of combinations becomes exceedingly large and to show all such combinations becomes prohibitive.

Accordingly, a series of combinations areinvestigated in quantitative detail, which are perceived to be of practical usefulness.

Unitized Output For comparative purposes in comparing the dwells, and other characteristics, of the mechanism of FIGS. 1 and 2, the crank mechanism of FIGS. 3 to 5, and the combination mechanism of FIGS. 7 and 8, it is convenient to scale the output of each system such that the index stroke is arbitrarily set to equal -14c-~ 2 ~

l. Similarly, the input angle is defined in terms of the clock angle which has a range of 360 to create the output stroke of l. Under these arbitrary scaling procedures, equation (3) becomes DU .5 [l - cos(~C)] (4) where DU = "unitized" output ~C = "clock" angle This rescaling is dependent on the following reasoning relative to equation (3). The minimum position occurs when ~ =
Q, 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 l when ~ = 360~ and it is by substituting these values for R and ~ into equation (3) that equation (4) is obtained.

The output displacement from eguation (4), in the near dwell area, is tabulated in Table I and shown graphically by curve Ref A in FIG. 9.

T~RLE I

Unitized Displacement of a Simple Crank Mechanism_Near Dwell Clock Anqle Unitized Displacement -20 .007596 -15 .004~78 -10 .001903 - 5 .000~76 O O
.000476 .001903 .004278 .007596 The operation of the mechanism 30, which is analyzed in the reference patent, may be ~ualitatively and briefly described as follows. The total motion of the output gear is a superposition of a group of individual components, each of which will be individually analyzed as if it were the only component creating a motion of the output gear 50.

Referring to the background patent, the generalized approximate displacement e~uation, for the situation in which the axis Al rotates about the axis Ao through two revolutions for one revolution of the axes A2 and A3 about each other, is:

.

V = ~ - El sin~ + E2 sin 2~ (5) 1~-~6 ~

wher~
U = Angular output displacement of output shaft 52~ having a range of 2~ units independent of the index angle ~ = Clock angle in radians El = Distance between axes A2 and A3 expressed as a ratio to the radius of the eccentric gear 48 E2 = Distance between axes Al and Ao also expressed as a ratio to the radius of the eccentric gear 48 Similarly, if the axis Al rotates about axis Ao three revolutions for each revolution of the axes A2 and A3 about each other, the generalized approximate displacement equation, from the background patent is:

U = ~ - El sin~ ~ E2 sin 3~ (6) From equations (5) and (6), and by reference to the mechanism 30 and the background patent, it can be seen that if the axis Al rotates about axis Ao N times for each revolution of axes A2 and A3 about each other, as controlled by the ratio between the input gear 36 and the driving gear 40, the generalized approximate displacement equation for the output of the mechanism becomes:

U = ~ - El sina + E2 sin N~ ~7) As noted above, the output variable U is scaled to reach 2~ units during an index cycle; furthermore, the ~ 3 input angle, ~ , is dimensioned in radians. In order to compare the output of the independent mechanism 30 with the output of the crank and connecting rod mechanism, noted as curve Ref. A, in FIG. 9, it is necessary to rescale equation (7) into unitized coordinates, which is accomplished by multiplying the entire equation by 1/2~ and to convert ~ to the clock angle ~C~ in degrees by setting:

9 180 ~C

Therefore, equation (7), in unitized coordinates becomes:

U 2~ [180 ~C ~ E1 sin~c + E2 sin N~ 1 (8) which reduces to:

DU = 360 ~ 1 sin~c + 2 sin N~C ~9) In the background patent, it was shown that the longest dwell without reversal, when using N = 3, is obtained with El = 1.125, and E2 = .04167 (1/24). Substituting these values into equation (9), the unitized displacement values at various clock angles are found to be:

~266~ 3 TABLE II
Clock AnqleUnitized Displacement -60 -.011605 -50 -.005045 ~40 -.001763 -30 -.000440 -20 -.00006Q
-10 -.000002 O O
.000002 .000060 .000440 .001763 .005045 .011605 ~2~ 363 This data is also graphically represented by curve Ref. B in FIG. 9.

It was further shown in the background patent that the longest dwell without reversal, when usin~ N = 2, is obtained with El = 1.33 (1 1/3) and E2 = ~167 (1/6).
Substituting these values into e~uation (9), the unitized displacement at various clock angles are found to be:

TABLF III
Clock AngleUnitized Displacement -60 -.005862 -50 -.00~45~
~40 -.000830 ~30 -.000202 -20 -.000027 -10 -.000001 O O
.000001 .000027 .000202 .000830 .002452 .005862 This data is also graphically represented by curve Ref. C in FIG. 9. In comparing curves Ref. A, Ref. B, and Ref~ Co, two primary points are obvious. First, in comparing the inherent dwells available in the independent mechanisms, the dwells of the mechanism 30 are significantly greater A

~2~6~9~:) than the dwell which occurs at top dead center or bottom dead center of a crank and connecting rod mechanism.

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 oE the center of d~ell, where the clock angle is 0, which is the top dead center or bottom dead center position, is unidirectional as would 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 30, 'he 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 rota-tion, the output will momentarily stop ater a given index, but then reaccelerate in the same direction it had before stoppiny.

The oregoing data on the near dwell eharacteristics of each of the mechanisms operating independently are provided as reference data for the new data to be shown.

In the combination mechanism of FIGS. 7 and 8 which comprises this invention, it is neeessary to rescale equation (7) such that it represents the true output angle of the shat 52 o the mechanism 30. If the number of index cycles per revolution of the output shat 52 is defined as M, then the instantaneous position Y of the shaft 52, as a function of clock angle, can be represented by multiplying the equation ~66~

(9), for unitized displacement, by 360/M which represents the degrees of rotation per index of shaft 52. Therefore:

Y M C60 2~ Sin~c + 2~ sinN~C] (10) This reduces to:

- ~C 360E1 360E~
Y - - 2~M ~C 2~M sinN~C (11) In the combined mechanism of FIGS. 7 and 8, the output angle of the shaft 52, as given by r of equation (11) is equal to the input angle ~ of the crank and connecting rod mechanism of FIG. 5 as approximated by equation (3). It is necessary to introduce a new variable Cl, which represents the phase angle in making the connection between the two mechanisms. Given the shaft 52 positioned such that it is positioned between index cycles of the mechanism 30, i.e., the clock angle ~C is 0, then the angle that the crank is beyond its dead center position is defined as the phase angle, Cl.

Therefore, ~ = Y + Cl (12) Substituting equation ~12) into equation (3):

~ = R Ll - cos(Y ~ Cl)~ (13) ~6~3~3 For an output stroke equal to 1, R = ~

DU = ~ [1 - cos(Y + Cl)~ (14) If the value foryfrom equation (11) is substituted into equation (14), the unitized displacement equation for the mechanism of this invention is obtained~

U [ (M - 2~M Sin~C + 2~M sinN~C ~ CJ~

There are five parameters in this equation, M, N, Cl, El and E~, each of which exerts its own influence on the characteristics of the output. Clearly~ the number of combinations is extremely large.

A ew combinations will be represented to illustrate the influence of these various variables. In these illustrations, the various Tables and curves were calculated using a computer. Velocity, for example, could be calculated using classical mathematical techniques, but it was clearly less laborious and time consuming to use computer numerical differentiation.

Long Dwells at ~ach ~nd of Stroke One of the important practical applications of this invention is to create long dwells at both ends of the stroke. This permits, for example, the operation of other systems while this mechanism is in dwell. By combining the individual mechanisms such that their dwell points are coincident, Cl = 0, and arranging mechanism 30 to have a ~6.~

180 index angle, M = 2, and using the El and E2 factors as were determined to give the "flatest'l dwel~.s, as obtained from the background patent, the following cases were calculated:

Case 1 Cl = M = 2 N = 3 El = 1.125 E2 = 1/24 The results are tabulated in Table IV.

TABLF IV
Clock AngleUniti ed Displacement -80 .003972 ~70 .001291 -60 .000332 -50 .0000~3 ~40 .000008 -30 to +30Less than .000001 .000008 .000063 .000332 .001~91 .003972 These results are also shown as curve D ln Fig.
9. Recalling that this dwell curve is the output of the combined mechanism, comprised of the independent mechanisms, whose dwell characteristics are presented in curves Ref. A
and Ref. Bl it can be seen that the dwell characteristics of the combined mechanism are far better than the mere sum of ~J~

~6~
the dwells of the individual mechanisms. It is further clear that the output of the combined mechanlsm, as would be expected, retains the reversing characterlstics of-the crank and connecting rod mechanism, and that the displacement curve D, Fig. 9, is symmetrical about the 0 axis, as was curve Ref. A.

Case 2 This is comparable to Case 1 except that the second harmonic version of the mechanism 30 is used, rather than the third ~iven by curve D. Therefore:

Cl = M = 2 N = 2 Fl = 1 1/3 F2 = 1/6 The results are tabulated in Table V.

TABLE V
Clock Angle Unitized D_splacement -90 .003520 0 .001228 70 .000360 -60 .000085 -50 .000015 40 .000002 -30 to ~30 Less than .000001 40 .000002 50 `.000015 60 .000085 70 .000360 .001228 90 .003520 6 ~

These results are also shown in curve E of FIG.
9, with the same observations applying as were made for curve D.

Very Lonq Dwells at Each ~nd o~ Stroke In the background patent, techniques were developed, for both the second and third harmonic, N - 2 and N
= 3, to find values of El and E2, 5uch that the displacement could be ~ade to go through O at four different null angles, Nhich are predetermined values of clock angle at which the output displacement is 0. The qualitative generic characteristics of such a condition is shown in FIG. 10. It will be noted that the output displacement of the mechanism 30, represented in FIG. 10, passes through O at a predetermined clock angle, defined as a null angle, at -~N2; "overshoots"
slightly, then returns to O output at a second predetermined null angle, -~Nl It then "undershoots" and returns to O
output displacement at O clock angle. The behavior of the mechanism 30 at positive clock angles is symmetrically opposite, but not a mirror image, of its behavior at negative clock angles. In essence~ therefore, the output of the mechanism 30 can be arranged to pass through O output five times during a dwell and will be defined as a 5 point dwell.

As again shown in the background patent, the amplitude of the overshoot and undershoot/ which will be referred to as oscillations, can be controlled by judicious selection of the null angles. Using a computer, it is possible to manipulate the null angles by trial and error~
successive approximation, or iteration, to achieve the predetermined amplitudes of oscillation, and the associated factors El and E2. Generally, the four distinct 02cillation amplitudes will be made equal to each other, but this need not b~ so.

The output displacement of the mechanism 30 is the cran~ angle of the crank and connecting rod mechanisms and i3 SO labelled in FIG. 10. If the phase angle Cl is 0, the resultant output o the combination mechanism will have the generic form shown in FIG. 11 as a result of the crank oscillation shown in FIG. 10. It will be noted that the output oscillation of thè combination mechanism is unidirectional because of the inherent characteristics of the crank mechanism, in which the output is symmetrical about a dead center position, i.e., the output for a given angle is the same whether the angle is "before" or "after" the dead center position. This is ~athematically confirmed by eq~ation (3) since cos(~) = cost~

If a given dwell amplitude ~unitized) is defined ~or a specific application, the following technique is useful.
Equation (3) is inverted, and R is set equal to ~, whereby:

cos~ 2 Du ~ = arc cos tl ~- 2 Du) (16) As applied to the combined mechanism, and noting the relationship between FIGS. lG and 11, it can be seen that equation ~16) defines the angle of permissible crank oscillation to yield a predetermined dwell amplitude. In Table VI is presented a tabulation of permissible crank ~6~

oscillation angles as a function of awell amplitude, for180~ output oE mechanism 30 (M = 2) which provides a long dwell at each end of the stroke.

TABLE VI

Unitized Permissible Crank Uniti~ed Crank Predetermined Oscillation Amplitude Oscillation Dwell Amplitude True De~ees180 Index .00001 ~.3~237~ +.00201 .00003 +.62765 +.00348 .00010 +1.14593 ~.00636 .00030 +1.98488 ~01103 .00100 +3.62~31 +.02014 .00300 +6.27958 +.03489 With the permissible crank oscillation amplitude determined for a given predetermined dwell amplitude for the combined mechanism, from equation ~16), and as illustrated by the examples of Table VI, it is possible to use these crank oscillation amplitudes to determine the null angles and the factors El and E2 which will create them. As noted above, this is accomplished by using successive approximation techniques with a computer.

Following this procedure, the values for the null angles were found which give rise to the permissible crank oscillation amplitudes which were listed in Table VI. These are listed in Table VIIA for N = 3 and in Table VIIB for N = 2 ~or a 180 index of mechanism 30, 6~

TABLE VIIA N = 3 . _ Dwell Null Angle 1 Null Angle 2 Amplitude Clock Deqrees Clock Deqrees ~00001 ~36.884 +62.047 .00003 ~40.110 +68.095 .00010 +~3.661 +75.045 .00030 46.816 _81.563 .00100 +50.040 +88.710 .00300 +52.642 +95.013 TABLE VIIB. _~ = 2 Dwell Null -Angle 1 Null Angle 2 Amplitude ~ Clock Deqrees .00001 +44.909 +74.615 .00003 +49.262 +82.361 .00010 +54.273 +91.502 .00030 +58.991 +100.389 .00100 +64.206 +110.624 .00300 +68.874 +120.266 From the null angles, ~uch as tabulated in Tables VIIA and B, it is possible to calculate the required factors El and E2, using the method outlined in the background patent.
When this is done using the specific null angle values tabulated in Tables VII~ and B, for the desired dwell amplitudes, the corresponding El and E2 factors are listed in Tables VIIIA and B.

Dwell Factor Factor Amplitude El E2 .00001 1.2149 .0913 .00003 1.2326 .1090 .00010 1.25~5 .1379 ,00030 1.2762 .1782 .00100 1.3008 .2483 .00300 1.3227 o3528 TABLE VIIIB N = 2 Dwell - - Factor --- Factor Amplitude El E2 .00001 1.~947 .2714 ,00003 ` 1.5311 .3037 .00010 1.5791 .3530 .00030 1.6309 .4170 .00100 1.6969 .5197 .00300 1.7647 .6603 The factors El and E~ tabulated above may now be used in equation (15) to calculate the unitized displacement output of the combination mechanism. Recalling that the procedure for determining E1 and E2~ in this instance, was predicated on the mechanism 30 ha~ing an output index angle of 180, M = 2, and that the phase angle, Cl, was 0, it becomes possible to establish the parameters for two illustrative cases.

Case 3 Cl - 0 M = 2 N = 3 El = 1.3008 E2 = .2483 The factors El and E2 were arbl-trarily chosen from Table VIIIA to illustrate a dwell condi-tion at the ends of the stroke that has an amplitude of .001 of the total stroke using a third harmonic N = 3. The factors listed above were substituted into equation (15), and the displacement calculated at suitably spaced clock angles. The results of these calculations are shown as curve F in FIG. 12, in which only the characteristics at positlve clock are shown. It will be understood that the hehavior at negative clock angles is a mirror image about the 0 clock angle line as shown in the generic curve, FIG. ll. From curve F, FIG. 12, it can be seen that the displacement oscillates within the predetermined dwell amplitude of .001 for a total of +95 or a total dwell of 190, this represents 190/360 or 52.7~ of the total cycle time. It will further be noted that the displacement curve F is tangent to the 0 displacement axis at clock angles of 50 and 80, agreeing with the null angles for .001 dwell amplitude shown in Table VIIA.

The same objective of very long dwell at each end of stroke will now be illustrated using N =2, as is generically shown in FIGS. 1 and 2.

.~2~

Case 4 Cl = M = 2 N = 2 El = 1.6969 E2 = .5197 The factors El and E2 were taken Erom Table VIIIB
for a dwell amplitude of .001 to permit a direct comparison of the dwell behavior for N - ~ relative to curve F where N =
3. Using these values again in e~uation (15), the results are plotted as curve G of FIG. 12. A marked improvement in the dwell lenyth will be noted, +118, or a total dwell length of 236 relative to the 360 total cycle clock angle.
The output is therefore stationary within a dwell amplitude of .001 for 236/360 or 65O5~ of the total cycle.

While achieving long dwells is of practical importance, it is also necessary to examine the kinematic behavior of the system during the movement between these dwells. As noted earlier, the velocity calculations are made using a computer and numerical dif~erentiation rather than classical differentiation and subsequent calculation of far more involved equations than equation (15). Using these techniques, the velocities during the stroke were calculated for the four previously described cases and are shown graphically in FIG. 13. Curve D' shows the veloci-ty characteristics of Case 1 whose dwell characteristics are shown by curve D oE FIG. 9. These velocity characteristics are symmetrical about the clock angle 180, and velocities at clock angles less than 60 are too small to be of any ;6~

interest. The velocities are plotted in terms oE relative velocity which is de~ined as the ratio oE the instantaneous velocity at a given clock angle divided by the average velocity which is the total stroke divided by the time required for the clock angle to move through 360.

Similarly, the velocity curve E' represents the conditions of Case 2 and is the counterpart of dwell curve E
o FIG. 9. The velocity curve F' is for Case 3 and is the counterpart of dwell curve F in FIG. 12; and velocity curve G' represents Case 4 and is the counterpart of the dwell curve G of F~G. 12. As a broad generalization, the peak velocities ~or the cases in which N = 2, as represented by curves E' and G' are higher than those for the case where N = 3, as represented by curves D' and F'! as is to be expected since the dwells for the N = 2 cases are longer than for those where N = 3. Interestingly, the curve F', which represents a configuration which has a longer dwell than the other third harmonic curve D', has a velocity reversal near midstroke, which is an inherent characteristics of having a large third harmonic component.

~6~

Lonq ~ells Between the ~nds of the Stroke In the foregoing four cases, it was shown how the dwell at each end of the stroke could be made very large as a fraction of the total cycle time per stroke; and the velocity characteristics between the ends of the stroke dependent on the conditions chosen were illustrated. Other applications arise in which it is desired to have dwells during the strokes, in addition to the reversal dwells at the ends of the stroke. Three additional cases will be used to show how this can be accomplished. The first method involves using a phase angle, Cl, to shift the dwell of mechanism 30 away from the reversal dwell of the crank and connecting rod mechanism. By positioning the crank on the output shaft of the mechanism 30 such that it is 90 from its dead center position when the mechanism 30 is in its center of dwell position, a value Cl = 90 is obtained. By further assigning the value M = 2, whereby the output index angle of the mechanism 30 is 180, a dwell will be created on both the forward and return midstroke. The dwell amplitude of the crank angular oscillation during dwell is arbitrarily set to +0.18 and the values Eor El and E2 obtained by computer iteration. N was set to 3, although, as previously shown, N = 2 provides a slightly longer dwell~ at the expense of higher velocities. Therefore the conditions for Case 5 were established as follows.

.

Case 5 Cl = 90 M = ~ ~ = 3 El = 1.196 E2 = .0761 -3~

.1~6~90 The results of these conditions were then calculated at suitable clock angle intervals and the results plotted as curve H, FIG. 14. The unitized displacement is shown over a clock angle interval of 720~ which represents two 180 indexes of the mechanism 30, as required for the crank to move through a full 360; this shows both the forward and return stroke. From curve H, it can be seen that a significant dwell has been created at midstroke, unitized displacement equals .5, while the dwells at the ends of the stroke are quite short.

In other applications, a l~ng dwell during the stroke is desired at one position during a forward stroke and at another position during the return stroke. Within certain limitations, this can be accommodated by changing the phase angle Cl to an appropriate angle different than the 90 utilized to create the conditions of curve H, while the other parameters are arbitrarily unchanged.

Case 6 Cl = 60 M = 2 N = 3 `El = 1.196 E2 = .0761 The results are shown by curve J of FIG. 14, in which, as noted, the phase angle Cl is 60. The intermediate long dwell is at a unitized output displacement of .25 on the forward stroke and at a unitized ou-tput displacement of .75 on the return stroke as would be expected by considering e~uation ~14) and substituting y = 0 for the first dwell position and y = 180 for the second dwell position.
Clearly then, for M - 2, the two dwell pssitions are always the same distance away from the previous reversal dwell;
stated another way, the sum of the unitized displacements for the two intermediate dwell posi-tions is always ~qual to 1. This can be modified by an intermediate linkage to -the final drive point.

Long Dwells at Ends o~ Stroke and at Midstroke Using the parameters illustrated by Cases 5 and 6, the dwells at the ends of the strokes were quite short, as is to be expected for a crank rotating at some angular velocity. Applications arise, however, in which a long dwell is required at the ends of the stroke as well as at the midpoints of the strokeO This can be achieved by selecting a 90 output index angle for the mechanism 30, which is accomplished by setting M = 4. A five point dwell, as illustrated by FIG. 10 was selected with a dwell amplitude of +.09 (.001 uniti7ed) for the crank oscillation, whereupon the final parameters, calculated as previously explained, are as follows.

Case 7 Cl = M = 4 N = 3 El = 1.196 E~ = .0761 The results of the calculations are shown by curve K of FIG. 15. This is plotted for a total clock angle range of 1440 as is required since four indexes of the mechanism are required for each revolution of the crank and each such index requires 360 of clock angle. It will be noted, from curve K, that, in addition to having long dwells at midstroke, ~6~

the dw-lls at the ends of the stroke are signiicantly longer than those for Cases 5 and 6 repr~sented by curves H and J
of FIG. 14.

onq ~ell at One End of 5troke ~nd Shor~ ~ell at O her End Some applications arise in which it is desired to have a reversing mechanism which has a very long dwell at one end of the stroke and a relatively short dwell at the other end of the stroke. This requirement can be met by this invention by using an output index angle of 360 for the mechanism 3Q, whereby M = 1, and positioning the crank such that the phase angle is 0, i,e., Cl = 0. Clearly, the crank is then at one dead center position when the mechanism 3Q is in dwell; at the crank's oppo~ite dead center position, the mechanism 30 will be at its mid index position and will be rotating at some relatively high angular velocity. This situation gives rise to the difference in system dwells at opposite ends of the stroke. Two specific examples are presented, one in which N = 2, the other in which N = 3. In each example, a five point dwell having a dwell amplitude of .001 was arbitrarily selected. This gave rise to the following parameter combinations.

Case 8 Cl = 0 M - 1 N = 3 El = 1.273 E2 = .1703 The results of the calculations using these parameters in equation ~15) are shown by curve L in FIG~ 16.

Case 9 Cl - 0 M = 1 N = 2 El = 1.622 E2 = .4048 The results of the calculations using these parameters are shown by curve M in FIG. 16.

Curve L is based on using N = 2, and curve M is based on using N = 3. In each instance, the parameters El and E2 were established by computer successive approxima-tion such that the dwell amplitude of the total system was ~001 as previously noted. The curves are plotted for only 180 of clock angle, since they are symmetrica~ about both the 0 and 180 clock angles. As expected from the knowledge of FIGS. 9 and 12, the dwell at one end of the stroke is greater for the N = 2 situation relative to the N = 3 situation. As a consequence, it follows that: because of the compensating higher midstroke angular velocity of the N = 2 situation, the dwell at the other end of stroke is shorter for N = 2 than for N = 3, or stated another way/ the reversal is faster for N = 2 than for N = 3.

Thre~ Point Dwells In the foregoing Cases 3-9, the parameters El and E2 were determined using a five point dwell as described in connection with FIGS. 10 and 11. This was more fully described in the background patent. As also more fully described in the background patent, it is also possible to arrange the mechanism 30 such that its displacement characteristic in the dwell area only goes through 0 three times, rather than five; this will be defined as a three-point dwell. The primary objective in rec~ucing the number of dwell points from 5 to 3 is that, in so doing, it becomes possible to find combinations of El and E2 which permit greater con-trol over the kinematics of the movement between the dwells. In connection with the inaependent mechanism 30, numerous illustrative examples are presented in the background patent, including the kinematic curves of FIGS. 12, 13, 30 and 31 of said patent.

The generic characteristics of the output displacement of the mechanism 30 in the three point dwell mode is shown in FIG. 17. Since this displacement becomes the crank angle of the crank and connecting rod mechanism it is again so labeled. There are several methods which may be employedto create a three point dwell, as will subsequently be shown. Assuming that the parameters El and E2 have been established to create a three point dwell condition for the mechanism 30, the output angular displacement of the mechanism 30, or crank angle, are generically shown by the curve of FIG. 17. It can be seen that the crank "overshoots" its O
position after crossing the zero point at some negative clock angle, which is defined as null angle -~Nl The crank angle displacement then reverses and passes through its O position again at a clock angle of 0, then undershoots before reversing to progress forward, again crossing the O displacement position at some positive clock angle defined as null angle ~Nl- In essence, when the parameters El and E2 are determined such as to create a three point dwell, the angular output displacement of mechanism 30 undergoes a double reversal crossing the O line three times, whereas when the parameters 9C~

El and E2 are determined to crea~e a five point dwell as previously described, the angular output displacement, which is crank an~le, undergoes four reversals and crosses the zero line five times.

I~ the crank is positioned on the output shaft of the mechanism 30 su~h that it is in its dead center position when the mechanism is in the center of its dwell, the unitized output displacement of this invention will be as shown by the generic curve of FIG. 18 which is derived from FIG. 17 by the same technique used in describing the curve of FIG.
11 derived from the curve o~ FIG. 10. In essence, the unitized output displacement of the crank is O at -~Nl~ ~
and ~Nl where the crank angle is O, and very slightly positive, wh~rever the crank angle i~ slightly positive or negative, again as described in connection with FIG. 11.

The method of determining the factors El and E2 ~or the three point dwell is comparable to that used for finding the ~ive point dwells. Using the techniques used in finding the groups of solutions ~or three point dwells shown in the background paten~, it is possible to calculate the total dwell amplitude, then adjust either El or E2 to obtain the desired dwell amplitude. The non used El or E2 ~for finding the desired dwell amplitude) is then varied to approximate the desired kinematic objective, but for each variationin the variable ~El or E2) used to seek the kinematic objective, it is necessary to reevaluate the variable (El or E2) which creates the dwell amplitude. This is again a successive approximation techni~ue for which a computer is practically indispensable.

~6~

Even without starting with the knowledge of the background patent, it is pcssible ~o find El and E2 as long as they arema-thematically obtainable. A value is arbitrarily assigned to either El or E2 and the non-assigned variable El or E2 is varied to create the desired dwell amplitude, again using equation (15) as the basis for making the unitized displacement calculations. The assigned variable El or E2 then can be modified by successive approximation, to provide the kinematic objectives for movement during the stroke, two examples of which will now be shown.

Long Dwell at Ends of Stroke and Nearly Constant Yelocity During Stroke Two cases will be investigated to meet the above conditions, one in which N is arbitrarily selected as 2 and the second in which N is arbitrarily selected as 3. ~tilizing the information of the previous cases, M was set e~ual to 2 to create a long dwell at each end of the stroke. The dwell amplitude was again arbitrarily selected as DOOl in unitized displacement coordinates.

With these conditions and parameters established and N set equal to 2, E2 was set from -0.1 to -0.3 in steps of .01 utilizing the precedent of curve B FIGo 12 of the background patent~ For each of these selected values of E2, a corresponding value of E1 was found, by successive approximation, to create a dwell displacement of .001. With El and E2 thus established, the velocity characteristics over the stroke were calculated at suitable clock angles using equation (15) and numerical differentiation. From .

these many combinations of El and E2, a result was selected which was judged best to meet the aforesaid requirements and is given as follows.

Case 10 Cl = 0 M = 2 N = 2 El = .9190 E2 = -.22 The dwell characteristics for this combination of parameters are shown as curve N in FIG. 19, with these characteristics symmetrical about 0 clock angle as demonstrated by the generic dwell curve FIG. 18. The velocity characteristics of this combination are shown by curve N' of FIG. 20, in which the velocities below a clock angle of 50 are too small to be of interest, and the velocities are symmetrical about a clock angle of 180. It should be pointed out that the dwells and velocities for the "neighboring"
solutionsfoundforE2= -.21 and -.23 are almostimperceptibly different. These combinations are:

E2 = -.21 El = .9361 E2 = -.23 El = .9018 Using these same procedures, except with N = 3, rather than N = 2 as for Case 10, the following El and E2 was selected to best meet the requirements.

Case 11 Cl - 0 M - 2 N - 3 El = 1.355 E2 = .11 The dt~ell characteristics for this combination of parameters are shown by c~rve P of FIG. 19 and the velocity characteristics are shown by curve P' o~ FIG. 20, with the same symmetries described in connection with curves N and N'.

Clearly, the number of variety of kinematic objectives which can be satisfied by this invention is extremely large. The disclosed cases are illustra-tive only.
Each of the cases involved a dwell of one type or another;
but this is not to say the in~ention is usable only when dwells are required. It can be generalized only that it is usable to meet any kinematic objective which can be approximated ~y equation (15), and this in turn is determined to a large degree by the knowledge, experience and ingenui-ty o~ a designer applying this equation, and the mechanism it represents.

All the performance cur~es were derived on the basis of equation (15), which, it will be recalled, was derived a~ter ma~ing 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 t~at a very high degree of correlation can be ~ound between the characteristics described herein and the exact characteristics numerically calculated. This has involved adjusting, by successive approximations the distances between axes ~O and A4 and between axes Al and A2 as well as the aforesaid distances between axis A2 and A3 ~El) and between axes Ao and Al (E2)-

Claims (8)

THE EMBODIMENTS OF THE INVENTION TO WHICH AN EXCLUSIVE
PROPERTY OR PRIVILEGE IS CLAIMED ARE DEFINED AS FOLLOWS:
1. Claim 1 A reciprocating mechanical drive system capable of providing an extremely wide variety of kinematic objectives, including very long dwells at the ends of the stroke, unequal dwells at opposite ends of the stroke, intermediate dwells between the ends of a stroke, and non-symmetrical movement when moving in one direction, as compared to the movement in the other direction, comprising:
   a. a combination mechanism comprising a rotary drive means which drives a reciprocating output drive system, and in which said rotary drive means comprises:
   1. a frame, 2. an output shaft member mounted for rotation in said frame, 3. an output member mounted on said output shaft member and adapted for tangential driving and having a given pitch radius, 4. a first rotating pair supported in said frame comprising:
   (i) a first rotating member mounted for rotation in said frame, (ii) a first eccentric member mounted eccentrically, in non-rotational relation to, and on said first rotating member, 5. a second rotating pair mounted in fixed spatial relationship with said first rotating pair comprising:
   (i) a second rotating member, (ii) a second eccentric member, having a given pitch radius, mounted eccentrically in non-rotational relation to, and on said second rotating member, 6. means connecting for rotation said first rotating pair and said second rotating pair for substantially an integral angular velocity ratio, 7. means connecting said output member and said second eccentric member in a driving relationship, and 8. power means connected to one of said rotating pairs to impart a rotary motion to that of said rotating pair; whereby rotation of said rotary pair by said power means at a presumed substantially constant angular velocity causes said output shaft member to undergo a series of acceleration-deceleration cycles and the angular distance traversed by said output shaft member during one such cycle is known as the index angle, b. and in which said reciprocating output drive system comprises:
   1. a crank member mounted at one end to said output shaft member, 2. connecting rod means journalled at one end to the other end of said crank member, 3. reciprocating output means mounted for reciprocation in said frame, and pivotally connected to the other end of said connecting rod means.
2. Claim 2 A reciprocating mechanical drive system as in claim 1 in which said power means is connected to said first rotating member.
3. Claim 3 A reciprocating mechanical drive system as in claim 1 in which said output member has a pitch radius which is two times the pitch radius of said second eccentric member, whereby the index angle of said output shaft member is 180°.
   
   Claim 4 A reciprocating mechanical drive system as in claim 1 in which the eccentricity between said first eccentric member and said first rotating member, and the eccentricity between said second eccentric member and said second rotating member are proportioned to provide acceleration-deceleration index cycles of said output shaft member with such cycles separated by an approximate stoppage of said output shaft member termed a dwell; and in which said crank member is positioned on said output shaft member, such that when said output member is positioned in the center of a said dwell, said crank member and said connecting rod member are substantially colinear.
   
   Claim 5 A reciprocating mechanical drive system as in claim 1 in which the pitch radii of said output member and said second eccentric member are equal, whereby the index angle of said output shaft member is 360°.
   
   Claim 6 A reciprocating mechanical drive system as in claim 1 in which said output member has a pitch radius which is four times the pitch radius of said second eccentric member, whereby the index angle of said output shaft member is 90°.
   
   Claim 7 A reciprocating mechanical drive system as in claim 1 in which said crank member is positioned on said output shaft member, such that when said rotary drive means is positioned equally between any two adjacent indexing cycles, said crank member is positioned by some predetermined phase angle from a reference position, in which said crank member and said connecting rod member are substantially colinear.
   
   Claim 8 A reciprocating mechanical drive system capable of providing an extremely wide variety of kinematic objectives, including very long dwells at the ends of the stroke, unequal dwells at opposite ends of the stroke, intermediate dwells between the ends of a stroke, and non-symmetrical movement when moving in one direction, as compared to the movement in the other direction, comprising:
   a. a combination mechanism comprising a rotary drive means which drives a reciprocating output drive system, and in which said rotary drive means comprises:
   1. a frame, 2. an output shaft member mounted for rotation in said frame, 3. an output gear member mounted on said output shaft member and adapted for tangential driving and having a given pitch radius,
4. 4. a first rotating pair supported in said frame comprising:
   (i) a first rotating member mounted for rotation in said frame, (ii) a first eccentric gear member mounted eccentrically, in non-rotational relation to, and on said first rotating member,
5. 5. a second rotating pair mounted in fixed spatial relationship with said first rotating pair comprising:
   (i) a second rotating member, (ii) a second eccentric gear member, having a given pitch radius, mounted eccentrically in non-rotational relation to, and on said second rotating member,
6. 6. means connecting for rotation said first rotating pair and said second rotating pair for substantially an integral angular velocity ratio,
7. 7. means connecting said output gear member and said second eccentric gear member in a driving relationship, and
8. 8. power means connected to one of said rotating pairs to impart a rotary motion to that of said rotating pair; whereby rotation of said rotary pair by said power means at a presumed substantially constant angular velocity causes said output shaft member to undergo a series of acceleration-deceleration cycles and the angular distance traversed by said output shaft member during one such cycle is known as the index angle, b. and in which said reciprocating output drive system comprises:
   1. a crank member mounted at one end to said output shaft member, 2. connecting rod means journalled at one end to the other end of said crank member, 3. reciprocating output means mounted for reciprocation in said frame, and pivotally connected to the other end of said connecting rod means.
   
   Claim 9 A reciprocating mechanical drive system as in claim 8 in which said power means is connected to said first rotating member.
   
   Claim 10 A reciprocating mechanical drive system as in claim 8 in which said output gear member has a pitch radius which is two times the pitch radius of said second eccentric gear member, whereby the index angle of said output shaft member is 180°.
   
   Claim 11 A reciprocating mechanical drive system as in claim 8 in which the eccentricity between said first rotating member and said first eccentric gear member and the eccentricity between said second rotating member and said second eccentric gear member are proportioned to provide acceleration-decleration index cycles of said output shaft member with such cycles separated by an approximate stoppage of said output shaft member termed a dwell; and in which said crank member is positioned on said output shaft member, such that when said output member is positioned in the center of a said dwell, said crank member and said connecting rod member are substantially colinear.
   
   Claim 12 A reciprocating mechanical drive system as in claim 8 in which the pitch radii of said output gear member and said second eccentric gear member are equal, whereby the index angle of said output shaft member is 360°.
   
   Claim 13 A reciprocating mechanical drive system as in claim 8 in which said output gear member has a pitch radius which is four times the pitch radius of said second eccentric gear member, whereby the index angle of said output shaft member is 90°.
   
   Claim 14 A reciprocating mechanical drive system as in claim 8 in which said crank member is positioned on said output shaft member, such that when said rotary drive means is positioned equally between any two adjacent indexing cycles, said crank member is positioned by some predetermined phase angle from a reference position, in which said crank member and said connecting rod member are substantially colinear.