GB2184196A - Reversing mechanism - Google Patents

Abstract

A mechanism 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, includes the combination of a unidirectional rotary drive means (30) having a cyclically varying output and a reciprocating output drive system (66, 70). The rotary drive means comprises an output shaft (52) mounted for rotation in a frame,an output gear (50) mounted on the shaft (52), a first rotating pair including a first eccentric member 34 mounted eccentrically, in non-rotational relation to, and on a first rotating member 36, and a second rotating pair mounted in fixed spatial relationship with the first rotating pair and including: a second eccentric member (48) mounted eccentrically in non-rotational relation to, and on a second rotating member 40. The first rotating pair and said second rotating pair are connected for rotation with substantially integral angular velocity ratio. The output member (50) and second eccentric member (48) are connected in a driving relationship, and a power means is connected to one of the two rotating pairs to impart a rotary motion thereto. The reciprocating output drive system comprises a crank member (66) mounted at its one end to the output shaft (52), a connecting rod (70) journalled at its one end to the other end of the crank member (66), and a reciprocating output means pivotally connected to the other end of the connecting rod. <IMAGE>

Description

SPECIFICATION Reversing mechanism having wide kinematic versatility The present invention relates two reversing mechanisms and is concerned in particular with 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.

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 isinadequateforsomeapplications.

It is an object of this invention to provide a mechanism which generates a reciprocating motion from a rotary motion and in which the output remains substantially stationary, that is, it is 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.

In accordance with the present invention there is provided a reciprocating mechanical drive system capable of providing a wide variety of kinematic objectives, including very long dwells at the ends ofthe stroke, unequal dwells at opposite ends ofthe 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) unidirectional rotary drive means having a cylicallyvarying output, comprising: (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 fortangential driving, (4) a first rotating pair supported by said frame comprising:: (i) a first rotating member mounted for rotation in said frame, and (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 paircomprising: (i) a second rotating member, and (ii) a second eccentric member 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 pairforsubstantiallyan integral angularvelocity 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, and (b) a reciprocating output drive system comprising: (1) a crank member mounted at its one end to said output shaft member, (2) connecting rod means journalled at its one end to the other end of said crank member, and (3) reciprocating output means mounted for reciprocation in said frame, and pivotally connected to the other end of said connecting rod means.

It is a feature of the present invention to enable the provision of a mechanism which, by its nature, can be economically constructed to achieve strokes of 6 feet or more.

It is anotherfeature ofthe present invention to enablethe provision of a reversing mechanism having a dwell at each end of its stroke and having an additional dwell art a predetermined point along its stroke along one direction of travel and another such additional dwell at another predetermined point along the reverse direction of travel, where such dwells may be instantaneous stops or significant reductions of velocity.

The invention is described further hereinafter, by way of example only, with reference to the accompanying drawings, in which: Figure lisa side semi-schematic view of one embodiment ofthe mechanism described in my existing U.S.Patent No.4,075,911; Figure2 is a top view of the mechanism of Figure 1; Figure3 is a side view of a well-known crank and connecting rod mechanism; Figure 4 is a section taken on line 4-4 of Figure 3; FigureSis a schematic diagram of the mechanism of Figure 3 useful for determining the equations of motion of that mechanism; Figure 6is a schematic diagram illustrating the definitions of dwell of dwell length and dwell amplitude;; Figure 7is a plan view of one embodimentofa mechanical combination in accordance with the present invention; Figure8is a sideviewofthe mechanism of Figure7; Figure 9 is an illustrative graphical presentation ofthe dwell characteristics of the crank and connecting rod mechanism, the mechanism of Figures 1 and 2 operating in the second and third harmonic arrangements with very long dwells; and the combined mechanism of Figures 7 and 8; Figure 10 is a generic dwell characteristic curve showing the behaviour of the mechanism of Figures 1 and 2 operating in a five point dwell configuration; Figure 1 list generic dwell characteristic curve, showing the output of a mechanism in accordance with this invention when the crank is positioned on the mechanism of Figures 1 and 2, such thatthe crank is ata dead centre position when the mechanism of Figures 1 and 2 is in the centre of dwell and configured to create afive point dwell; Figure 12 shows specific dwell characteristics curves of a mechanism in accordance with this invention configured to provide a dwell amplitude of 0.001 using a second and a third harmonic;; Figure 13 is a graph showing the velocity characteristics of a mechanism in accordance with this invention forthe configurations whose dwell characteristics were shown in Figures 9 and 12; Figure 14 is an illustrative graph showing the displacement characteristics of a mechanism in accordance with this invention when the crank is positioned on the mechanism of Figures 1 and 2 with phase angles of 90' and 60 ; Figure 15is an illustrative graph showing the displacement characteristics of a mechanism in accordance with this invention when the mechanism of Figures 1 and 2 is configured to produce a 90" index angle, with 0 phase angle;; Figure 16 is an illustrative graph showing the displacement characteristics of a mechanism in accordance with this invention when the mechanism of Figures 1 and 2 is configured to produce a 360 index angle, with 0 phase angle, and using a second and third harmonic; Figure 77is a generic dwell characteristics curve showing the behaviour of the mechanism of Figures 1 and 2operating in athree point dwell configuration;; Figure 18 is a generic dwell characteristic curve, showing the output of a mechanism in accordance with this invention when the crank is positioned on the mechanism of Figures 1 and 2, such thatthe crank is ata dead centre position when the mechanism of Figures 1 and 2 is in the centre of dwell and configured to create three point dwell; Figure 19 is an illustrative graphical presentation of the dwell characteristics of a mechanism in accordance with this invention when the mechanism of Figures 1 and 2 is configured to produce a three point dwell and the phase angle is 0; for both the second and third harmonic arrangements; and Figure 20 is a graph showing the velocity characteristics of a mechanism in accordance with this invention for the configurations whose dwell characteristics were presented in Figure 19.

First dwellmechanism - background 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 constantangularvelociW. Subsequently, in this disclosure, U.S. Patent 4,075,911 will be referred to as "the background patent". Reference is hereby directed to the background patent for further information. A review ofthis background patent will indicatethatthere are several embodiments, e.g., Figures 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 Figures 51,52 and 53 ofthe 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 resultofthe gear 330 having a pitch diameterwhich is 1/4the pitch diameterofthe output gear 332. In the present invention which will be described hereinafter, that portion of the mechanism arising from the background patentwill initially utilize an index angle of approximately 1800. Such a mechanism is described in Figures 1 and 2 ofthe present Application.

Figures 1 and 2 are simplified schematic drawings of this embodiment which is proportioned to provide a 180 output for one acceleration-deceleration cycle of its output shaft. Referring to Figures 1 and 2, this mechanism 30 is comprised of an inputshaft32 which rotates on axis A0 in stationary bearings in a housing which is notshown. An eccentric segment 34, on the shaft 32, is concentricaboutan axis A1 displaced a small amount from the axis Ao. An input gear 36, fastened on the eccentric segment 34, is also concentric about axis A1.Tangential links 38 are journalled on the eccentric segment 34.Adriving gear40 is mounted on a shaft42 journalled in thetangential links 38 and rotates on a moving axis A2; it is driven by the inputgear36through an intermediate gear44 also journalled in the tangential links 38. In this instance, the ratio between the input gear36 and the driving gear40 is exactly 2:1, i.e.,the input gear 36 rotates two times for every revolution 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 housing not shown. The eccentric gear48is shown as being one-halfthe pitch diameter of the output gear 50 creating one indexcycleforeach 1 80" of rotation of the output gear 50, as will be described. The eccentric gear48 is held in mesh with the output gear 50 bya radial link54which isjournalled on the output shaft 52 and on a stub shaft 56 mounted onthe eccentricgear48 concentric about axis A3.

The operation of the mechanism 30, which is analyzed in the background patent, may be qualitatively 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.

Assuming temporarilythatthe axes Ao and A1 are coincident, and furtherthatthe axes A2 and A3are coincident, it can be seen that the mechanism 30 would, in effect, be a simple gear reducer with the output gear 50 rotating atone-fourth the angularvelocity ofthe inputgear36. The ratio from the output gear 50to its driving "eccentric" gear40 is 2:1; this gear 40 is coupled to and rotates with the driving gear48, whose ratio relative to the input gear36 is also 2:1; hence the 4:1 ratio. Assuming the input shaft 32 rotates at a constant angularveRocity, the output shaft 52 would also rotate at a constant angularvelocity 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 gears40 and 48 rotate about each other with the centerline A3 of gear 48 oscillating about the axis A4, since the distance between axes A3 and A4 is fixed by link 54; and with axis A2 oscillating the coincident axes A0 A1 since the distance between axes A2 and A1 is fixed by links 38. The magnitude ofthese oscillations is determined by the magnitude ofthe 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 axis A1 is displaced from the axis Ao, and still assuming thatthe input shaft 32 is rotating at some constant angularvelocity, it can be seen thatthe axis A1 rotates aboutthe axis A0 creating a circular motion atthe right end ofthe link38. This in turn superimposes another oscillation on the gear50 whose amplitude is determined by the spacing of axis A1 from A0. Furthermore, this latter oscillation has a frequency that is double the frequency of the oscillation ofthe output gear created by the displacement of axis A3 from axis A2 since the input gear36 rotates at twice the angularvelocity as the average angular velocity ofthe driving gear 40 due to their2: 1 pitch diameter ratios.

The final component of motion ofthe output gear 50 is created by the angular oscillation ofthe links 38. As these links move through space with their right ends moving in the circular path created by axis A1 rotating about axis Ao, their left ends oscillate up and down about the moving axis A1 as driven by the axes A2 and A3 rotating about each other. This complex motion also creates a slight component of motion in the output gear, which becomes increasingly smaller as the length ofthe links 38 is increased. The angularoscillation ofthe links 38 creates a slight change in the projected length ofthese links on a base line passing through axisA0 and tangential to the output gear 50, and it is this change in projected length which creates the motion component in gear 50.Since the lengthening ofthe links 38 reduces their angular excursionsforgiven motions of the axes As and A2, the projected length variations decrease rapidly with increase in link length.

The total motion of the output gear 50, is thereby created by the superposition of the three primary design components summarized as follows: 1 .Aconstantvelocity determined by the gear ratios described.

2. Afirst oscillating component created by the rotation of axes A2 and A3 about each other.

3. A second oscillating component created by the rotation of axis A1 about axis A0.

Additionally, afourth incidental component is created inevitably by the angular excursion ofthe links 38, which can be made very small as their length is increased.

Thefourcomponents described above create a cyclical variation in the motion ofthe output gear 50, and a given cycle repeats once for every revolution ofthe eccentric gear 40. Therefore, for a given cycle, the output gear50 rotates through an angle represented by the ratio ofthe pitch diameterofthe eccentric gear48 tothe pitch diameter of the output gear 50. For example, and to the scale shown in Figures 1 and 2, in which gear48 is half as large as gear 50, the output will complete a given cycle in 1 80" of motion ofthe output gear 50. If gear 48 were the same size as gear 50, clearly a cycle would take place during a 360" rotation ofthe output gear 50.

The distance from axis Ao to axis A1 is defined as eccentricity E2, while the eccentricity between axis A2 and axis A3 is defined as eccentricity E1. The addition ofthis second eccentricity E2, which rotates at an integral multiple number of timers for each rotation ofthe eccentricity E1, makes it possible to achieve a wide variety of 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.

The mechanism of Figures 1 and 2, designated 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 ofthe output shaft about the center of this oscillation,which is defined asthezero pointforoutputangle measurement.

Whereas the rotary output embodiment of the background patent shown in Figures 51, 52, 53therein produced an output index angle of 90", duetothe proportions of gears 330 and 332, the output index angle of the embodiment shown in Figures 1 and 2 herein produces an output index angle of 1800 as previously described. Furthermore, in the background patent, the mechanism of Figures 51,52,53 shows a chain connection 332 from the member, sprocket 324, on axis A1 to the member, sprocket 321, on axis A2, whereas in the embodiment, Figures 1 and 2, shown herein, this equivaient drive connection is shown as being through gears 36,44 and 40. This minor structural modification was made to achieve greater drive stiffness.

Second dwell mechanism - background The second background mechanism utilized in the invention ofthe presentApplication is comprised of a crank and connecting rod mechanism described in many books on fundamental kinematics. It is illustrated here schematically in Figures 3,4and 5.

Referring to Figures 3 and 4, a shaft 60 rotates on axis and isjournalled in a frame 62 through a bushing 64; this shaft 60 can be driven byanysuitable prime mover. Acrank66 is fastened to the shaft 60, and at its outer wend 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 block72 through a pivot pin 74 on axis A7.

The slide block72 is supported by the frame 62 in which it is free to slide along an axis A8, which, as shown in Figure3,intersectstheaxisA5.

In Figure 5 is shown a schematic diagram useful to analyze the kinematic characteristics of the system.The distance on the crank 66 between axis A5 and A6 is defined as Rand 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 #. From this diagram, it is easily seen that the amountthe 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 + Lcosa (1)

where a = sin1(Rn(k) (2) If it is assumed that L is large compared to Rand therefore the angle a is small, even when it is ata maximum, then cos a is very closely approximated by 1, whereupon:: D=R-Rcos=R(1 R - R cos # R (1 - (1cos4) (3) This approximate equation is for the kinematic displacement characteristics of the crank and slider block motion.

Dwell and clock angle The term "dwell", in the generally accepted kinematic sense and as applied to any mechanism, is taken to mean thatthe output of that mechanism is stationary while its input continues to move. In thetheoretical 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 ofthe output is acceptable. Such a situation will be defined,for the purposes of thins disclosure as a "near dwell"; and furthermore, it will be characterized buy a numerical value which givesthe maximum peak-to-peak amplitude ofthe output oscillation, expressed as a fraction of the total output stroke ofthe 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 ofthe mechanism.This is shown schematically in Figure 6 whichfurther schematically defines theterm "dwell length".If it is assumed that a mechanism is driven by an in put shaft which rotates art 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 ofclockangle. A dwell length of 90 clock angle, for example, would represent a cycle in which theoutputwould be in neardwell for 90/360 orforone quarterofthe cycle. Clearly, if the inputshaft rotates through one revolution during an index cycle, then one degree ofinputshaft rotation equals one degree of clock angle; or, if, for example, the input shaft rotates through three revolutions during an index cycle, then everythree degrees of input shaft rotation equals one degree of clock angle. Stated anotherway, 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 ofthe invention The invention to be described herein is a combination ortandem 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 Figures 1 and 2 herein and having an output index angle of 180 (initially); and the second stage of which is comprised ofthe 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 madeto ascertain the numerous system characteristics achievable.

Referring to Figures 7 and 8, the mechanism 30, previously described in connection with Figures 1 and 2, is enclosed in the housing 80 and mounted on a base 82. Its inputshaft 32 is driven through a coupling 84 by the output shaft 86 of a gear reducer 88 also mounted on the base 82. The inputshaft90 of this gear reducerisin turn driven bya motor92 through a coupling 94. Depending on the application the motor may run continuously, orit may be stopped during the mechanism dwell with suitable conventional limit switches and electrical circuits. The crank 66 (Figures 3,4 and 5) is directly mounted on the output shaft 52 ofthe mechanism 30, whereupon axes A4 and A5 become coincident.Clearly the shaft 60 and frame 62 (Figures3 and 4) could be retained and a coupling used to connect shafts 52 and 60 if this were more convenient. The crankpin 68 on crank 66 is used to drive the connecting rod 70 in a reciprocating motion. The other end ofthe connecting rod 70 is connected to a reciprocating output member, which may be a slider block, such as shown in Figure 3, from which the load is driven, orthe connecting rod 70 may be directly connected to an input member ofthe load to be driven. Such an input member may be a link, a bellcrank, ora sliding member.

In any case, the output movement will be as given by the approximate equation (3) derived above,wherethe angle 4 is now the output angle ofthe mechanism 30.

Unitized output For comparative purposes in comparing the dwells, and other characteristics, of the mechanism of Figures 1 and 2, the crank mechanism of Figures 3to 5, and the combination mechanism of Figures7 and 8, itis convenientto scale the output of each system such thatthe index stroke is arbitrarily setto equal 1. Similarly, the input angle is defined in terms ofthe clock angle which has a range of 360"to create the output stroke of 1.

Underthese arbitrary scaling procedures, equation (3) becomes

where Du = "unitized" output 'C = "clock" angle This rescaling is dependent on the following reasoning relative to equation (3). The minimum position occurs when 4) = 0, and D = 0 independent ofthe value of R. The maximum position occurs when 4) = 180' and D is equal to 2R. Therefore, by setting

the maximum reaches 1 when 4 = 360'and it is by substituting these values for Rand 4 into equation (3)that equation (4) is obtained.

The output displacementfrom equation (4), in the near dwell area, is tabulated in Table 1 and shown graphically by curve Ref A in Figure 9.

TABLEI Unitized displacement ofa simple crank mechanism near dwell Clockangle Unitized displacement -20 .007596 -15 .004278 -10 .001903 - 5 .000476 0 0 5 .000476 10 .001903 15 .004278 20 .007596 The operation of the mechanism 30, which is analyzed in the reference patent, may be qualitatively and briefly described as follows. The total motion ofthe 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 outputgear50.

Referring to the background patent, the generalized approximate displacement equation, for the situation in which the axis A1 rotates aboutthe axis A0 through two revolutions for one revolution ofthe axes A2 and A3 about each other, is: U =0- E1 sinO + E2 sin 20 (5) where U = Angular output displacement of output shaft 52, having a range of 2 Tr units independent ofthe index angle 6 = Clock angle in radians E1 = Distance between axes A2 and A3 expressed as a ratio to the radius of the eccentric gear 48 E2 = Distance between axes A1 and Ao also expressed as a ratio to the radius of the eccentric gear 48 Similarly, if the axis A1 rotates about axis Ao three revolutions for each revolution ofthe axes A2 and A3 about each other, the generalized approximate displacement equation, from the background patent is:: U = 0 - E, sinO + E2 sin 30 (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 A1 rotates about axis Ao N times for each revolution of axes A2 and A3 about each other, as controlled bythe ratio between the inputgear36 and the driving gear40,the generalized approximate displacement equation for the output of the mechanism becomes: U = 6 - E1 sine + E2 sin Ne (7) As noted above, the output variable U is scaled to reach 2ir units during an index cycle; furthermore, the input angle, 0, is dimensioned in radians.In orderto compare the output of the independent mechanism 30 with the output of the crank and connecting rod mechanism, noted as curve Ref. A, in Figure 9, it is necessary to rescale equation (7) into unitized coordinates, which is accomplished by multiplying the entire equation by 1/21r and to convert 0 to the clock angle c, in degrees bysetting:

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

which reduces to:

In the background patent, it was shown that the longest dwell without reversal,when using N = 3, is obtained with F1 = 1.125, and F2 = .04167 (1/24).Substituting these values into equation (9), the unitized displacementvalues at various clockangles arefoundto be: TABLEII Clockangle Unitized displacement -60 -.011605 -50 -.005045 -40 -.001763 -30 -.000440 -20 -.000060 -10 -.000002 0 0 10 .000002 20 .000060 30 .000440 40 .001763 50 .005045 60 .011605 This data is also graphically represented by curve Ref. B in Figure 9.

Itwasfurther shown in the background patentthatthe longest dwell without reversal, when using N = 2, is obtained with F1 = 1.33(11/3) and F2 = .167 (1/6). Substituting these values into equation (9), the unitized displacement at various clock angles are found to be: TABLEIII Clockangle Unitized displacement -60 -.005862 -50 -.002452 -40 -.000830 -30 -.000202 -20 -.000027 -10 -.000001 0 0 10 .000001 20 .000027 30 .000202 40 .000830 50 .002452 60 .005862 This data is also graphically represented by curve Ref. C in Figure 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 greaterthan the dwell which occurs attop dead center or bottom dead centerof a crank and connecting rod mechanism.

The second observation concerns the directional behaviour of the displacement in the vicinity ofthe dwell.

Relativeto the crank and connecting rod mechanism, it can be seen thatthe displacementon eitherside of the center of dwell, where the clock angle is0, 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, the displacement on eithersideof the center of dwell is bidirectional; this is again as would be expected for an indexing mechanism ofthis type; i.e., for unidirectional input shaft rotation, the output will momentarily stop after a given index, butthen reaccelerate in the same direction it had before stopping.

The foregoing data on the near dwell characteristics of each ofthe mechanisms operating independently are provided as reference data forthe new data to be shown.

In the combination mechanism of Figures 7 and 8 in accordance with the present invention, it is necessary to rescale equation (7) such that it represents the true output angle of the shaft 52 of the mechanism 30. lf the numberof index cycles per revolution ofthe output shaft 52 is defined as M,then the instantaneous position yofthe shaft 52, as a function of clock angle, can be represented by multiplying the equation (9), forunitized displacement, by 360/M which represents the degrees of rotation per index of shaft 52.Therefore:

This reduces to:

In the combined mechanism of Figures 7 and 8, the output angle ofthe shaft 52, as given by y of equation (11) is equal to the input angle # ofthe crank and connecting rod mechanism of Figure 5 as approximated by equation (3). It is necessary to introduce a new variable C1, 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 ofthe mechanism 30, i.e., the clock angle Xc is 0, then the anglethatthe crank is beyond its dead center position is defined as the phase angle, C1.

Therefore, 4)="+C1 (12) Substituting equation (12) into equation (3): D=R[1 -cos(+C1)j (13) For an output stroke equal to 1, R = 1/2 Du = 1/2 [1cos(^y + C)] (14) If the va l ue for y from equation (11) is substituted into equation (14), the unitized displacement equation for the mechanism ofthis invention is obtained.

There are five parameters in this equation, M, N, C1, E1 and E2, each of which exerts its own influence on the characteristics of the output. Clearly, the number of combinations is extremely large.

Afew combinations will be represented to illustrate the influence of these various variables. In these illustrations,the various Tabies 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 each endofstroke One of the important practical applications ofthis invention is to create long dwells at both ends of the stroke. This permits, for example, the operation of other systems whilethis mechanism is in dwell. By com- biningthe individual mechanisms such thattheirdwell points are coincident, C1 = 0, and arranging mechanism 30to have a 80 indexangle, M = 2, and using the F1 and F2 factors as were determined to givethe "flatest" dwells, as obtained from the background patent, the following cases were calculated: Case 1 C1 =0 M=2 N=3 E=1.125 E2=1/24 The results are tabulated in Table IV.

TABLEIV Clockangle Unitized displacement -80 .003972 -70 .001291 -60 .000332 -50 .000063 -40 .000008 -30 to + 30 Less than .000001 40 .000008 50 .000063 60 .000332 70 .001291 80 .003972 These results are also shown as curve D in Figure 9. Recalling that this dwell curve is the output ofthe combined mechanism, comprised of the independent mechanisms, whose dwell characteristics are presented in curves Ref. Aand Ref. B, it can be seen that the dwell characteristics ofthe combined mechanism arefar betterthan the mere sum ofthe dwells ofthe individual mechanisms. It is furtherclearthatthe outputofthe combined mechanism, as would be expected, retains the reversing characteristics of the crank and connecting rod mechanism, and that the displacement curve D, Figure 9, is symmetrical about the 0 axis, as was curve Ref. A.

Case2 This is comparable to Case 1 except that the second harmonic version ofthe mechanism 30 is used, rather than the third given by curveD. Therefore: C1 =0 M=2 N=2 F1=11/3 F2=1/6 The results aretabulated inTableV.

TABLE V Clockangle Unitized displacement -90" .003520 -80" .001228 -70" .000360 -60" .000085 -50" .000015 -40" .000002 -30 to + 30 Less than .000001 40 .000002 50 .000015 60 .000085 70 .000360 80 .001228 90 .003520 These results are also shown in curve E of Figure 9, with the same observations applying as were madefor curve D.

Very long dwells at each end ofstroke In the background patent, techniques were developed,for both the second and third harmonic, N = 2 and N = 3, to find values of E1 and E2, such that the displacement could be made to go through 0 atfourdifferentnull angles, which are predetermined values of clock angle at which the output displacement is0. The qualitative generic characteristics of such a condition is shown in Figure 10.It will be noted that the output displacement ofthe mechanism 30, represented in Figure 10, passes through 0 art a predetermined clock angle, defined as a null angle, at-#N2; "overshoots" slightly,then returns to 0 output second predetermined null angle, -0N.ltthen "undershoots" and returns to 0 output displacement at 0 clock angle. The behaviour of the mechanism 30 at positive clock angles is symmetrically opposite, but nota mirror image, of its behaviourat negative clock angles. In essence, therefore, the output ofthe mechanism 30 can be arranged to pass through 0 outputfivetimes 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 byjudicious selection ofthe null angles. Using a computer, itis possible to manipulatethe null angles by trial and error, successive approximation, oriteration,to achieve the predetermined amplitudes of oscillation, and the associated factors E1 and E2. Generally, the four distinct oscillation amplitudes will be made equal to each other, but this need not be so.

The output displacement of the mechanism 30 is the crank angle of the crank and connecting rod mechanisms and is so labelled in Figure 10. If the phase angle C1 is 0, the resultant output ofthe combination mechanism will have the generic form shown in Figure 11 as a result of the crank oscillation shown in Figure 10. It will be noted that the output oscillation ofthe combination mechanism is unidirectional because ofthe inherent characteristics ofthe crank mechanism, in which the output is symmetrical about a dead center position, i.e., the outputfora given angle is the samewhetherthe angle is "before" or "after" the dead center position. This is mathematically confirmed by equation (3) since cos(6) = cos(-0).

If a given dwell amplitude (unitized) is defined for a specific application,thefollowing technique is useful.

Equation (3) is inverted, and R is set equal to , whereby: cos = -2Du (b=arccos(1 -2Du) (16) As applied to the combined mechanism, and noting the relationship between Figures 10 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 oscillation angles as a function of dwell amplitude, for 1800 output of mechanism 30 (M = 2) which provides a long dwell at each end of the stroke. 2) which provides a long dwell at each end ofthestroke.

TABLE Vl Unitized Permissible crank Unitized crank predetermined oscillation amplitude oscillation dwell amplitude true degrees 1800 index .00001 + .362370 +.00201 .00003 + .62765 +.00348 .00010 # 1.14593 i.00636 .00030 +1.98488 c.01103 .00100 # +3.62431" .02014 .00300 +6.27958 +.03489 With the permissible crank oscillation amplitude determined for a given predetermined dwell amplitude forthe combined mechanism, from equation (16), and as illustrated by the examples of Table VI, it is possible to use these crankoscillation amplitudes to determinethe null angles and the factors E1 and E2whichwill create them. As noted above, this is accomplished by using successive approximation techniques with a computer.

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

TABLE VIVA N=3 Dwell Null angle 1 Null angle 2 amplitude clock degrees clock degrees .00001 +36.884 #62.047 .00003 +40.110 +68.095 .00010 "43.661 #75.045 .00030 +46.816 +81.563 .00100 +50.040 +88.710 .00300 #52.642 + 95.013 TABLE VIIB N = 2 Dwell Nullangle 1 Nullangle2 amplitude clock degrees clock degrees .00001 +44.909 + 74.615 .00003 +49.262 t 82.361 .00010 +54.273 + 91.502 .00030 +58.991 t100.389 .00100 t64.206 # 110.624 .00300 +68.874 # 120.266 From the null angles, such as tabulated in Tables VllA and B, it is possible to calculate the required factors E1 and E2, using the method outlined in the background patent. When this is done using the spacific null angle values tabulated in Tables VIIA and B, for the desired dwell amplitudes, the corresponding E1 and E2factors are listed in Tables VIIIA and B.

TABLE VIII A N= 3 Dwell Factor Factor amplitude E7 E2 .00001 1.2149 .0913 .00003 1.2326 .1090 .00010 1.2545 .1379 .00030 1.2762 .1782 .00100 1.3008 .2483 .00300 1.3227 .3528 TABLE VlllB N = 2 Dwell Factor Factor amplitude E1 E2 .00001 1.4947 .2714 .00003 1.5311 .3037 .00010 1.5791 .3530 .00030 1.6309 .4170 .00100 1.6969 .5197 .00300 1.7647 .6603 The factors E1 and E2 tabulated above may now be used in equation (15) to calculate the unitized displacemont output ofthecombination mechanism. Recalling that the procedurefordetermining E1 and E2, inthis instance, was predicted on the mechanism 30 having an output index angle of 180 , M = 2, and thatthe phase angle, C1, was 0, it becomes possible to establish the parameters for two illustrative cases.

Case 3 C1=0 M=2 N=3 E1=1.3008 E2=.2483 The factors E1 and E2were arbitrarily chosen from Table VIllAto illustrate a dwell condition at the ends of the stroke that has an amplitude of .001 ofthetotal stroke using athird harmonic N = 3. Thefactorslisted 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 Figure 12, in which only the characteristics at positive clock are shown. It will be understoodthatthe behavior at negative clock angles is a mirror image aboutthe 0 clock angle line as shown in the generic curve, Figure 11.From curve F, Figure 12, it can be seen thatthe displacement oscillates within the predetermined dwell amplitude of .001 fora total of +95 oratotal dwell of 190", this represents 190/360 or 52.7% of the total cycle time. Itwill further be noted thatthe displace- mont curve F is tangent to the 0 displacement axis atclockangles ofSO"and 800, 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 Figures 1 and 2.

Case 4 C1 =0 M=2 N=2 E1=1.6969 E2=.5197 The factors E1 and E2 were taken from Table VIIIB for a dwell amplitude of .001 to permit a directcomparison ofthe dwell behaviorfor N = 2 relative to curve Fwhere N = 3. Using these values again in equation (15), the results are plotted as curve G of Figure 12. A marked improvement in the dwell length will be noted, -1 18", ora 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 or65.5% ofthetotal cycle.

While achieving long dwells is of practical importance, it is also necessary to examine the kinematic behavior ofthe system during the movement between these dwells. As noted earlier, the velocity calculations are made using a computerand numerical differentiation ratherthan classical differentiation and subsequent calculation offar more involved equations than equation (15). Using these techniques, thevelocitiesduring the stroke were calculated forthe four previously described cases and are shown graphically in Figure 13.

Curve D' shows the velocity characteristics of Case 1 whose dwell characteristics are shown by curve D of Figure 9. These velocity characteristics are symmetrical aboutthe clock angle 180", and velocities at clock angles less than 60" are too small to be of any interest. The velocities are plotted in terms of relative velocity which is defined as the ratio ofthe instantaneous velocity at a given clock angle divided bythe average velocity which is the total stroke divided bythetime required forthe clock angle to move through 360".

Similarly, the velocity curve E' represents the conditions of Case 2 and is the cou nterpart of dwell curve Eof Figure 9. Thevelocity curve F' is for Case 3 and is the counterpart of dwell curve F in Figure 12; and velocity curve G' represents Case4and is the counterpartofthe dwell curve G of Figure 12. As a broad generalization, the peakvelocitiesforthe cases in which N = 2, as represented by curves E' and G' are higherthan thosefor the case where N = 3, as represented by curves D' and F', as is to be expected since the dwells forthe N = 2 cases are longerthan forthosewhere N = 3.Interestingly, the curve F', which represents a configuration which has a longer dwell than the otherthird harmonic curve D', has a velocity reversal near midstroke, which is an inherent characteristics of having a large third harmonic component.

Long dwells between the ends ofthe 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 ofthe total cycle time per stroke; and the velocity characteristics between the ends ofthe 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 ofthe stroke. Three additional cases will be used to show howthis can be accomplished. The first method involves using a phase angle, C1,toshift the dwell of mechanism 30 away from the reversal dwell ofthe crank and connecting rod mechanism.By positioning the crank on the output shaft ofthe 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 C1 = 90" is obtained. Byfurtherassigningthe value M = 2, whereby the output index angle ofthe mechanism 30 is 180", a dwell will be created on both the forward and return midstroke. The dwell amplitude ofthe crank angular oscillation during dwell is arbitrarily setto i0.18"and the values forE1 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 condition for Case were established as follows.

Case 5 C1 = 90 M = 2 N = 3 E1=1.196 E2=.0761 The results ofthese conditions were then calculated at suitable clock angle intervals and the results plotted as curve H, Figure 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,whilethe dwells atthe ends ofthe stroke are quite short.

In otherapplications, a long 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 changingthe phase angle Ct to an appropriate angle different than the 90" utilized to create the conditions ofcurve H,whilethe other parameters are arbitrarily unchanged.

Case 6 C1 = 60" M=2 N=3 E1=1.196 E2=.0761 The resultsareshown bycurveJ of Figure 14, in which, as noted,the phase angle C1 is 60 . The inter- mediate long dwell is ata unitized output displacement of 25 on theforward stroke and at a unitized output displacement of .75 on the return stroke as would be expected by considering equation (14) and substituting = = O for the first dwell position and y = 180"forthe second dwell position. Clearly then, for M = 2, thetwo dwell positions are always the same distance away from the previous reversal dwell; stated another way, the sum ofthe unitized displacementsforthetwo intermediate dwell positions is always equal to 1.This can be modified by an intermediate linkage two the final drive point.

Long dwells at ends of stroke andatmidstroke Using the parameters illustrated by Cases 5 and 6, the dwells at the ends ofthe strokes were quite short, as isto be expected fora crank rotating at some angularvelocity. Applications arise, however, in which a long dwell is required attheends ofthe stroke as well as atthe midpoints ofthe stroke. This can be achieved by selecting a 90" output index angleforthe mechanism 30, which is accomplished by setting M = 4. Afive point dwell, as illustrated by Figure 1 was selected with a dwell amplitude of +.09" (.001 unitized) for the crank oscillation,whereuponthefinal parameters, calculated as previously explained, are as follows.

Case 7 C1=0 M=4 N=3 E1=1.196 E2=.0761 The results ofthe calculations are shown by curve K of Figure 15. This is plotted for atotal clock angle range of 1440" as is required since four indexes of the mechanism are required for each revolution ofthe crankand each such index requires 360" of clock angle. It will be noted, from curve K, that, in addition to having long dwells at midstroke,the dwells at the ends ofthe stroke are significantly longer than thoseforCases 5 and 6 represented by curves H and J of Figure 14.

Long dwell at one end or strokeand ofstroke and short dwell at other end Some applications arise in which it is desired to have a reversing mechanism which has a very long dwell at one end ofthe stroke and a relatively short dwell at the other end ofthe stroke. This requirement can be met by this invention by using an output index angle of360"forthe mechanism 30, whereby M = 1, and position ing thecranksuch that the phase angle isO, i.e., C1 = O. Clearly, the crank is then at one dead center position when the mechanism 30 is in dwell; at the crank's opposite dead center position, the mechanism 30 will be at its mid index position and will be rotating at some relatively high angularvelocity. This situation gives riseto 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 C1 =0 M = 1 N=3 E1=1.273 E2=.1703 The results ofthe calculations using these parameters in equation (15) are shown by curve L in Figure 16.

Case 9 C1 =0 M = 1 N =2 E1=1.622 E2=.4048 The results ofthe calculations using these parameters are shown by curve M in Figure 16.

Curve L is based on using N = 2, and curve M is based on using N = 3. In each instance, the parameters E1 and E2 were established by computer successive approximation such that the dwell amplitude ofthetotal system was .001 as previously noted. The curves are plottedforonly 180" ofclockangle, sincetheyare symmetrical about both the 0" and 180" clock angles. As expected from the knowledge of Figures 9 and 12,the dwell atone end ofthestroke is greaterforthe N = 2 situation relative to the N = 3 situation.As a consequ ence, it follows that because ofthe compensating higher midstrokeangularvelocity ofthe N = 2situation, the dwell at the other end of stroke is shorterfor N = 2than for N = 3, or stated another way, the reversal is fasterfor N = 2 than for N = 3.

Three point dwells In the foregoing Cases 3-9, the parameters E1 and E2 were determined using a five point dwell as described in connection with Figures 10 and 11. This was more fully described in the background patent. As also more fully described in the background patent, it is also possibleto arrangethe mechanism 30 such that its dis- placement characteristic in the dwell area only goes through 0 three times, rather than five; this will be defined as athree-pointdwell. The primary objective in reducing the number of dwell points from 5to 3 is that, in so doing, it becomes possible to find combinations of E1 and E2which permit greater control overthe kinematics of the movement between the dwells.In connection with the independent mechanism 30, numerous illustrative examples are presented in the background patent, including the kinematic curves of Figures 12,13,30 and 31 of said patent.

The generic characteristics ofthe outputdisplacementofthe mechanism 30 in thethree point dwell mode is shown in Figure 17. Since the displacement becomes the crank angle ofthe crank and connecting rod mechanism it is again so labeled. There are several methods which may be employed to create a three point dwell, as will subsequently be shown. Assuming that the parameters E1 and E2 have been established to create athree point dwell condition forthe mechanism 30, the outputangulardisplacement ofthe mechanism 30, or crank angle, are generically shown by the curve of Figure 17.It can be seen thatthecrank "overshoots" its 0 position after crossing the zero point at some negative clock angle, which is defined as null angle --0N1. The crank angle displacement then reverses and passes through its 0 position again at a clock angle of 0, then undershoots before reversing to progress forward, again crossing the 0 displacementposl- tion at some positive clock angle defined as null angle 6N1 In essence, when the parameters E1 and Eare determined such as to create a three point dwell, the angular output displacement of mechanism 30 under goes a double reversal crossing the 0 linethreetimes, whereas when the parameters E1 and E2 are deter- mined to create a five point dwell as previously described, the angular output displacement, which is crank angle, undergoes four reversals and crosses the zero line five times.

If the crank is positioned on the output shaft ofthe mechanism 30 such that it is in its dead centerposition when the mechanism is in the center of its dwell, the unitized output displacement of this invention will beas shown by the generic curve of Figure 18 which is derived from Figure 17 by the same technique used in describing the curve of Figure 11 derived from the curve of Figure lOIn essence, the unitized output displace- ment ofthe crank is Oat -0N1, 0, and eN1 where the crank angle is 0, and very slightly positive, whereverthe crank angle is slightly positive or negative, again as described in connection with Figure 11.

The method of determining thefactors E1 and E2 for the th ree point dwell is comparable to that used for finding the five point dwells. Using thetechniques used in finding the groups of solutionsforthree point dwells shown in the background patent, it is possibleto calculate the total dwell amplitude, then adjust either E1 or E2to obtain the desired dwell amplitude.The non used E1 orE2 (forfinding the desired dwell amplitude) is then varied to approximate the desired kinematic objective, but for each variation in the variable (E1 orE2) used to seek the kinematic objective, it is necessary to re-evaluate the variable (E1 orE2) which creates the dwell amplitude. This is again a successive approximation techniqueforwhich a computer is practically indispensable.

Even without starting with the knowledge ofthe background patent, it is possible to find E1 and E2 as long astheyare mathematically obtainable. Avalue is arbitrarily assigned to either E1 orE2and the non-assigned variable E1 orE2 is varied to create the desired dwell amplitude, again using equation (15) as the basisfor making the unitized displacement calculations. The assigned variable E1 or E2then can be modified bysuc- cessive 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 andnearly constant velocity 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. Utilizing the information ofthe previous cases, M was set equal to 2to create a long dwell at each end ofthe stroke. The dwell amplitude was again arbitrarily selected as .001 in unitized displacement coordinates.

With these conditions and parameters established and N set equal to 2, E2was setfrom -0.1 to -0.3 in steps of .01 utilizing the precedent of curve B Figure 12 ofthe 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 E1 and E2, a result was selected which was judged best to meet the aforesaid requirements and is given as follows.

Case 10 C1 =0 M =2 N=2 E1=.9190 E2=-.22 The dwell characteristics for this combination of parameters are shown as curve N in Figure 19, with these characteristics symmetrical about0 clock angle as demonstrated by the generic dwell curve Figure 18. The velocity characteristics ofthis combination are shown by curve N' of Figure 20, in which the velocities below aclockangle ofSO" are too small to be of interest, and the velocities are symmetrical about a clockangleof 180". It should be pointed outthatthe dwells and velocitiesforthe "neighboring" solutionsfoundfor E2 = -.21 and -.23 are almost imperceptibly different. These combinations are: E2=-.21 E1=.9361 E2=-.23 E1=.9O18 Using these same procedures, except with N = 3, ratherthan N = 2 as for Case 10, the following E1 and E2 was selected to best meetthe requirements.

Claims (15)

Claim 11 C1 =0 M =2 N=3 E1=1.355 E2=.11 The dwell characteristics for this combination of parameters are shown by curve P of Figure 19 and the velocity characteristics are shown by curve P' of Figure 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 illustrative only. Each of the cases involved a dwell of one type or another; but this is notto say the invention 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 by equation (15), and this in turn is determined to a large degree bythe knowledge, experience and ingenuity of a designer applying this equa- tion, and the mechanism it represents. All the performance curves were derived on the basis of equation (15), which, itwill 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 nonapproximating calculations become hopelessly complex), it has been found that a very high degree of correl ation can befound between the characteristics described herein and the exact characteristics numerically calculated.This has involved adjusting, by successive approximations the distances between axes Ao and A4 and between axes A1 and A2 as well as the aforesaid distances between axis A2 and A3 (E1) and between axes Ao and Al (E2). CLAIMS

1. A reciprocating mechanical drive system capable of providing a wide variety of kinematic objectives, including very long dwells atthe ends ofthe stroke, unequal dwells at opposite ends ofthe stroke, inter mediate dwells between the ends of a stroke, and non-symmetrical movementwhen moving in one direc- tion, as compared to the movement in the other direction, comprising: (a) unidirectional rotary drive means having a cylicallyvarying output, comprising: (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 fortangential driving, (4) a first rotating pair supported by said frame comprising:: (i) a first rotating member mounted for rotation in said frame, and (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 paircomprising: (i) a second rotating member, and (ii) a second eccentric member 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 pairfor substantially an integral angularvelocity 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, and (b) a reciprocating output drive system comprising:: (1 ) a crank member mounted at its one end to said output shaft member, (2) connecting rod means journalled at its one end to the other end of said crank member, and (3) reciprocating output means mounted for reciprocation in said frame, and pivotally connected to the other end of said connecting rod means.

2. A reciprocating mechanical drive system as claimed in claim 1, in which said power means is connected to said first rotating member.

3. A reciprocating mechanical drive system as claimed in claim 1, in which said output member has a pitch radius which is two times the pitch radius of said second eccentric member.

4. A reciprocating mechanical drive system as claimed 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 and said connecting rod memberare substantially colinear.

5. A reciprocating mechanical drive system as claimed in claim 1, in which the pitch radii of said output member and said second eccentric member are equal.

6. A reciprocating mechanical drive system as claimed in claim 1, in which said output member has a pitch radius which is fourtimes the pitch radius of said second eccentric member.

7. A reciprocating mechanical drive system as claimed 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.

8. A reciprocating mechanical drive system capable of providing a wide variety of kinematic objectives, including very long dwells atthe ends ofthe stroke, unequal dwells at opposite ends ofthestroke, 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) unidirectional rotary drive means having a cyclically varying output, comprising: (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 fortangential driving, (4) a first rotating pair supported by said frame comprising:: (i) a first rotating member mounted for rotation in said frame, and (ii) a first eccentric gear 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, and (ii) a second eccentric gear member 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 pairfor substantially an integral angularvelocity ratio, (7) means connecting said outputgearmemberand said second eccentric gear 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, and (b) a reciprocating output drive system comprising: : (1) a crank member mounted at its one end to said output shaft member, (2) connecting rod means journalled at its one end to the other end of said crank member, and (3) reciprocating output means mounted for reciprocation in said frame, and pivotally connected to the other end of said connecting rod means.

9. A reciprocating mechanical drive system as claimed in claim 8, in which said power means is connected to said first rotating member.

10. A reciprocating mechanical drive system as claimed 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.

11. A reciprocating mechanical drive system as claimed 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 and said connecting rod member are substantially colinear.

12. A reciprocating mechanical drive system as claimed in claim 8, in which the pitch radii of said output gearmemberand said second eccentric gear member are equal.

13. Areciprocating mechanical drive system as claimed in claim 1, in which said output gear member has a pitch radius which is fourtimesthe pitch radius of said second eccentric gear member.

14. A reciprocating mechanical drive system as claimed 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 crankmemberand said connecting rod member are substantially colinear.

15. A reciprocating mechanical drive system, substantially as hereinbefore described with reference to and as illustrated in Figures 7to 20 of the accompanying drawings.