Large-ratio strain wave gearing speed changing apparatus

Abstract

A strain wave gearing speed changing apparatus has a coaxial pair of circular splines including a first with tooth number T.sub.A and a second with T.sub.D. A coaxial pair of flex splines includes a first with tooth number T.sub.B and a second with T.sub.C. First flex spline meshes first circular spline and second flex spline meshes second circular spline at two, preferably more, meshing engagements. A wave generator is connected to one of the input and output shafts. Two flex splines are fixed together to operate flexingly on the wave generator with equal spline tooth engagement pitch circle circumference lengths. One circular spline is fixed to the apparatus frame and the other is connected to the other of the input and output shafts not connected to the wave generator. The four splines satisfy T.sub.A=T.sub.K+T.sub.i, T.sub.B=T.sub.K, T.sub.C=T.sub.KT.sub.j and T.sub.D=T.sub.K+T.sub.iT.sub.j.

Claims

1. A strain wave gearing speed changing apparatus for changing an input speed at an input shaft to an output speed at an output shaft, the apparatus comprising: a coaxial pair of circular splines including a first circular spline having a spline tooth number T.sub.A and a second circular spline having a spline tooth number T.sub.D; a coaxial pair of flex splines including a first flex spline having a spline tooth number T.sub.B and a second flex spline having a spline tooth number T.sub.C; the first flex spline meshing with the first circular spline and the second flex spline meshing with the second circular spline, forming two meshing pairs; and a wave generator connected to one of the input and output shafts of the apparatus; wherein the coaxial pair of flex splines being fixed together to operate flexingly on the wave generator and having equal spline tooth engagement pitch circle circumference lengths; one circular spline being fixed to a frame of the apparatus and another circular spline being connected to another of the input and output shafts that is not connected to the wave generator; and the coaxial pairs of circular and flex splines satisfying spline tooth number relationships of T.sub.A=T.sub.K+T.sub.i, T.sub.B=T.sub.K, T.sub.C=T.sub.KT.sub.j and T.sub.D=T.sub.K+T.sub.iT.sub.j.

2. The apparatus of claim 1 wherein both T.sub.i and T.sub.j are smaller than 5.

3. The apparatus of claim 1 wherein T.sub.K/T.sub.i is smaller than about 30/1 or T.sub.K/T.sub.j is smaller than about 30/1.

4. The apparatus of claim 1 wherein T.sub.i equals T.sub.j.

5. The apparatus of claim 1 wherein the wave generator is connected to the input shaft.

6. The apparatus of claim 1 wherein the wave generator is connected to the output shaft.

7. A strain wave gearing speed changing apparatus for changing an input speed at an input shaft to an output speed at an output shaft, the apparatus comprising: a coaxial pair of circular splines including a first circular spline having a spline tooth number T.sub.A and a second circular spline having a spline tooth number T.sub.D; a coaxial pair of flex splines including a first flex spline having a spline tooth number T.sub.B and a second flex spline having a spline tooth number T.sub.C; the first flex spline meshing with the first circular spline and the second flex spline meshing with the second circular spline, forming two meshing pairs; and a wave generator connected to the input shaft of the apparatus; wherein the coaxial pair of flex splines being fixed together to operate flexingly on the wave generator and having equal spline tooth engagement pitch circle circumference lengths; one circular spline being fixed to a frame of the apparatus and another circular spline being connected to the output shaft that is not connected to the wave generator: and the coaxial pairs of circular and flex splines satisfying spline tooth number relationships of T.sub.A=T.sub.K+T.sub.i, T.sub.B=T.sub.K, T.sub.C=T.sub.KT.sub.j and T.sub.D=T.sub.K+T.sub.iT.sub.j.

8. The apparatus of claim 7 wherein both T.sub.i and T.sub.j are smaller than 5.

9. The apparatus of claim 7 wherein T.sub.K/T.sub.i is smaller than about 30/1 or T.sub.K/T.sub.j is smaller than about 30/1.

10. The apparatus of claim 7 wherein T.sub.i equals T.sub.j.

11. A strain wave gearing speed changing apparatus for changing an input speed at an input shaft to an output speed at an output shaft, the apparatus comprising: a coaxial pair of circular splines including a first circular spline having a spline tooth number T.sub.A and a second circular spline having a spline tooth number T.sub.D; a coaxial pair of flex splines including a first flex spline having a spline tooth number T.sub.B and a second flex spline having a spline tooth number T.sub.C; the first flex spline meshing with the first circular spline and the second flex spline meshing with the second circular spline, forming two meshing pairs; and a wave generator connected to the output shaft of the apparatus; wherein the coaxial pair of flex splines being fixed together to operate flexingly on the wave generator and having equal spline tooth engagement pitch circle circumference lengths; one circular spline being fixed to a frame of the apparatus and another circular spline being connected to the input shaft that is not connected to the wave generator; and the coaxial pairs of circular and flex splines satisfying spline tooth number relationships of T.sub.A=T.sub.K+T.sub.i, T.sub.B=T.sub.K, T.sub.C=T.sub.KT.sub.j and T.sub.D=T.sub.K+T.sub.iT.

12. A strain wave gearing speed changing apparatus for changing an input speed at an input shaft to an output speed at an output shaft, the apparatus comprising: a coaxial pair of circular splines including a first circular spline having a spline tooth number T.sub.A and a second circular spline having a spline tooth number T.sub.D; a coaxial pair of flex splines including a first flex spline having a spline tooth number T.sub.B and a second flex spline having a spline tooth number T.sub.C; the first flex spline meshing with the first circular spline and the second flex spline meshing with the second circular spline at two or more meshing engagements, forming two meshing pairs; and a wave generator connected to one of the input and output shafts of the apparatus; wherein the coaxial pair of flex splines being fixed together to operate flexingly on the wave generator; one circular spline being fixed to a frame of the apparatus and another circular spline being connected to another of the input and output shafts that is not connected to the wave generator; and the coaxial pairs of circular and flex splines satisfying spline tooth number relationships of T.sub.A=T.sub.K+T.sub.i, T.sub.B=T.sub.K, T.sub.C=T.sub.KT.sub.j and T.sub.D=T.sub.K+T.sub.iT.sub.j.

13. The apparatus of claim 12 wherein both T.sub.i and T.sub.j are smaller than 5.

14. The apparatus of claim 12 wherein T.sub.K/T.sub.i is smaller than about 30/1 or T.sub.K/T.sub.j is smaller than about 30/1.

15. The apparatus of claim 12 wherein T.sub.i equals T.sub.j.

16. The apparatus of claim 12 wherein the wave generator is connected to the input shaft.

17. The apparatus of claim 12 wherein the wave generator is connected to the output shaft.

18. A strain wave gearing speed changing apparatus for changing an input speed at an input shaft to an output speed at an output shaft, the apparatus comprising: a coaxial pair of circular splines including a first circular spline having a spline tooth number T.sub.A and a second circular spline having a spline tooth number T.sub.D; a coaxial pair of flex splines including a first flex spline having a spline tooth number T.sub.B and a second flex spline having a spline tooth number T.sub.C; the first flex spline meshing with the first circular spline and the second flex spline meshing with the second circular spline at two or more meshing engagements, forming two meshing pairs; and a wave generator connected to the input shaft of the apparatus; wherein the coaxial pair of flex splines being fixed together to operate flexingly on the wave generator; one circular spline being fixed to a frame of the apparatus and another circular spline being connected to the output shaft that is not connected to the wave generator; and the coaxial pairs of circular and flex splines satisfying the dimensional spline tooth number relationships of T.sub.A=T.sub.K+T.sub.i, T.sub.B=T.sub.K, T.sub.C=T.sub.KT.sub.j and T.sub.D=T.sub.K+T.sub.iT.sub.j.

19. The apparatus of claim 18 wherein both T.sub.i and T.sub.j are smaller than 5.

20. The apparatus of claim 18 wherein T.sub.K/T.sub.i is smaller than about 30/1 or T.sub.K/T.sub.j is smaller than about 30/1.

21. The apparatus of claim 18 wherein T.sub.i equals T.sub.j.

22. A strain wave gearing speed changing apparatus for changing an input speed at an input shaft to an output speed at an output shaft, the apparatus comprising: a coaxial pair of circular splines including a first circular spline having a spline tooth number T.sub.A and a second circular spline having a spline tooth number T.sub.D; a coaxial pair of flex splines including a first flex spline having a spline tooth number T.sub.B and a second flex spline having a spline tooth number T.sub.C; the first flex spline meshing with the first circular spline and the second flex spline meshing with the second circular spline at two or more meshing engagements, forming two meshing pairs; and a wave generator connected to the output shaft of the apparatus; wherein the coaxial pair of flex splines being fixed together to operate flexingly on the wave generator; one circular spline being fixed to a frame of the apparatus and another circular spline being connected to the input shaft that is not connected to the wave generator; and the coaxial pairs of circular and flex splines satisfying spline tooth number relationships of T.sub.A=T.sub.K+T.sub.i, T.sub.B=T.sub.K, T.sub.C=T.sub.KT.sub.j and T.sub.D=T.sub.K+T.sub.iT.

23. A strain wave gearing speed changing apparatus for changing an input speed at an input shaft to an output speed at an output shaft, the apparatus comprising: a coaxial pair of circular splines including a first circular spline having a spline tooth number T.sub.A and a second circular spline having a spline tooth number T.sub.D; a coaxial pair of flex splines including a first flex spline having a spline tooth number T.sub.B and a second flex spline having a spline tooth number T.sub.C; the first flex spline meshing with the first circular spline and the second flex spline meshing with the second circular spline at a single meshing engagement, forming two meshing pairs; and a wave generator connected to one of the input and output shafts of the apparatus; wherein the coaxial pair of flex splines being fixed together to operate flexingly on the wave generator and having equal spline tooth engagement pitch circle circumference lengths; one circular spline being fixed to a frame of the apparatus and the other spline of another circular spline being connected to another of the input and output shafts that is not connected to the wave generator; and the coaxial pairs of circular and flex splines satisfying spline tooth number relationships of T.sub.A=T.sub.K+T.sub.i, T.sub.B=T.sub.K, T.sub.C=T.sub.KT.sub.j and T.sub.D=T.sub.K+T.sub.iT.sub.j.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIG. 1 schematically illustrates a prior art large-ratio cycloidal speed reducer.

(2) FIG. 1A schematically illustrates another prior art large-ratio strain wave gearing speed reducer.

(3) FIG. 2 schematically illustrates the off-axis power extraction coupling used for a prior art cycloidal drive.

(4) FIG. 3 is a cross-sectional view of a speed changing apparatus of the present invention that schematically illustrates the off-axis power extraction stage thereof.

(5) FIG. 4 schematically illustrates a cross-sectional view of a speed changing apparatus of the present invention outlining the dimensional configuration of all members thereof.

(6) FIG. 4A schematically illustrates a cross-sectional view of a strain wave gearing speed changing apparatus of the present invention outlining the dimensional configuration of all members thereof.

(7) FIG. 4B schematically illustrates the double flex spline for the apparatus of FIG. 4A.

(8) FIG. 4C schematically illustrates the cross-sectional view of the speed changing apparatus of FIG. 4A taken along the 4C-4C line.

(9) FIG. 4D schematically illustrates the cross-sectional view of the speed changing apparatus of FIG. 4A taken along the 4D-4D line.

(10) FIGS. 5 and 6 schematically illustrate cross-sectional views of the speed changing apparatus of the present invention in different input- and output-member arrangements.

(11) FIG. 7 schematically illustrates a cross-sectional view of a speed changing apparatus of the present invention with a dimensional configuration for optimized speed-changing application.

(12) FIG. 8A schematically illustrates a cross-sectional view of another preferred embodiment of the strain wave gearing speed changing apparatus of the present invention outlining the dimensional configuration of all members thereof.

(13) FIG. 8B schematically illustrates the double flex spline for the apparatus of FIG. 8A having equal spline tooth engagement pitch circle circumference lengths.

(14) FIG. 8C schematically illustrates the cross-sectional view of the speed changing apparatus of FIG. 8A taken along the 8C-8C line.

(15) FIG. 8D schematically illustrates the cross-sectional view of the speed changing apparatus of FIG. 8A taken along the 8D-8D line.

(16) FIG. 9A schematically illustrates the cross-sectional view of another preferred embodiment of the speed changing apparatus of the present invention similar to FIG. 8C.

(17) FIG. 9B schematically illustrates the cross-sectional view of the preferred embodiment of the speed changing apparatus of the present invention for FIG. 9A similar to FIG. 8D.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

(18) FIG. 3 is a cross-sectional configuration of a speed changing apparatus of the present invention that schematically illustrates an equivalent arrangement of the off-axis power extraction stage thereof. With simultaneous reference also to FIGS. 1 and 2, instead of the plate 14 with multiple pin-rollers 18 that engages with their corresponding holes 17 formed in the cycloidal disc 13, a speed changing apparatus of the present invention has a different arrangement for power extraction.

(19) As is illustrated, while the planet gear 32 moves epicyclically inside the frame ring gear 31 as a first ring-spur gear pair, another planet gear 33 that is fixed coaxially with gear 32 also moves epicyclically inside its ring gear 34, a second pair of ring-spur gears. As the gear 33 spins and moves epicyclically inside gear 34, its outer most edge (of its pitch circle) 33P plots a trace 33T. This trace 33T is made to exactly coincide with the pitch circle of the ring gear 34. Essentially, ring gear 34 of the second pair, together with its meshing spur gear 33, serves a similar function as the off-axis power extraction means of a conventional cycloidal drive but allows the present inventive apparatus to produce a speed change ratio that is much larger, as is described hereinafter.

(20) FIG. 4 schematically illustrates in a cross-sectional view the configuration of a speed changing apparatus of the present invention outlining the dimensional configuration of all members thereof. The speed changing apparatus has a coaxial pair of ring gears that includes a large ring gear 41 having a pitch diameter A and a small ring gear 44 having a pitch diameter D. The apparatus also has a coaxial pair of spur gears that includes a large spur gear 42 having a pitch diameter B and a small spur gear 43 having a pitch diameter C. The large spur gear 42 meshes with the large ring gear 41 and the small spur gear 43 meshes with the small ring gear 44, forming two meshing pairs. A carrier member 45E is connected to the input shaft 45 of the speed changing apparatus. The carrier member 45E, essentially a twistedvery short armversion of that found in conventional planetary gear, is formed by combining the input shaft 45 (on the central axis 40 of the entire system) and the central shaft for the pair of gears 42 and 43 (on its own axis 49).

(21) Further, the two coaxial spur gears 42 and 43 are fixed together to each other to operate epicyclically on the carrier 45E. The large ring gear 41, in this depicted example of FIG. 4, is fixed to the frame of the apparatus serving as the reaction member of the system and the small ring gear 44 is connected to the output shaft 46.

(22) In this gear train system, the four gears 41, 42, 43 and 44 satisfy the dimensional relationship of A=K+i, B=K, C=Kj and D=K+ij wherein K is pitch diameter of the large spur gear 42, i is the difference of pitch diameters between the large ring gear 41 and large spur gear 42 (and also the difference of pitch diameters between the small ring gear 44 and small spur gear 43), and j is the difference of pitch diameters between the large ring gear 41 and small ring gear 44 (and also the difference of pitch diameters between the large spur gear 42 and small spur gear 43).

(23) The speed changing apparatus of FIG. 4 has the carrier 45E acting as the input, the small ring gear 44 as the output, and the large ring gear 41 the reaction member. Meanwhile, the two coaxial spur gears 42 and 43 that are fixed together move epicyclically in the system. The illustrated speed changing apparatus of FIG. 4 has a speed change ratio of K(K+ij)/ij. For a gear-based system with dimensions A, B, C and D pitch diameters that of 16T (teeth), 15T, 14T and 15T module 10 gears respectively, or, K=150 mm (15 cm), i=10 mm (1 cm) and j=10 mm (1 cm), the speed changing (reduction) ratio is 225. The apparatus can also be used for speed increasing by swapping the input and output assignment.

(24) By contrast, a conventional cycloidal drive (of FIG. 1) with A pitch diameter that of a 16T gear and B of 15T, the speed-changing ratio is 15. This means a speed changing apparatus of the present invention is able to achieve a ratio that is the square in numerical value that of a cycloidal drive with comparable tooth number.

(25) FIG. 4A schematically illustrates a cross-sectional view of a strain wave gearing speed changing apparatus of the present invention outlining the dimensional configuration of all members thereof. The strain wave gearing speed changing apparatus has a coaxial pair of circular splines that includes a large circular spline 141 having a tooth number T.sub.A and a small circular spline 144 having a tooth number T.sub.D. The apparatus also has a coaxial pair of flex splines that includes a large flex spline 142 having a tooth number T.sub.B and a small flex spline 143 having a tooth number T.sub.C. The large flex spline 142 meshes with the large circular spline 141 and the small flex spline 143 meshes with the small circular spline 144, forming two meshing pairs. A wave generator 145E is connected to the input shaft 145 of the speed changing apparatus. The wave generator 145E is formed by combining the input shaft 145 (on the central axis 140 of the entire system) and the central shaft for the pair of flex splines 142 and 143.

(26) Further, the two coaxial flex splines 142 and 143 are fixed together to each other to operate flexingly on the wave generator 145E. The large circular spline 141, in this depicted example of FIG. 4A, is fixed to the frame of the apparatus serving as the reaction member of the system and the small circular spline 144 is connected to the output shaft 146.

(27) In this spline-based gear train system, the four splines 141, 142, 143 and 144 satisfy the tooth number relationship of T.sub.A=T.sub.K+T.sub.i, T.sub.B=T.sub.K, T.sub.C=T.sub.KT.sub.j and T.sub.D=T.sub.K+T.sub.iT.sub.j wherein T.sub.K is tooth number of the large flex spline 142, i is the difference between tooth numbers of large circular spline 141 and large flex spline 142 (and also the difference between tooth numbers of small circular spline 144 and small flex spline 143), and T.sub.j is the difference between tooth numbers of large circular spline 141 and small circular spline 144 (and also the difference between tooth numbers of large flex spline 142 and small flex spline 143).

(28) The strain wave gearing speed changing apparatus of FIG. 4A may have the wave generator 145E acting as the input, the small circular spline 144 as the output, and the large circular spline 141 the reaction member. Meanwhile, the two coaxial flex splines 142 and 143 that are fixed together move flexingly in the system. The illustrated speed changing apparatus of FIG. 4A has a speed change ratio of T.sub.K(T.sub.K+T.sub.iT.sub.j)/T.sub.iT.sub.j. For such a spline-based system with a tooth number of T.sub.A=16T (teeth), T.sub.B=15T, T.sub.C=14T and T.sub.D=15T, or, T.sub.K=15, T.sub.i=1 and T.sub.j=1, the speed changingreductionratio is 225. Certainly the apparatus can also be used for speed increasing by swapping the input and output assignment.

(29) FIG. 4B schematically illustrates that the pair of flex splines 142 and 143 are fixed together to form a double flex spline component 148 for the speed changing apparatus of FIG. 4A. In a preferred embodiment of the strain wave gearing speed changing apparatus such as illustrated in FIG. 4A, component 148 can be made from one single piece of metallic tube. Two groups of spline teeth 142S and 143S are formed respectively on the exterior cylindrical surface of the flex splines 142 and 143. Note that only a few spline teeth are shown in the drawing although they will encircle the entire periphery of flex splines 142 and 143.

(30) FIG. 4C schematically illustrates the cross-sectional view of the speed changing apparatus of FIG. 4A taken along the 4C-4C line and FIG. 4D the cross-sectional view taken along the 4D-4D line.

(31) A speed changing apparatus of the present invention can be used in different configurations of input, output and reaction member assignments among its constituent gear and carrier members. Essentially, a general-purpose speed changing apparatus of the present inventionused either as a speed reducer or an increaser having either a fixed ring gear or a fixed spur gearcan be constructed to have a coaxial pair of ring gears that includes a large ring gear having a pitch diameter A and a small ring gear having a pitch diameter D. Such an apparatus also has a coaxial pair of spur gears that includes a large spur gear having a pitch diameter B and a small spur gear having a pitch diameter C. The large spur gear meshes with the large ring gear and the small spur gear meshes with the small ring gear, forming two meshing pairs. A carrier member is connected to one of the input and output shafts of the apparatus. Two gears of one of the two coaxial pairs are fixed together to operate epicyclically on the carrier. One gear of the other of the two coaxial pairs is fixed to the frame of the apparatus and the other gear is connected to the other of the input and output shafts. In such a system, the four gears satisfy the dimensional relationship of A=K+i, B=K, C=Kj and D=K+ij.

(32) FIGS. 5 and 6 schematically illustrate cross-sectional views of the speed changing apparatus of the present invention that are in different input- and output-member arrangements. The examples of FIGS. 5 and 6 show the construction of reducers with 200-plus speed reduction ratio using two ring-spur gear pairs of different module numbers. The first pair with large ring and spur gears includes an 80-tooth ring gear 51, 61 with a module number of 2 making a pitch diameter of 160 mm and a 75T, M2 spur gear 52, 62 with 150 mm pitch. The second pair of small ring and spur includes a 60T, M2.5 ring gear 54, 64 with 150 mm pitch and a 56T, M2.5 spur 53, 63 with 140 mm pitch. Thus, with the large spur gear fixed to the device frame 52F as the reaction member as is the configuration of FIG. 5, the speed changing apparatus delivers a reduction ratio of 224.

(33) The apparatus of FIG. 6, on the other hand, has a different configuration although using all the same gears as in FIG. 5, essentially the same gear role assignment as that described in FIG. 4with the large ring 61 fixed to device frame 61F as the reaction member.

(34) Note that the examples of FIGS. 5 and 6 have a dimensional configuration of K:i:j=15:1:1 (75TM2:(80TM275TM2):(80TM260TM2.5)=150 mm:10 mm:10 mm=15:1:1).

(35) In summary, a speed changing apparatus of the present invention outlined in FIG. 4 may have four different speed-changing setup configurations, as listed in Table 1. In Table 1, as well as 2 below, R, O and I in the Role row indicate, respectively, the reaction, the output and the input roles of the rotary elements of the inventive apparatus.

(36) TABLE-US-00001 Large Large Small Small Ring Spur Spur Ring Carrier Re- Gear Gear Gear Gear Member duction Element 41 42 43 44 45E Ratio Config- uration 1 Role R O I K(K + Motion Fixed Epicy- Epicy- Rotary Rotary i j)/ij Speed 0 clic clic ij/K(K + 1 i j) Config- uration 2 Role O R I (K Motion Rotary Epicy- Epicy- Fixed Rotary j)(K + Speed ij/ clic clic 0 1 i)/ij (K j) (K + i) Config- uration 3 Role R O I (K + Motion Epicy- Fixed Rotary Epicyclic Rotary i)(K Speed clic 0 ij/(K + 1 j)/ij i)(K j) Config- uration 4 Role O R I K(K + Motion Epicy- Rotary Fixed Epicyclic Rotary i j)/ij Speed clic ij/K(K + 0 1 i j)

(37) As is comprehensible for those skilled in the art, the speed-reducing configurations in Table 1 can be easily changed into speed-increasing simply by swapping the I and O role assignment of each.

(38) FIG. 7 schematically illustrates a cross-sectional view of a speed changing apparatus of the present invention that has a dimensional configuration optimized for speed-changing application in terms of weight and size, or power density. Under this special case, configurations in Table 1 become that listed in Table 2.

(39) TABLE-US-00002 Large Large Small Small Ring Spur Spur Ring Carrier Re- Gear Gear Gear Gear Member duction Element 71 72 73 74 75E Ratio Config- uration 1 Role R O I K.sup.2/i.sup.2 Motion Fixed Epicy- Epicy- Rotary Rotary Speed 0 clic clic i.sup.2/K.sup.2 1 Config- uration 2 Role O R I 1 Motion Rotary Epicy- Epicy- Fixed Rotary K.sup.2/i.sup.2 Speed i.sup.2/ clic clic 0 1 (K.sup.2 i.sup.2) Config- uration 3 Role R O I 1 Motion Epicy- Fixed Rotary Epicy- Rotary K.sup.2/i.sup.2 Speed clic 0 i.sup.2/(K.sup.2 clic 1 i.sup.2) Config- uration 4 Role O R I K.sup.2/i.sup.2 Motion Epicy- Rotary Fixed Epicy- Rotary Speed clic i.sup.2/K.sup.2 0 clic 1

(40) Speed reduction ratios listed in Tables 1 and 2 show that with gears having tooth numbers centered at a value of K (with i and j values reduced to 1), a speed reducer of a ratio of, at the optimized case, K.sup.2 can be constructed. This compares to the conventional cycloidal drive's reduction ratio of K.

(41) Note, as is comprehensible, that a spur gear meshed inside a ring gear usually must have a tooth number sufficiently smaller than that of the ring. For example, with the popular 20-degree pressure angle gears, a minimum of 8-tooth difference is necessary. One typical approach to avoid gear interference for small tooth number difference is to employ profile shifting for the gears. Alternatively, with larger gear pressure angle, smaller tooth number difference without gear interference is possible.

(42) Also, since the epicyclic elements of one coaxial pair of the speed-changing apparatus of the present invention is normally so large in size comparable to the other coaxial pair that only one pair is possible. A counterweight is therefore necessary in practical implementations of this inventive speed-changing apparatus, as is schematically illustrated as counterweight 65W in the embodiment depicted in FIG. 6. The counterweight is used to balance the mass of the epicyclic coaxial pair of gears opposite across the center axis of the apparatus.

(43) A speed changing apparatus of the present invention outlined in FIG. 4A may have, practically, two different speed-changing setup configurations, as listed in Table 3. In Table 3 and 4 below, again, R, O and I in the Role row indicate, respectively, the reaction, the output and the input roles of the rotary elements of the inventive apparatus. These correspond to Configurations 1 and 2 in Tables 1 and 2 above that describe the speed changing apparatus of the present invention based on conventional gearing, either involute or cycloidal gearing. Strain wave gearing implementations of the present invention taking structural configuration similar to Configurations 3 and 4 in Tables 1 and 2 are possible, but are believed to be less practical. In other words, Configurations 1 and 2 in Tables 3 and 4 are the better implementation of the speed changing apparatus of the present invention.

(44) TABLE-US-00003 Large Large Small Small Circular Flex Flex Circular Wave Spline Spline Spline Spline Generator Reduction Element 141 142 143 144 145E Ratio Config- uration 1 Role R O I T.sub.K(T.sub.K + Motion Fixed Flexing Flexing Rotary Rotary T.sub.i T.sub.j) Speed 0 T.sub.iT.sub.j 1 T.sub.K(T.sub.K + T.sub.iT.sub.j T.sub.i T.sub.j) Config- uration 2 Role O R I (T.sub.K Motion Rotary Flexing Flexing Fixed Rotary T.sub.j)(T.sub.K + T.sub.i) Speed T.sub.iT.sub.j 0 1 (T.sub.K T.sub.j) T.sub.iT.sub.j (T.sub.K + T.sub.i)

(45) The strain wave gearing-based speed-reducing configurations in Table 3 can be easily changed into speed-increasing simply by swapping the I and O role assignment of each.

(46) An optimized version of the apparatus of FIG. 4Athough not illustrated in the drawings but based on the same principle as that of the gearing version described in FIG. 7 as compared to FIG. 6may have a dimensional configuration optimized for speed-changing application in terms of weight and size, or power density. Under this special case, configurations in Table 3 become that in Table 4.

(47) TABLE-US-00004 Large Large Small Small Circular Flex Flex Circular Wave Spline Spline Spline Spline Generator Reduction Element 141 142 143 144 145E Ratio Config- uration 1 Role R O I T.sub.K.sup.2/T.sub.i.sup.2 Motion Fixed Flexing Flexing Rotary Rotary Speed 0 T.sub.i.sup.2/T.sub.K.sup.2 1 Config- uration 2 Role O R I 1 T.sub.K.sup.2/T.sub.i.sup.2 Motion Rotary Flexing Flexing Fixed Rotary Speed Ti.sup.2/(T.sub.K.sup.2 0 1 T.sub.i.sup.2)

(48) FIG. 8A schematically illustrates a cross-sectional view of another preferred embodiment of the strain wave gearing speed changing apparatus of the present invention outlining the dimensional configuration of all members thereof.

(49) Essentially similar to the case in the embodiment of FIG. 4A, the strain wave gearing speed changing apparatus depicted has a coaxial pair of circular splines that includes a first circular spline 181 having a tooth number T.sub.A and a second circular spline 184 having a tooth number T.sub.D. The apparatus also has a coaxial pair of flex splines that includes a first flex spline 182 having a tooth number T.sub.B and a second flex spline 183 having a tooth number T.sub.C. The first flex spline 182 meshes with the first circular spline 181 and the second flex spline 183 meshes with the second circular spline 184, forming two meshing pairs. A wave generator 185E is connected to the input shaft 185 of the speed changing apparatus. The wave generator 185E is formed by combining the input shaft 185 (on the central axis 180 of the entire system) and the effective central shaft for the pair of flex splines 182 and 183.

(50) Further, the two coaxial flex splines 182 and 183 are fixed together to each other to operate flexingly on the wave generator 185E. The first circular spline 181, in this depicted example of FIG. 8A, is fixed to the frame of the apparatus serving as the reaction member of the system and the second circular spline 184 is connected to the output shaft 186.

(51) In this spline-based gear train system, the four splines 181, 182, 183 and 184 satisfy the tooth number relationship of T.sub.A=T.sub.K+T.sub.i, T.sub.B=T.sub.K, T.sub.C=T.sub.KT.sub.j and T.sub.D=T.sub.K+T.sub.iT.sub.j wherein T.sub.K is tooth number of the first flex spline 182, T.sub.i is the difference between tooth numbers of first circular spline 181 and first flex spline 182 (and also the difference between tooth numbers of second circular spline 184 and second flex spline 183), and T.sub.j is the difference between tooth numbers of first circular spline 181 and second circular spline 184 (and also the difference between tooth numbers of first flex spline 182 and second flex spline 183).

(52) Compared to the conventional gearing implementations, dimensional configuration of the strain wave gearing implementation of the speed changing apparatus of the present invention, as described above, is required to satisfied a relationship among its four spline elements expressed in terms of spline tooth numbers. Pitch diameters are not used as in the case of the conventional gearing implementation because, while the two circular splines have definite pitch diameters, the two flex splines do nottheir mechanical force transmitting engagement circle flexes all the time when operating. Though, regardless of whether it is the convention gearing or strain wave gearing implementation, the dimensional discrepancy parameters, i and j in the case of conventional gearing and T.sub.i and T.sub.j for strain wave gearing, must be made as small as possible if large speed changing ratio is desired.

(53) The strain wave gearing speed changing apparatus of FIG. 8A may have the wave generator 185E acting as the input, the second circular spline 184 as the output, and the first circular spline 181 the reaction member. Meanwhile, the two coaxial flex splines 182 and 183 that are fixed together move flexingly in the system. The illustrated speed changing apparatus of FIG. 8A has a speed change ratio of T.sub.K(T.sub.K+T.sub.iT.sub.j)/T.sub.iT.sub.j. For such a spline-based system with a tooth number of T.sub.A=63T (teeth), T.sub.B=60T, T.sub.C=57T and T.sub.D=60T, or, T.sub.K=60, T.sub.i=3 and T.sub.j=3, the speed changingreductionratio is 400. Certainly the apparatus can also be used for speed increasing by swapping the input and output assignment.

(54) FIG. 8B schematically illustrates that the pair of flex splines 182 and 183 are fixed together to form a single component of double flex spline component 188 for the speed changing apparatus of FIG. 8A. In a preferred embodiment of the strain wave gearing speed changing apparatus such as illustrated in FIG. 8A, component 188 can be made from one single piece of metallic tube. Two groups of spline teeth 182S and 183S are formed respectively on the exterior cylindrical surface of the flex splines 182 and 183. Note that only a few spline teeth are shown in the drawing although they will encircle the entire periphery of flex splines 182 and 183.

(55) Also note that the double flex spline construction 188 of FIG. 8B made for the apparatus of FIG. 8A has equal spline tooth engagement pitch circle circumference lengths for its spines 182 and 183. This has the advantage of avoiding mechanical stress concentration between the two splines as they flex when operatingas in the case of the double spline construction of FIG. 4B. Such eased stress condition in the double spline component translates into improved device service life.

(56) Note that to allow the two flex splines to have equal spline tooth engagement pitch circle circumference length, their effective module, the equivalent to the module number for conventional gears, must be different from each other due to their different spline tooth numbers. This does not cause problem in practical implementations because splines are much easier to make than gears.

(57) FIG. 8C schematically illustrates the cross-sectional view of the speed changing apparatus of FIG. 8A taken along the 8C-8C line and FIG. 8D the cross-sectional view taken along the 8D-8D line. Note that when compared to the counter parts in FIGS. 4C and 4D, a total of three spline tooth meshings both between the circular and flexing spline pair 181 and 182 and between pair 184 and 183 increases the load capacity for the speed changing apparatus.

(58) As an example, take the exemplified 400-to-1 reduction ratio apparatus of FIG. 8A described above with a tooth number of T.sub.A=63T (teeth), T.sub.B=60T, T.sub.C=57T and T.sub.D=60T, or, T.sub.K=60, T.sub.i=3 and T.sub.j=3. There are 21 spline teeth of the first circular spline 181 between its meshing teeth identified in FIG. 8C at 1812a and 1812b and 20 spline teeth of the first flex spline 182 between the same two meshing teeth at 1812a and 1812b. This is possible as there is at least one tooth discrepancy between the two meshing points (1812a and 1812b) on the two engaging splines 181 and 182. The same situation goes between the meshing points 1812b and 1812c for the two splines and between 1812c and 1812a.

(59) For the second engagement pair shown in FIG. 8D, there are 20 spline teeth of the second circular spline 184 between its meshing teeth identified in FIG. 8D at 1834a and 1834b and 19 spline teeth of the second flex spline 183 between the same two meshing teeth at 1834a and 1834b. This is acceptable as there is one tooth discrepancy between the two meshing points (1834a and 1834b) on the two engaging splines 184 and 183. The same situation goes between the meshing points 1834b and 1834c for the two splines and between 1834c and 1834a.

(60) For this example the meshing distribution can be arranged in perfect symmetry that the rotary component, namely, the two flex splines 182 and 183 shaped by the wave generator 185E can be well balanced all the time as the system operates. There is no issue of center of mass.

(61) As another example, assume the apparatus of FIG. 8A has T.sub.A=63T, T.sub.B=59T, T.sub.C=57T and T.sub.D=61T, or, T.sub.K=63, T.sub.i=4 and T.sub.j=2. According to Table 3 above the system has a reduction ratio of 449.875. For meshing arrangement among the three meshing points, there can be 21 spline teeth of the first circular spline 181 between its meshing teeth identified in FIG. 8C at 1812a and 1812b and 20 spline teeth of the first flex spline 182 between the same two meshing teeth at 1812a and 1812b. This is possible as there is one tooth discrepancy between the two meshing points (1812a and 1812b) on the two engaging splines 181 and 182. The same situation goes between the meshing points 1812b and 1812c for the two splines. But between 1812c and 1812a, there are 21 spline teeth of the spline 181 but 19 teeth on spline 182, a discrepancy of 2 teeth.

(62) For the second engagement pair in FIG. 8D, there are 20 spline teeth of the second circular spline 184 between its meshing teeth identified in FIG. 8D at 1834a and 1834b and 19 spline teeth of the second flex spline 183 between the same two meshing teeth at 1834a and 1834b. There is one tooth discrepancy between the two meshing points (1834a and 1834b) on the two engaging splines 184 and 183. The same situation goes between the meshing points 1834b and 1834c for the two splines. But and between 1834c and 1834a, there are 21 spline teeth of the spline 184 but 19 teeth on spline 183, a discrepancy of 2 teeth.

(63) For this example the meshing distribution can not be arranged in perfect symmetry that the rotary component, namely, the two flex splines 182 and 183 shaped by the wave generator 185E can be well balanced all the time as the system operates. However, the center of mass of the wave generator can be easily corrected as the deviation is small.

(64) FIG. 9A schematically illustrates the cross-sectional view of another preferred embodiment of the speed changing apparatus of the present invention similar to FIG. 8C and FIG. 9B similar to FIG. 8D. The speed changing apparatus exemplified in FIGS. 9A and 9B has even more power capacity than that of FIGS. 8C and 8D because it has four meshings as compared to three.

(65) Note, however, that while more meshing points allow for increase capacity, yet if only one single meshing is used, the flexing of the flexing splines can, substantially, be avoided. In this extreme case of configuration, the service life of the speed changing apparatus can be optimized, with the sacrifice of power capacity of course.

(66) While the above is a full description of the specific embodiments, various modifications, alternative constructions and equivalents may be used. Therefore, the above description and illustrations should not be taken as limiting the scope of the present invention.