Differential planetary gearbox

Abstract

A torque transfer device has plural planets arranged for planetary rotation about one or more sun gears and within one or more ring gears. Each planet includes at least one planetary gear set comprising plural planetary gears connected to rotate together, but having a different diameter to form a differential gear system. To improve load sharing, the plural planetary gears of each planetary gear set may have a different helical angle, the plural planetary gear sets being axially movable with respect to one another. Alternatively or in addition, the planetary gears may be made flexible with respect to radial forces.

Claims

1. A torque transfer device, comprising: a plurality of planet assemblies, each planet assembly including a respective first set of planetary gears comprising plural planetary gears connected to rotate together and wherein the plural planetary gears of the first set of planetary gears each have an equal number of gear teeth, and a respective second set of planetary gears comprising plural planetary gears corresponding to and arranged axially symmetrically with respect to the first set of planetary gears such that the plural planetary gears of the first set of planetary gears and the plural planetary gears of the second set of planetary gears are connected to rotate together on a shared axis; at least one sun gear, the plurality of planet assemblies arranged for planetary rotation about the at least one sun gear; and at least one ring gear, the plurality of planet assemblies arranged for planetary rotation within the at least one ring gear; wherein a first output gear of the at least one sun gear or the at least one ring gear is arranged to mesh with a respective planetary gear of each first set of planetary gears, wherein a first reference gear of the at least one sun gear or the at least one ring gear is arranged to mesh with a respective planetary gear of each first set of planetary gears, and wherein a first input gear of the at least one sun gear or the at least one ring gear is arranged to mesh with a respective planetary gear of each first set of planetary gears.

2. The torque transfer device as defined in claim 1, wherein the first output gear is provided as a first sun gear of the at least one sun gear, wherein the first reference gear is provided as a second sun gear of the at least one sun gear, and wherein the first input gear is provided as a ring gear of the at least one ring gear.

3. The torque transfer device as defined in claim 1, wherein the first output gear is provided as a first ring gear of the at least one ring gear, wherein the first reference gear is provided as a second ring gear of the at least one ring gear, and wherein the first input gear is provided as a sun gear of the at least one sun gear.

4. The torque transfer device as defined in claim 1, wherein the first input gear is provided as a first sun gear of the at least one sun gear, wherein the first reference gear is provided as a second sun gear of the at least one sun gear, and wherein the first output gear is provided as a ring gear of the at least one ring gear.

5. The torque transfer device as defined in claim 1, wherein the first input gear is provided as a first ring gear of the at least one ring gear, wherein the first reference gear is provided as a second ring gear of the at least one ring gear, and wherein the first output gear is provided as a sun gear of the at least one sun gear.

6. The torque transfer device as defined in claim 1, wherein the first output gear is provided as a first sun gear of the at least one sun gear, wherein the first input gear is provided as a second sun gear of the at least one sun gear, and wherein the first reference gear is provided as a ring gear of the at least one ring gear.

7. The torque transfer device as defined in claim 1, wherein the first output gear is provided as a first ring gear of the at least one ring gear, wherein the first input gear is provided as a second ring gear of the at least one ring gear, and wherein the first output gear is provided as a sun gear of the at least one sun gear.

8. The torque transfer device as defined in claim 1, wherein the plural planetary gears each have a number of teeth on each part, and wherein each part has a different pitch diameter.

9. The torque transfer device as defined in claim 1, wherein a second output gear of the at least one sun gear or the at least one ring gear is arranged to mesh with a respective planetary gear of each second set of planetary gears, and wherein a second reference gear of the at least one sun gear or the at least one ring gear is arranged to mesh with a respective planetary gear of each second set of planetary gears.

10. The torque transfer device as defined in claim 9, wherein the first and second reference gears are connected via a positioning shim for adjusting a relative axial positioning of the first and second reference gears.

11. The torque transfer device as defined in claim 9, wherein the first and second output gears are connected via a shim for adjusting a relative axial positioning of the first and second output gears.

12. The torque transfer device as defined in claim 9, wherein the second output gear is the first output gear or the second reference gear is the first reference gear or both.

13. The torque transfer device as defined in claim 1, wherein the second set of planetary gears of each planet assembly has a gear tooth profile axially symmetric with respect to a gear tooth profile of the corresponding first set of planetary gears.

14. The torque transfer device as defined in claim 1, wherein the first set of planetary gears are mounted on double bearings that are each adjustable by one or more bearing shims to adjust pre-load of the bearings.

15. The torque transfer device as defined in claim 1, wherein the plurality of planet assemblies number at least three.

16. The torque transfer device as defined in claim 15, wherein the plurality of planet assemblies number from five to twenty.

17. The torque transfer device as defined in claim 1, wherein the at least one sun gear or the at least one ring gear is formed of a first material with a yield strength-to-stiffness ratio between 0.010 and 0.030.

18. The torque transfer device as defined in claim 1, wherein the first set of planetary gears, the at least one sun gear and the at least one ring gear each have one or both of a conical taper and a profile shift.

19. The torque transfer device as defined in claim 1, wherein the first reference gear and the first output gear are connected via bearings, and wherein the bearings are connected to at least one of the first reference gear and the first output gear via a shim.

20. The torque transfer device as defined in claim 1, wherein the first input gear is supported by the planet assemblies.

21. The torque transfer device as defined in claim 20, wherein the first input gear comprises a rotor of an electric motor.

Description

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS

(1) Embodiments will now be described with reference to the figures, in which like reference characters denote like elements, by way of example, and in which:

(2) FIG. 1 is a side cutaway view of an exemplary actuator including an electric motor and a differential gearbox that uses planets each having portions with different helix angles.

(3) FIG. 2 is a closeup side cutaway view of the actuator of FIG. 1.

(4) FIG. 3 is a side cutaway view of the actuator of FIG. 1.

(5) FIG. 4 is an isometric cutaway view of the actuator of FIG. 1.

(6) FIG. 5 is a front view of the actuator of FIG. 1.

(7) FIG. 6 is a side view of the actuator of FIG. 1.

(8) FIG. 7 is a rear view of the actuator of FIG. 1.

(9) FIG. 8 is an isometric view of the actuator of FIG. 1.

(10) FIG. 9 is an exploded view of the actuator of FIG. 1.

(11) FIG. 10 is an exploded view of the actuator of FIG. 1 without housing or input connector.

(12) FIG. 11 is an exploded view of a gearbox of the actuator of FIG. 1.

(13) FIG. 12 is a side cutaway view of the ring gears of the actuator of FIG. 1.

(14) FIG. 13 is an isometric view of the ring gears of the actuator of FIG. 1.

(15) FIG. 14 is an exploded view of a planet for the gearbox of the actuator of FIG. 1.

(16) FIG. 15 is a side section view of the planet of FIG. 14.

(17) FIG. 16 is a side view of the planet of FIG. 14.

(18) FIG. 17 is a side view of the planet of FIG. 14 showing prestressed forces.

(19) FIG. 18 is a side cutaway view of the exemplary actuator of FIG. 1 showing forces on a nominal planet.

(20) FIG. 19 is a side cutaway view of the exemplary actuator of FIG. 1 showing forces on a planet with one side small.

(21) FIG. 20 is a side cutaway view of the exemplary actuator of FIG. 1 showing forces on a planet with both sides small.

(22) FIG. 21 is a front view of the actuator of FIG. 1 with the front output and housing portions removed.

(23) FIG. 22 is an isometric view of the actuator of FIG. 1 with the front output and housing portions removed.

(24) FIG. 23 is an isometric view of the actuator of FIG. 1 with the front end springs of the planets also removed.

(25) FIG. 24 is a front view of the actuator of FIG. 1 with the front output and housing portions removed, also schematically showing planet positioning changes.

(26) FIG. 25 is an isometric view of a planet for the actuator of FIG. 1 having aligned teeth.

(27) FIG. 26 is an isometric view of a planet for the actuator of FIG. 1 having offset teeth.

(28) FIG. 27 is an isometric cutaway view of an exemplary gearbox.

(29) FIG. 28 is a front view of the gearbox of FIG. 27.

(30) FIG. 29 is a side view of the gearbox of FIG. 27.

(31) FIG. 30 is a rear view of the gearbox of FIG. 27.

(32) FIG. 31 is an isometric view of the gearbox of FIG. 27.

(33) FIG. 32 is a rear view of the gearbox of FIG. 27 with the stationary ring gears and portions of the housing removed.

(34) FIG. 33 is an exploded view of the gearbox of FIG. 27.

(35) FIG. 34 is a side cutaway view of a portion of the gearbox of FIG. 27 including a planet gear.

(36) FIG. 35 is a side cutaway view of the gearbox of FIG. 27.

(37) FIG. 36 is a side cutaway view of the gearbox if FIG. 27 with the planets removed.

(38) FIG. 37 is an isometric cutaway view of the gearbox of FIG. 27.

(39) FIG. 38 is a side view of an exemplary planet for the gearbox of FIG. 27.

(40) FIG. 39 is an isometric view of a planet for the gearbox of FIG. 27, formed as one piece of injection molded plastic.

(41) FIG. 40-42 are isometric views of additional embodiments of planets suitable for the gearbox of FIG. 27.

(42) FIG. 43 is an isometric view of a planet with axial slots and no tube.

(43) FIG. 44 is a cutaway isometric view of the planet of FIG. 43.

(44) FIG. 45 is an isometric view of a planet with axial slots and a central tube.

(45) FIG. 46 is a cutaway isometric view of the planet of FIG. 45.

(46) FIG. 47 is a cutaway view of the gearbox of FIG. 27 showing axial forces on a planet.

(47) FIG. 48 is an isometric cutaway view of a planet in the gearbox of FIG. 27 showing load paths on the planet.

(48) FIG. 49 is a schematic illustration of a gearbox showing outer gear deformation.

(49) FIG. 50 is a schematic illustration of a gearbox showing sun gear deformation.

(50) FIG. 51 is a schematic illustration of a gearbox showing planet gear deformation.

(51) FIG. 52 is a bar chart showing material strength to stiffness to density ratio for selected materials.

(52) FIG. 53 is a bar chart showing material strength to stiffness ratio for selected materials.

(53) FIG. 54 is a cutaway isometric view of another exemplary gearbox.

(54) FIG. 55 is an isometric view of the gearbox of FIG. 54.

(55) FIG. 56 is an axial end view of the gearbox of FIG. 54.

(56) FIG. 57 is an isometric view of an exemplary planet for the gearbox of FIG. 54.

(57) FIG. 58 is another isometric view of the planet of FIG. 57.

(58) FIG. 59 is an axial end view of the planet of FIG. 57.

(59) FIG. 60 is a side cutaway view of another exemplary embodiment of an actuator.

(60) FIG. 61 is an isometric cutaway view of the actuator of FIG. 60.

(61) FIG. 62 is an isometric cutaway view of the actuator of FIG. 60 without motor input components.

(62) FIG. 63 is a top isometric view of upper motor components for the actuator of FIG. 60.

(63) FIG. 64 is a bottom isometric view of upper motor components for the actuator of FIG. 60.

(64) FIG. 65 is a cutaway isometric view of an upper portion of the actuator of FIG. 60 showing airflow paths.

(65) FIG. 66 is an isometric view of an exemplary planet for the actuator of FIG. 60 with continuous features to ease injection molding.

(66) FIG. 67 is an exploded view of an upper half of the actuator of FIG. 60.

(67) FIG. 68 is a side section view of another exemplary planet for the actuator of FIG. 60.

(68) FIG. 69 is a side section view of an expandable sun ring interfacing with the planet of FIG. 68.

(69) FIG. 70 is a side section view of an adjustable sun ring interfacing with a planet to provide a safety brake.

(70) FIGS. 71-78 are side section views of different configurations of gearboxes suitable to act as bearings.

(71) FIG. 79 is an axial end view of another exemplary gearbox.

(72) FIG. 80 is an isometric cutaway view of the gearbox of FIG. 79 showing gearsets.

(73) FIG. 81 is a side view of two planets contacting a sun gear, out of phase.

(74) FIG. 82 shows a view of a gear tooth with a profile shift.

DETAILED DESCRIPTION

(75) Immaterial modifications may be made to the embodiments described here without departing from what is covered by the claims.

(76) Embodiments of the device allow load sharing through the use of one or more strategies as described below. Other benefits of some embodiments may include reducing or preventing backlash, and maintaining appropriate axial and circumferential location of planets without the use of a planet carrier.

(77) One strategy is to use planets that have different portions with different helix angles. In this strategy, an input, output and reference gear may each contact the planets. The different gears contacting the planets may collectively be referred to as i/o gears. For a speed reducer, typically the input will be on one side of the planets (e.g., a sun gear) and the output and reference on the other (e.g., ring gears). In this document, a “sun gear” refers to any gear with a radial outer surface meshing with planet gears, and a “ring gear” refers to any gear with a radially inner surface meshing with planet gears. A “sun ring” is a ring-shaped sun gear, not a ring gear by this definition. The two of the input, output or reference gears on one side, in this strategy, have different helix angles, meshing with corresponding helix angles of the planet gears. This allows load balancing through axial shifting of the planet gears. To keep overall axial alignment, two axially symmetric sets of gears may be provided, with the planet gears of the two sets combined into single planets with halves connected by axial springs. The axial inner ring and/or sun gears of the two sets may also be combined. Embodiments using this strategy are further described in the section below entitled “DIFFERENTIAL HELIX ANGLE WITH AXIAL SPRING LOCATION.”

(78) Another strategy is to use flexible gears. Gears may be made with the use of a flexible material such as plastic. A surprising benefit is found from plastic which might conventionally be expected to have lower torque to weight than steel. Embodiments using flexible materials are further described in the section below entitled “PLASTIC GEARS.”

(79) Flexibility depends not only on the material choice but also on the shape of the gears.

(80) Also described in this document are further applications of the strategies summarized here. The section entitled “EXAMPLE PLANET DRIVEN ACTUATOR” provides an additional example of an actuator comprising an electric motor combined with a speed reducing gearbox.

(81) Additional features are also disclosed that may be combined with embodiments of one or more of the strategies described.

(82) The section entitled “PLANETARY BEARING” describes how a planetary gearbox may also act as a bearing, for example for a motor.

(83) The section entitled “OUT OF PHASE GEARS” describes how different planets may mesh with the ring gears at two or more tooth mesh positions at any given moment to reduce noise and vibration.

(84) Differential Helix Angle with Axial Spring Location

(85) In an embodiment, an electric motor is housed within the gearbox enclosure.

(86) FIGS. 1-24 show an exemplary cylindrical actuator including an electric motor and a differential gearbox that uses planets each having portions with different helix angles and elastic elements which bias the pinion portions to a preferred but movable axial position. This allows consistent enough load sharing between pinions to take advantage of a large number of smaller pinions. A simplified electric motor stator and rotor is shown inside the housing. An internal electric motor allows the two outer ring gears 10, 10 to be attached to housing members 12A, 12B connected through an annular housing portion 12C defining the center bore so the ring gears 10, 10 are held from relative rotation to each other. Housing members 12A, 12B and 12C comprise portions of housing 12.

(87) A side section view of the exemplary embodiment is shown in FIG. 1. FIGS. 1-3 show cutaway views of this exemplary embodiment and FIGS. 5-8 show views of the outside of the actuator.

(88) The motor in this embodiment is configured with an inner stator 22 and outer rotor 13, with the rotor supported by stacked bearing assemblies 46 and 48. Bearing assembly 46, as shown here and further described below, comprises a ring 18 that links two sets of bearings 17 and 19.

(89) The outer rotor drives a connecting plate 15, which drives the sun gears 14 through a spline fit. Note that instead of using a connecting plate 15, it would also be possible to integrate the rotor 13 into the sun gears 14. This would enable a more axially compact actuator albeit with a smaller center hole.

(90) The sun gears drive the planets 23 with central straight spur gear teeth. A small amount of backlash is introduced to this interface via a tooth offset in order to ensure proper meshing. In the embodiment shown there are 18 planets.

(91) The planets do not require a carrier as would be found in many planetary gear configurations. Instead, they mesh with an axially outer ring gear 10 on the outer helical teeth. Axial location of the planet gears is also provided within tolerances by the load balancing mechanism described below. Because the axially outer ring gear is stationary, the planets orbit the sun input as the input rotates. The central spur gear teeth on the planets then mesh with the center ring gears 11. The pitch diameter of the center spur teeth on the planets is different than the pitch diameter of the helical teeth on the planets, causing a differential output between the center and axially outer ring gears. The output from the center ring gears 11 then connects to a connecting tube 16 with a spline fit and contains a bolt group for fastening to other parts of the mechanism.

(92) Also shown in FIG. 1 are a heat sink 20 and holes 21 in the housing 12, further described below. FIG. 2 shows a closeup cutaway view of the gears and connecting plate 15 only. Also visible in FIG. 2 is a central spring 7 connecting two halves A and B of the geared portions of a planet 23, the halves moveably mounted on a tube 6, and outer springs 9 connecting the halves to stops 8 mounted on the tube 6. The function of these parts of the planet 23 is further described below in relation to FIGS. 14-20.

(93) FIG. 3 shows the actuator of FIG. 1 with the motor and planets omitted for clarity. FIG. 4 shows an isometric cutaway view of the actuator of FIG. 1.

(94) FIGS. 5-8 show external views of the actuator of FIG. 1. FIG. 5 shows a front view of the actuator of FIG. 1. FIG. 6 shows a side view. An outer portion corresponding to one of the axially outer ring gears 10 is visible, but the axially outer ring gears 10 in this embodiment are fixed to the housing 12 and could alternatively both be enclosed in the housing. FIG. 7 shows a rear view. 8 shows a front isometric view.

(95) FIGS. 9-11 show exploded views of the actuator of FIG. 1. The actuator may be connected to an external structure through the housing 12, for example at a first end 38 of the actuator, and may be connected to driven items through output connector 16, for example at a second end 40 of the actuator. The gearbox 42 and motor 44 each take up respective annular portions of the actuator in this embodiment.

(96) FIG. 10 shows the actuator without the housing or output connector. Bearing assemblies 46 and 48 are seen, which when the actuator is assembled connect both sides of rotor 13 to the heatsink 20.

(97) FIG. 11 shows an exploded view of the gearbox. As can be seen, the axially inner sun gears 14 in this embodiment are formed as a single piece, and the axially inner ring gears 11 are formed as a single piece.

(98) FIG. 12 is a side cutaway view and FIG. 13 is an isometric view of the ring gears 10 and 11 of the actuator of FIG. 1, better showing the patterns of the teeth of these gears.

(99) FIGS. 14-16 are closeup views of planet gears 23 of the actuator of FIG. 1, showing a load balancing mechanism.

(100) FIG. 14 is an exploded view of a planet 23, FIG. 15 is a side section view, and FIG. 16 is a side view. As shown in these views, an axially inner and an outer planet gear 1, 2 are manufactured to act as one piece (gearset A) with symmetric axially inner/outer gears 3, 4 comprising gearset B. Both gearsets A and B are held in coaxial alignment by a center tube or rod 6. The term “rod” may encompass the term “tube.” The fit between the gearsets A and B and the rod 6 is such that axial and rotational movement of the gearsets A, B on the tube 6 is possible. A center spring 7 between the gearsets A, B, and an outside spring 9 between the gearsets A, B and the retaining rings 8 at the ends of the shaft 6 allow axial motion of the gearsets A, B on the tube 6, and also rotational motion of gearset A relative to the other symmetric set B. The inner and outer gears on each set A and B are created with different helical angles (In this example, a helical angle of zero is used for the inner gear 1 but any helical angle can be used as long as the axially inner and outer gears have different angles. The gears having the same magnitude of helix angle with different handedness also provides a difference of helix angle. This helical angle difference must also compensate for the different diameter of the inner and outer gears such that axial movement of the gearset results in the loading of the inner gear teeth on the inner gear ring in the opposite direction of the outer gear teeth on the outer gear ring). As a result, any axial movement of a gearset A will cause the whole gearset A to rotate due to the larger helical gear angle on one of the gears 2 as it meshes with the helical gear teeth on the reference ring gear 10 which is fixed to the housing 12. We will refer to a stationary output ring gear 11 in this description for simplicity of explanation) The rotation of the gearset A during axial movement of gearset A will cause the axially inner spur gears 1 to rotate relative to the axially inner (output) ring gear 11 spur gears (FIG. A6) until the spur gears on gear 1 are contacting and transmitting torque to the axially inner (output) ring gear 11.

(101) The relative forces on and movements of the components of the planets 23 in this embodiment are illustrated in FIGS. 17-20. The center spring 7 may exert a force 24 and the end springs 9 may exert forces 26 and 28. Optionally, as shown in FIG. 17, the springs may be prestressed so that in the absence of the external forces, all of these spring forces are non-zero. This can enable all springs to remain in compression as the forces change, as may be useful for springs using Belleville and wave washers as shown. For other designs, it could be useful for the springs to be and remain in tension.

(102) An arrow 78 in FIGS. 18-20 indicates direction of motion of the teeth of the planet.

(103) Axial movement of the gearset A (or B) is caused by the opposing torque that is transferred through the pinions when the reference ring gear 10 experiences a resisting torque during operation (operation referring to the torque that is applied by the electric motor rotor 13 to the axially inner (input) sun gears 14 through the sun gear flange 15. This torque applied to the gearset A will result in a torque being transferred through the outer helical gear 2 to the outer helical ring gear 10. In other embodiments other ring or sun gears could mesh with and transfer torque through the helical gears. The torque applied through this helical gear mesh will result in an axial force 30 on the gearset A as shown in FIG. 18. This axial force is similar to a nut applying axial force to a threaded bolt. This axial force 30 results in an axial displacement 32 of the gearset A that is opposed by one or more of the springs. When the axial force of the spring (e.g., the force 24 exerted by center spring 7) equals the axial force experienced by the gearset A as a result of torque transfer on the helical gear mesh 2, the gearset A reaches an equilibrium where axial motion ceases. Due to the spring rate of the springs 7, 9 (which may be, for example, Belleville washers and wave washers as shown here), each gearset A, B on each of the planets 23 will find its own equilibrium where the axial position and resulting relative rotation results in all of the gearsets in the planet (A and B on each of the multiple planets 23) transmitting a more consistent load than if all the gearsets A were one piece with the symmetric gearsets B. This allows the use of more than 3 pinons with relatively consistent load sharing between all of the pinions. Corresponding forces and displacements are also shown for gearset B in FIG. 18. FIG. 18 shows forces and displacements in default conditions with good contact.

(104) FIG. 19 shows forces and displacements if one side is small. Helical gear 3 is small and does not initially experience an axial force from the corresponding gear 10. The forces and displacements on gearset A are initially the same as those shown in FIG. 18. The displacement of gearset A increases the center spring force 24 which forces gearset B to displace in motion 34. This will force gear 4 into contact with corresponding gear 10 to share some of the load.

(105) FIG. 20 shows the case of both gearsets A and B being small. Neither helical gears 2 or 4 would experience an axial force from the corresponding gears 10 if the gears are in the positions of FIG. 18. Compared with the situation in FIG. 18, the center spring force 24 is less opposed by other axial forces and displaces both gearsets outwards as shown by arrows 36 to contact the corresponding gears 10 and share some of the load.

(106) In this embodiment, torque on the helical gears and corresponding gears in one rotational direction will result in the pinion gearsets A, B on each pinion assembly to move inward (toward each other) compressing wave spring 7, which exerts a corresponding outward force 24. When torque is reversed, the gearsets A, B on each planet 23 will move in the opposite axial direction, compressing the end springs 9.

(107) Including both gearsets A and B allows balancing of axial forces so that the planetary gears do not axially shift out of alignment with the sun and ring gears. The gear system could also work with only one of gearsets A and B, so long as the axial forces were balanced in another way, such as for example by mounting the rod 6 on a planet carrier so that one end spring 9 could transmit a net axial force from the planet carrier to the planetary gears to balance the axial force on the gears. The symmetric gearsets A and B also prevent twisting of the planet assemblies by balancing the loading of the planets from end to end.

(108) FIGS. 21-24 show the actuator of FIG. 1 with the front output and housing portions removed. FIG. 21 is a front view, and FIG. 22 is an isometric view. FIG. 23 is an isometric view with the front end springs of the planets also removed. FIG. 24 schematically shows planet positioning changes 50 for load sharing. Because all the gears mesh with the input and output gears, which in the embodiment shown are straight, these relative positioning changes 50 are smaller than shown, but the small positioning changes help share the load.

(109) As shown in FIGS. 25-26, the teeth of the gears 1 and 2, and those of gears 3 and 4, can be aligned (as shown in FIG. 25) or offset (as shown in FIG. 26). As described further below, for some manufacturing techniques it may be easier to produce gearsets with aligned teeth.

(110) Double Bearing: One of the challenges in selecting bearings for large diameter applications is that the maximum rated rotation speed is often limited due to inconsistencies in the bearing tolerances. In order to use off-the-shelf bearings, but allow for higher rotational speeds, multiple bearings may be stacked concentrically as shown in FIG. 1. Each bearing would then see a significantly reduced rotation speed.

(111) With each bearing maintaining rolling contact, n bearings would each see 1/n of the rotation speed.

(112) This premise consists of two or more concentric bearings with axial constraint appropriate for the loads applied in that application. One embodiment, shown in FIG. 1 consists of a pair of concentric bearings 17 and 19, with a supporting ring 18 between them. This ring allows for a precise fit to each of the bearings, while retaining the bearing in the loaded direction. Axial force can then be transmitted from the rotating end, through the outer bearing, through the retaining ring, through the inner bearing, and on to the internal shaft.

(113) Aluminum Heat Sink: Because of the fact that the gearbox makes use of stationary ring gears on either side of the assembly, the motor, in embodiments of the device, is contained within the structure 12 connecting the stationary (reference) ring gears 10. This poses a potential problem with heat dissipation within this structure. In certain applications, the surrounding structure may be constructed of a poor heat conducting material. Heat generated by a motor would then have a highly resistant heat flow path out of the enclosure. By making use of an aluminum (or other highly heat conductive material) heat sink 20 as shown in FIG. 1, the heat generated by a motor has a significant sink to collect in, ensuring that the stator does not overheat from periodic and short temperature spikes, In FIG. 1, the heat sink is exposed to the external support structure through holes 21 in the enclosure, allowing heat energy to be efficiently dissipated by contact with another heat conducting body in the structure, or by convection cooling, without the heat needing to pass through the enclosure material directly.

(114) Other arrangements of the input, output and reference could also be used. In general, for the gear system to act as a large ratio gear reducer (amplifying torque), as in the embodiment shown in the figures, the output and reference should be both radially inner or radially outer with respect to the planet arrangement, and the input should be the opposite, connected to either of the gears the output or reference is connected to, or, in principle, to still another gear. For the system to act as a large ratio gear increaser (reducing torque), the input and reference should be both radially inner or radially outer with respect to the planet arrangement, and the output should be the opposite, connected to either of the gears the input or reference is connected to, or, in principle, to still another gear. For the system to act as a small ratio gear increaser or reducer, the input and the output should be both radially inner or radially outer with respect to the planet arrangement, and the reference should be the opposite, connected to either of the gears the input or output is connected to, or, in principle, to still another gear.

(115) Where a planet gear connected to one of the input, output or reference in one of the radially inward or outward directions, but not connected to any of those in the other of the radially inward or outward directions, a floating gear can be added if desired.

(116) In an embodiment, a high torque LiveDrive™ electric motor may be used, such as disclosed in U.S. Pat. No. 9,755,463, the content of which is hereby incorporated by reference in its entirety.

(117) Differential gearboxes are typically lower efficiency because the full output torque is also meshing at high speed resulting in a high percentage of work required to overcome this friction. But with the higher motor torque at lower speed of the LiveDrive™ a significantly lower gear ratio can be used, thus increasing efficiency. With 18 planets and a mechanism to ensure proper load sharing, the contact ratio is 6× that of a traditional planetary gearbox, thus increasing torque capabilities significantly. The low-ratio allows the input rotor to run slower for a given output speed. This allows for the use of low-profile bearings, which when radially stacked as described above, results in lower total bearing weight. Low maintenance: Very few moving parts. Frequency of maintenance activities and overall downtime are expected to be reduced.

(118) The actuator may be used for high torque applications where a hydraulic actuator might otherwise be used. Advantages over hydraulics include the following. Highly reliable: damage to one power line does not affect multiple actuators. Higher MTBF with electrical actuation. Easy to monitor: only the actuator needs monitoring. Controllability: highly responsive and precise due to low-ratio gear-reduction. Electric actuation allows more sophisticated control algorithms. Environmentally safe: no possibility of leakage or dangerous emissions.

(119) Plastic Gears

(120) The use of plastic gears in a planetary gear box is generally expected to provide lower torque and lower torque to weight than a steel gearbox of the same size and geometry. In one simple example, a conventional steel planetary gearbox using high strength steel for all the gears and housing and using three large planets would provide approximately three times the torque-to-weight of the same gearbox made from carbon reinforced PEEK (which is a very strong injection moldable plastic).

(121) When configured as shown here, the use of plastic gears is believed to have the potential of providing a surprising result, which is to approach or even exceed the torque to weight of an equivalent construction gearbox made from high strength steel.

(122) FIGS. 27-37 show a non-limiting example of this construction. As shown in FIG. 27, an array of 12 planets 123 are constructed to drive an output ring gear 111 relative to stationary ring gears 110 with a 15:1 differential ratio when driven with a sun gear 114. Note that for clarity, the frame of reference describing the gears is relative to the axial direction of the gearbox, with the center gear teeth closer to the axial center of the gearbox and the outer gear teeth further from the axial center of the gearbox as labeled in FIG. 27. The sun gear 114 has teeth 154 that can be designed to mesh with either the center planet gear teeth 101 (which are preferably larger in pitch diameter) or the outer planet gear teeth 102 (which are preferably smaller pitch diameter). A motor rotor (not shown) may be positioned on the ID of the sun gear 114. In the embodiment shown, the sun gear has an exposed grooved portion 156 that is designed for input by hand as a demonstration. In another embodiment, the grooves could be replaced by gear teeth so that the grooved portion 156 may mesh with an input gear (not shown). If the input gear is smaller than the sun gear 114 at the exposed gear portion 156 a further gear reduction may be obtained. A direct input could be provided here with limited range of motion, or alternatively, the housing 112 could be enlarged such that it surrounds a motor, which allows for continuous input.

(123) The sun gear 114 is supported in this embodiment from the housing 112 by a bearing 158 on a bearing sleeve 160.

(124) The center planet gear teeth mesh with the center ring gears 111 which in an embodiment are the output of the gearbox. The outer gear teeth 102 on the planets mesh with the two outer ring gears 110 which, in this exemplary embodiment, are attached to ground via housing 112. Ball bearings 117 may support the output ring 111 for rotation relative to the stationary rings 110. A bearing retaining ring 152 in this embodiment is attached to the output.

(125) Rotation of the sun gear 114 causes the planets 123 to rotate and to orbit around the ID of the ring gears 110 and 111. As a result of the different ratios between the inner planets and the inner ring gear 111, and the outer planet gears and the outer ring gear 110, a differential reduction is provided which, in this case, equals approximately 15:1 with the following gear tooth numbers:

(126) TABLE-US-00001 TABLE 1 Gear Number of Teeth Pitch Diameter (mm) Sun gear 84 82.63 Inner ring gear (Output) 132 129.85 Outer ring gear 144 127.5 (Stationary) Inner planet gear 24 23.61 Outer planet gear 24 21.25

(127) FIGS. 28-32 show further views of the gearbox of FIG. 27. FIG. 28 is a front view, FIG. 29 is a side view, and FIG. 30 is a rear view. As shown in FIG. 30, the housing 112 may have static mounting features/keyways 162 on an inner diameter of housing 112 to better enable the gearbox to be mounted to another object. FIG. 31 is an isometric view. FIG. 32 is a rear view with the stationary ring gears, and portions of the housing that would obscure the planet gears 123, removed.

(128) FIG. 33 is an exploded view of the gearbox of FIG. 27. As seen in FIG. 33, an inner shim 164 allows axial adjustment of the bearing sleeve relative to the housing 112, thus allowing axial adjustment of the sun gear 114, and an outer shim 166 separates the two output gears 111 from each other, allowing axial adjustment of the output gears 111. Uses of such axial adjustments are described further below in relation to FIGS. 54-56. FIG. 33 also shows the teeth 174 of the output gears 111 and the teeth 176 of the stationary gears 110.

(129) FIG. 34 shows a side cutaway view of a portion of the gearbox of FIG. 27 including a planet gear 123. FIG. 35 shows a side cutaway view of the whole gearbox of FIG. 27. FIG. 36 shows a side cutaway view with the planets removed. This allows the teeth 174 of the output gears to be seen. FIG. 37 shows an isometric cutaway view.

(130) In embodiments of the device, at least one outer planet gear on each planet gear assembly must be rotationally fixed to an inner planet gear so torque can be transmitted from a fixed ring gear to the inner ring gear output. The inner planet gear on each planet may be a single gear such as a spur gear or two symmetrical helical gears as shown in FIG. 38. Note that, in flexibility-based embodiments, it is not necessary for the inner planet gear teeth 101 and outer planet gear teeth 102 to have different helical angles. FIG. 39 shows a preferred configuration of a plastic planet gear for this exemplary device made of plastic where the outer planet gear teeth and inner planet gear teeth are made of one piece of injection molded plastic. A continuous tooth profile fill 168 connects the inner teeth 101 to the outer teeth 102. The helix angle on the inner and outer is similar or the same which allows the gears to be pulled out of a two part mold. One half of the mold comprising the negative of the clockwise helix teeth and the other half of the mold comprising the negative of the counter clockwise helix teeth.

(131) In a preferred embodiment, the number of teeth on the inner planet gears and outer planet gears is the same to allow the part to be removed from the mold, or to allow gear tooth cutters to shape the teeth without interference with either the inner or outer teeth.

(132) Load sharing in this embodiment is accomplished with plastic gears (and possibly a plastic housing) as follows:

(133) The use of steel gears in this exemplary embodiment can be used but are problematic because steel gears are very rigid and are subject to variations in manufacturing tolerances, especially in a low cost actuator. As a result, only 3-5 of the 12 planet gears would be expected to transmit a higher percentage of the torque if the gearbox is made of steel.

(134) By using plastic for the one or two or all of the planet gears and/or the ring gears, and/or the sun gears (and possibly the housings) a more flexible assembly is created. As an example, carbon fiber PEEK may have a tensile modulus of 3200 ksi (22 gpa) while a high strength steel such as maraging steel would have a tensile modulus of 27600 ksi (190 gpa). Maraging steel is stronger than carbon fiber PEEK. In a conventional planetary gearbox with three large planets per stage, this would give a steel gearbox greater torque-to-weight compared to a carbon fiber PEEK gearbox of the same design. In the embodiments shown, plastic planet gears are used. However, it would also be possible to use plastic ring and/or sun gears in combination with metal planets. This would have performance and wear life benefits, and would still provide adequate load sharing, for example via the shape changes shown in FIGS. 49 and 50, if the consistency of the metal parts is high.

(135) As the number of planets is increased, however, the load sharing of a steel gearbox, with its high tensile modulus (high stiffness) will result in a reduction in the load sharing consistency (as a result of slight variations in the manufacturing tolerances). By contrast, a carbon fiber PEEK gearbox may have approximately 6× lower stiffness from the components which allows the teeth to flex much more than the steel gears. This flexibility would, in a conventional three-pinion-per-stage planetary gearbox, result in 6X the flexibility for a given size, and as much as an estimated 5× the flexibility for the same torque-to-weight. This would be seen as a detrimental combination of effects and would steer a designer away from using plastic gears in a gearbox where high torque is required from a given size or given weight.

(136) Proposed here is a way to provide torque-to-weight and torque to size from a plastic gearbox that is higher than would be expected, by combining plastic gears of a certain range of stiffness-to-strength with a gearbox design having a high number of planets such as disclosed here.

(137) The stiffness of steel or other metal, is ordinarily seen as a benefit in terms of creating a gearbox with high stiffness but in a device like embodiments shown here with many pinions, the stiffness of the steel gears can actually be a detriment because it can reduce the consistency of load sharing.

(138) The higher flexibility of plastic is believed to be beneficial to the torque to weight of embodiments of the present device because at a certain number of pinions, the high stiffness of the steel gears becomes detrimental to load sharing while the flexibility of the plastic gears allows load sharing to be more consistent above this number of pinions. The result is believed to be a range of high pinion number gearbox geometry that provides better performance in certain regards such as torque to weight when the geometry of embodiments of the device are combined with the use of plastic gears rather than steel gears, or even a combination of steel and plastic such as but not limited to steel pinons and plastic ring gears and sun gears.

(139) Above some number of pinions and below a certain strength to stiffness ratio (more flexible is better for load sharing), the increased load sharing which results from the flexibility of the plastic (or mechanical torsion flex member between the inner and outer pinion gears (which also applies to metal gears) it will be possible to achieve higher torque with a weaker material. The looser the manufacturing tolerances in the construction of the gears, the more variability in the gears and the more benefit will be obtained from torsional flexibility of the pinions.

(140) The result is the potential for a very low cost gearbox by virtue of making all or part of it injection moldable combined with much better performance in terms of torque to weight than would be expected from a plastic gearbox and possibly even similar or better torque to weight than a steel gearbox of the same design made with reasonable manufacturing tolerances.

(141) As shown in FIG. 40, another embodiment of a pinion, suitable for use in a gearbox of the embodiment of FIG. 27, has outer and inner gears which are all one piece and made of plastic (although other materials can be used with various effects). An optional cylindrical section 170 is located between the inner and outer gears 101 and 102 (and possibly between the two inner gears as shown in FIG. 41). A steel or aluminum or other material (such as possibly a thick walled plastic or thin-walled metal) bar or tube 106 provides bending stiffness so lengthwise bending of the pinion is reduced during torque transmission. The plastic gear is created with an ID that is slightly larger than the OD of the tube or bar such that the plastic gear is able to rotate freely on the tube 106. The plastic gear may be bounded axially on the tube 106 by stops 108, for example lips as shown here. The tube can also be omitted as shown in FIG. 42. The optional cylindrical sections between the inner and outer gears is thin enough that the opposing torque direction on the inner and outer gears of a pinion will result in a small amount of torsional twist of the cylindrical sections. This torsional stiffness can be decreased by increasing the length of the cylindrical sections or by decreasing the thickness of these cylindrical sections and/or by creating slots 172 in the cylindrical sections. The slots may be for example axial or helical. FIGS. 43 and 44 show a version with axial slots 172, with no inner tube, and FIGS. 45 and 46 show a version with axial slots 172 and an inner tube 106. Decreasing the torsional stiffness of the cylindrical sections is considered to be beneficial in this design because the twisting of cylinder sections allows the inner and outer gears on the pinion to rotate slightly relative to each other. As a result, manufacturing intolerance can be compensated for by this relative rotation so a high number of pinions can be used while still achieving a high consistency of load sharing.

(142) It should be noted that plastic gears are used as an example here, but metal gears will benefit from the same construction even if to a lesser degree. FIGS. 42-44 show pinions with no inner cylinder. This may in some configurations provide enough bending stiffness and torsional flexibility to provide adequate load sharing between all pinions.

(143) Backlash is detrimental to the performance and precision of gearbox reducers in many applications such as robotics.

(144) Disclosed here are mechanisms and constructions for equalizing the load sharing between four or more pinions in a differential planetary geartrain. Also disclosed here are mechanisms and constructions for reducing or eliminating backlash in a differential geartrain.

(145) One object of the present device is to simplify and reduce the cost of the assembly through the elimination of the need for a planet carrier to position the gears axially in the assembly. This is accomplished in embodiments of the device, through the use of opposite helical gears on either end of the planet gears. Straight gears may also be used, as disclosed below in relation to FIGS. 54-56. These gears are also designed with a taper which has the benefit of making them easier to pull out of a mold. The helical gears are beneficial for smooth operation while the taper allows easy removal from an injection mold for low cost production.

(146) The symmetric construction of the design together with the opposing helical gears on either side of the center plane and/or the tapering of the planets on either side of the center plane eliminates the need for a planet carrier to keep the planets axially positioned. The symmetrical configuration of embodiments of the device eliminates the need for a planet carrier because twisting of the planets perpendicular to their axis is virtually eliminated. This allows the planets to be hollow which reduces weight and allows them to compress radially under radial preloading to remove backlash while preventing binding during heat expansion as shown in FIG. 51.

(147) FIG. 47 shows axial forces on a planet gear of FIG. 38 in a gearbox of FIG. 27, when the teeth of the planet gear are rotating in the direction shown by curved arrow 178. The directions of axial forces are shown by arrows 180. FIG. 48 is an isometric cutaway view showing the load paths on the planet 123 leading to the axial forces shown in FIG. 47. The circumferential forces of the load paths are shown by arrows 182. All but one planet and the retaining rings and bearings are omitted in FIG. 48.

(148) Load sharing can be provided for example by outer gear deformation, as shown schematically in FIG. 49, by sun ring deformation, as shown schematically in FIG. 50, or by planet gear deformation, as shown schematically in FIG. 51.

(149) While the embodiment shown above has a sun input and outer output and reference ring gears, an outer input ring and sun output and reference gears is another possible arrangement.

(150) Some properties of selected materials are shown in the below table.

(151) TABLE-US-00002 TABLE 2 Yield Tensile Strength/ Strength Modulus Density Strength/ Stiffness/ Material (ksi) (ksi) (g/cm3) Stiffness Density Delrin 11 450 1.42 0.0244 0.0172 Nylon 10.5 365 1.14 0.0288 0.0252 Glass- 28.3 1490 1.38 0.0190 0.0138 PEEK 16 540 1.3 0.0296 0.0228 Carbon 40.6 3200 1.4 0.0127 0.0091 Filled PEEK Glass 29 1700 1.52 0.0171 0.0112 Filled PEEK 6061 40 10000 2.7 0.0040 0.0015 4140 70.3 29700 7.85 0.0024 0.0003 Steel Maraging 245 27600 8 0.0089 0.0011 Steel

(152) FIGS. 52 and 53 are bar charts showing some material properties from table 2 in visual form.

(153) FIG. 52 shows material strength to stiffness to density ratio. FIG. 52 shows clear difference between plastics and metals when comparing this ratio. For this application it is better to have higher strength with lower stiffness, and lower density. FIG. 53 shows a material strength to stiffness ratio.

(154) In an embodiment, pinions may preferably have a ratio of yield strength to stiffness of greater than 0.010.

(155) In an embodiment, pinions may have a ratio of torsion twist stiffness to bending stiffness of less than 1.

(156) FIGS. 54-56 show another example of a differential gearbox. Unlike the embodiment in FIG. 27, this one has straight cut gears.

(157) The gearbox comprises one or more sun gears 114 in geared contact with plural planet gears 123, the plural planet gears each in contact with different ring gears 110 and 111. The planets may have a different diameter in contact with different ring gears. Thus, if the sun gear(s) 114 is the input, a gear reduction may be obtained by the planets differentially moving the ring gears. One or more ring gears may be fixed and one or more may be an output. There may also be one or more additional floating sun gears contacting parts of the planets that are not contacted by the sun gear(s) which are providing input torque.

(158) As with other examples shown in this document, in different embodiments all these input, output, fixed and optional floating gears may be arranged differently. For example, there may be output and fixed sun gears and input ring gear(s) and optional floating ring gear(s). The input and output gears could be switched in any embodiment to change from a reducer to an increaser.

(159) The gears may be arranged in an axially symmetric arrangement with axial centering provided as described below, avoiding the need for a planetary carrier.

(160) The gears in the particular embodiment shown in FIGS. 54-59 use straight cut (spur) gears for both the inner planetary gear teeth 101 and the outer planetary gear teeth 102, and all the other gear teeth that mesh with these gear teeth. Helical gears as disclosed in other embodiments in the incorporated material may also be used.

(161) FIG. 59 shows a conical taper plus a profile shift, and a gear tooth 508 with a profile shift is more specifically shown in FIG. 82. The taper uses both a conical taper of the gear as well as a taper of the gear tooth involute profile by means of a profile shift that is varied across the width of a tooth. This allows the gear tooth contact to behave in a similar way to a conical taper, but retain the involute profile's ability to have proper gear tooth contact and conjugate motion. The profile shift acts to offset the involute profile in a positive direction on one axial direction of the tooth and in a negative direction on the axial direction. The meshing gear has the same shift except in opposite directions. Profile shift is often used in gears but will be constant across a tooth (partly due to manufacturing concerns) This can help make up for small errors in tooth contact or can help to optimize a gear set. The magnitude of this is typically quite small, but can be of similar magnitude as we are using. The profile shift across the tooth width is nominally linear, but could possibly be non-linear across the tooth width, providing the positive shift on one tooth matches the negative shift on the matching tooth. This profile shift changes across the depth of the tooth can be described as a tapering of the tooth itself along the axial direction which is independent of the conical taper of the gears. The profile shift may be applied to any of the gears. A suitable profile shift is shown for example in PCT/IB2018/055087, the content of which is hereby incorporated by reference.

(162) One or both taper effects may be combined with shims between any one or more of symmetrical output ring halves, output rings and axed rings or symmetrical sun gear halves to allow preload adjustment of the bearings and of the gears to reduce or eliminate backlash.

(163) The double helical or herringbone gears of the embodiment of FIG. 27 provide a stabilizing force to center the planets axially, without causing a net axial load due to the symmetric design, and would also provide such a benefit in the embodiment of FIG. 54. In the embodiment shown in this document, the planet gears and corresponding gears on the sun gear and ring gears are tapered. The taper also provides this stabilizing force to center the planets, so helical gears are not required for axial centering.

(164) As described above, helical gears with different angles (or helical gears paired with spur gears), in combination with springs allowing changes in an axial separation of the gears of each planet, may be used to provide load sharing. This is particularly useful for allowing load sharing between relatively inflexible gears. In this particular embodiment shown, spur gears are used only, and the planets are a single piece. Thus, the above load sharing mechanism is not operative in this embodiment. The gears being spur gears and the planets being formed of a single piece is not necessary to the operation of the gear reducer, but these features simplify construction.

(165) Load sharing may be provided in this embodiment by flexibility of the planet gears. The planet gears may be hollow and flex radially (for example changing in cross sectional shape from circular to slightly elliptical) to achieve a reduction or elimination of backlash. This may be facilitated by the use of a relatively flexible material to make the gears, and by the thinness of the walls of the hollow gears. The absence of a planet carrier aids in flexibility. Otherwise shafts and bearings associated with a planet carrier device would impede radial flexing.

(166) In a typical rigid gear system, some space between meshing gears for thermal expansion is required to prevent binding, but this space allows backlash. The flexibility of the planets in this embodiment means that additional space to allow backlash is not necessary. The planets may be preloaded radially using shims between the elements holding the ring gears, which combined with the radial taper are adjusted during assembly to reduce or eliminate backlash. The radial flexibility of the hollow gears allows thermal expansion to flex the gears, making them oval shaped, for example as shown in FIG. 51, without causing binding.

(167) The shims may be for example flat and may include a shim along the axial central plane of the gearbox, and others on either side of the bearing parts as shown in the figures below. The shims position the ring gears axially, which allows the tapered ring gears to engage with the tapered planets, taking up backlash.

(168) Shims may be applied to adjust relative axial position of any of the elements relative to the axial center plane or each other. To maintain symmetry, it would generally not be desirable to change the axial position of elements that straddle the center plane. Such elements could however also be used as a reference to shim other elements, for example in an embodiment (not shown) with floating sun gears on either axial side of the input sun gear, and connected to it with bearings, shims analogous to shims B and C described below could be used to adjust the axial positions of the floating sun gears relative to the input sun gear and axial center plane.

(169) The embodiment shown in FIGS. 54-56 has central output ring gears separated by a center shim 184, and fixed outer ring gears connected to the output ring gears by bearings with inner shim 186 and outer shim 188, described below. Center shim 184 adjusts the axial position of the output ring gears relative to each other and to the planets. Inner shims 186 and outer shim 188 adjust the positions of the fixed ring gears 110 relative to the output ring gears 111, and in combination with the center shim 184, relative to the planets. There is also shown in FIG. 54 a sun gear shim 187. Sun gear shim 187 adjusts the axial position of two sun gear halves (sun gears) relative to each other. This can be used to adjust the backlash as well. Sun gear shim 187 is not shown in the other figures for this embodiment. Corresponding elements are symmetrically arranged on the other side of the center plane, so only one side is described. Different shim adjustments may be used on different sides, but typically this would not be done except to correct another asymmetry.

(170) In this particular embodiment, the sun gear 114 is one piece and straddles the axial central plane, and does not have a shim. Alternatively, the sun gear may be made of two pieces, similar to the output gear 111 of this embodiment, with a shim between the two pieces.

(171) The embodiment shown may be formed by injection molding, for example out of plastic. Helical gears also provide a more consistent contact ratio and potentially less noise and transmission error, but may be more difficult to injection mold. The gears shrink axially as well as radially after molding, which makes it harder to get accurate final parts. A spur gear may therefore be easier to construct, and may make it easier to get precision parts, which may compensate for the advantages of helical gears.

(172) As shown in FIGS. 57-59, the planets each include portions with two different pitch diameters in order to differentially drive the fixed and output gears. To enable injection molding with no interference as the planets leave the mold, for example if the mold is formed of two halves separated at an axial central plane of the planets, in the embodiment shown the portions with the two different pitch diameters have the same number of teeth, and the teeth of the portions are aligned, as shown most clearly in the end view of a planet in FIG. 59.

(173) The planets may also be formed by machining, or be machined after injection molding. The portions with the two different pitch diameters having the same number of teeth, and the teeth being aligned, also allows easier machining.

(174) The fixed and output ring gears, on the other hand, would have different numbers of teeth in this embodiment to be driven differentially by the planet gears.

(175) Metal gears, for example of steel, may also be used. To compensate for the greater stiffness, thinner walls may be used to allow radial flexibility.

(176) As described below in relation to FIGS. 79-81, different planet gears may be arranged to be out of phase in terms of gear meshing. There may be sets of gears, the gears of each set being at the same phase, different sets being at different phase, or all gears may be at different phase. (Or they may all be at the same phase). For example, in an embodiment with 12 gears as shown here, there may be two sets of 6 gears each, for example every second gear being in a set, or all twelve gears may be at a different phase of meshing at any given moment. This distributes changes in forces due to the gear meshing or due to imperfections similarly aligned in different gears, so that they do not occur all at once.

(177) In the embodiment shown in FIGS. 54-56, dual bearings are included between the fixed and output ring gears on each side of the axial center plane. The bearings are each angular contact bearings and may be preloaded using inner shim 186 and outer shim 188. The difference of width between inner shim 186 and outer shim 188 may be used to preload the bearings and adding or subtracting from the width of both of inner shim 186 and outer shim 188 equally may be used to determine the axial separation between the fixed and output ring gears. This arrangement has good stability. The sets of bearings on each side of the axial center plane may be preloaded separately. The set on the opposite side may be preloaded using the shims symmetric to inner shim 186 and outer shim 188 with respect to the axial center plane.

(178) In an embodiment, the bearings may be made out of plastic. This allows reduced weight of the bearings compared to metal bearings.

(179) FIG. 54 shows an isometric cutaway view, and FIG. 55 shows an isometric view, of this embodiment. FIG. 56 shows an axial end view.

(180) FIGS. 57-59 show an exemplary planet for the differential planetary gearbox if FIGS. 54-56. FIGS. 57 and 58 show isometric views and FIG. 59 shows an axial end view.

(181) Thus, there is provided a differential gearbox with a driving sun input on the ID of the pinions and one or more fixed ring gears on the OD of the pinions and one or more output ring gears on the OD of the pinions with a number of pinions greater than 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20 pinions with pinions and/or inner or outer ring gears: having a yield strength-to-stiffness ratio of greater than 0.10; made of plain or fiber reinforced polymer resin; with pinions having a torsionally flexible section between inner and outer gears to provide a torsion twist stiffness-to-bending stiffness of less than 1. There may be axial or helical slots in the cylindrical sections to increase torsional flexibility. There may be symmetrical opposing tapered pinions that allow backlash adjustment by axial shimming or other fixed positioning means for fixed and/or output ring gears. The gears may be straight or helical. There may be two sets of opposed bearing races integrated into housing and output ring gear.

(182) Example Planet Driven Actuator

(183) Embodiments of an exemplary actuator as shown in FIGS. 60-67 include an integrated symmetric differential gearbox coupled to a direct drive motor with two stators. Rectangular boxes in FIG. 60 show the portions of the gearbox corresponding axially to the output gear (in the axial center) and the fixed gears (above and below the output gear). Embodiments of the exemplary actuator further include the use of the pinions as permanent magnet carriers which serve the purpose of a rotor without the need for a separate rotating magnet carrier. Components may be enclosed in a sealed housing 212 and rotate about a common axis indicated by reference numeral 290, and may be symmetric about the axial center plane indicated by reference numeral 292. One or more electromagnetic stators provide the input torque to the gearbox and may be located outward from the axial center plane 292 of the device. Air coils (that is, electromagnetic coils with no soft magnetic core) may be used in the stators, and are commutated to act on permanent magnets which are inserted into the pinion gears. The pinion gears may be radially preloaded by a floating rolling contact sun ring 294 shown in FIG. 61. The pinion gear teeth have two symmetric tooth profiles which may be one or more of helical, tapered, or have an involute profile. The pinion teeth which are located at the axial center of the device, referred to as the inner pinion teeth 201, mesh with the output ring gear teeth 274 of output gear 211 at the axial center plane of the device. The pinion teeth located outward from the axial center of the device, referred to as the outer pinion teeth 202, mesh with the teeth 276 of two fixed input ring gears 210 which are located axially outward from the axial center of the device. The fixed ring gears 210 are secured together, such as through the axial center of the device. A different gear tooth ratio between the pinion and the fixed ring gear, and pinion and the output ring gear, is what causes the output ring to spin at a reduced speed relative to the orbiting speed of the pinions. The non-limiting exemplary embodied shown here has a 10:1 ratio and can be scaled accordingly to provide multiple ratios for different applications. FIG. 62 shows the device without the motor input components.

(184) A non-limiting exemplary embodiment shown here comprises 8 planetary gears that have no sun gear input. A high number of planetary pinion gears 223 allows for a large torque capacity from the device. Load sharing is accomplished by applying magnetic force directly to the pinions 223 together with the rolling contact free spinning sun ring 294 which preloads the pinons against the fixed rings 210 and output rings 211 while allowing each pinion to find it is ideal circumferential position so all of the pinions are reasonably equally loaded when torque is applied through the electromagnetic stators. The pinons are kept in gear engagement with the outer rings 210 and 211 by using a rolling contact sun ring 294 closest to the radial center of the device. It is worth noting that the two fixed ring gears 210 are attached to each other in this embodiment as if they are one piece by means of a cylindrical member 296 that connects the fixed ring gears through the large center through hole of the actuator. The use of a traction interface between the rolling contact sun ring 294 and pinions 223 allows the pinions 223 to each find their own individual position with respect to the fixed and output gear rings. This may allow each of the pinons to more equally share the load that results from torque transfer of the device than if the inner ring was geared, for example.

(185) The rotation of the planetary gears 223 is accomplished by the influence of an electromagnetic force produced by electromagnetic conductor coils 298 acting on permanent magnets 300 which are secured in the pinion gears 223 through both axial ends of the gears by an attracting magnetic force to a ferrous cylinder 302, such as but not limited to steel or iron, centered in the planets. In a non-limiting embodiment, motor stators use air coils 298 in combination with back iron 304 and a small enough air gap between magnets and back iron that a reasonably high torque can be achieved while at the same time eliminating passive cogging effects because there are no steel posts in the stator. Steel posts may be used as well for different torque effects. Alternatively, the electromagnets may have soft magnetic posts (not shown). If air coils are used, or if electromagnets with unusually small soft magnetic posts are used, the stator may use a soft magnetic material backiron to improve the efficiency of the electromagnetic coils with minimal or no cogging.

(186) The laminated back iron 304 in the motor stators may be made up of alternating layers of laminates and protruding aluminum fins 306 which extend through openings in the fixed input ring gear 210/housing. Manufacturing is simplified because the back iron 304 is made of spirals of steel (represented by concentric rings in FIG. 63 which shows an upper view of components of the upper motor) and does not require any alignment of pole sections. Periodic layers (such as every second layer) of the concentric winding can be steel and serve as a flux path between air coils, but is preferably hard anodized aluminum or some other high heat conductivity material such but not limited to aluminum.

(187) In this non-limiting configuration the aluminum provides a heat path directly from the coil to the heat extraction surfaces on the outside of the actuator. Heat is transferred from the copper conductors of the air coils 298 into the back iron 304 and dispersed at openings in the housing as air passes through the fins 306. An air fence component 308 with extrusions 312 formed in a serpentine pattern overlaps with openings 310 in the housing to guide air from an input past the fins 306 and out of the device, best shown in FIG. 65. Arrows 316 show air flow through cavities of the air fence 308.

(188) FIG. 64 shows a bottom view of components of the upper motor. FIG. 64 shows a circumferential offset of cavities defined by the air fence 308 above aluminum fins 306.

(189) In order to simplify manufacturing, planet gears can be made to be injection moldable such as from plastic. A configuration of the planet gears can include continuous features such as the helical teeth along their axes without an undercut as shown in FIG. 66 to ease injection molding.

(190) FIG. 67 shows an exploded view of an upper half of the gearbox of FIG. 60.

(191) The taper required for injection molding then requires that the maximum addendum diameter of the axially outer section of a planetary gear must be smaller than the minimum addendum diameter of the axially inner section. A preferred embodiment of the planet gears would include a number of teeth in the axially outer section to be either a factor of or equal to the number of teeth of the axially inner gears. In an embodiment with injection moldable planet gears, a geared floating inner ring can be used to preload pinion gears and keep them in engagement with outer rings. A geared floating inner ring may have the advantage of transferring torque from pinions that are under high magnetic force to pinions that are in between phases of EM force input. It is worth noting that if the number of teeth on the axially outer section is a factor of the number of teeth on the axially inner section the whole gear can still be injection molded with step change at the start of the tooth on the axially inner one that does not align with a tooth on the axially outer.

(192) An embodiment includes seals that are added along the inputs and outputs of the motor to protect inner components from dust and particulate.

(193) The tapered gears allow geared parts to be removed from an injection mold or other process such as compacted powder process such as powdered metal. The taper may have a different helix angle on leading and training faces of each gear tooth and/or taper of addendum and dedendum so that the gear releases from the mold with no binding. Other characteristics of the tapered tooth design allow the involute shape to operate correctly.

(194) There may be a rolling feature (e.g., cylindrical section) between the inner and outer gears on the pinion 223. This provides a mid-force position for the preload provided by the rolling sun ring 294.

(195) This also allows the steel pinion core 302 width to be wide enough (axially long enough) so rolling contact of sun ring 294 on plastic pinion race (rolling feature) transfers compression load to steel core 302 rather than to magnets 300 on either end of steel core. Steel has much better strength and endurance than typical PM magnet material so this will contribute to increased service life.

(196) The magnets 300 are preferably not stressed by the preload of the sun ring 294, so the PM magnets can be magnetically attracted to and therefore attached to the axial ends of the steel cores without contacting the ID of the ends of the plastic pinion gears. A cylindrical boss on the inner axial end of the PM's will fit into a circular bore in the end of the steel core to center the PM's.

(197) The PM's 300 may have a larger OD beyond the axial ends of the pinions 223 to provide a larger magnetic pole to interact with the electromagnetic stators.

(198) Assembly sequence may be as follows and is enabled by a symmetric split output ring 210.

(199) If the pinons 223 are placed into the ring gears as a prior step, the sun ring contacts would interfere with the pinions preventing assembly of the sun ring. Likewise, if the sun ring and pinions are assembled first, the output ring would interfere with the pinons and would prevent assembly. By using a split output ring gear 210, however, it is possible to assemble the pinions 223 and sun ring 294 or sun ring assembly first, and then to assemble each of the two output ring gear halves 211 together toward the center plane. The two tapered fixed gear rings 210 are then assembled. This prevents any interference during assembly and allows a zero backlash final result.

(200) Note that to achieve a true zero backlash final assembly it is provided that the axial position of the fixed rings 210 can be adjusted relative to the output ring gear 211 assembly. The problem with that solution is it makes an integrated bearing race 314 between the fixed and output rings very difficult to implement. Instead, an embodiment uses an expandable sun ring 318, as shown below, which can provide gear preload at a range of radial positions for the pinion center axes. FIG. 68 shows a planet 223 having a shape suitable to be used with an expandable sun ring 318 for example as shown in FIG. 69. The planet 232 may have a magnet 300 arranged with clearances 320 between the magnet and the planet gear teeth portion, and between the magnet and radially separated portions of the steel core 302. A line 322 indicates a tooth angle of the inner 201 and outer 202 teeth.

(201) A replaceable/adjustable shim (not shown) is provided in the assembly between the two output ring gear halves to adjust their relative axial position to each other at the center plane. This shim can be a replaceable ring or ring sections that can be inserted during assembly, or it can be a rotating ring with ramps or threads that can be adjusted via rotation around the actuator center axis after assembly of all the components but before the two output ring halves are secured together such as by tightening together with bolts. By creating the assembly so the output ring gears 210 have backlash when at the maximum shim adjustment thickness, the fixed 210 and output 211 ring gears and pinions 223 and expandable sun gear 318 can be loosely arranged but assembled close to their final positions. At this point, the preload of the sun ring 318 will push the outer pinion gears 202 and fixed ring gear 210 teeth into engagement with no backlash. Reducing the axial distance between the output gear rings 211 will then remove the backlash from the inner gears 201 and output rings 211. To allow a single shim stack (between only the two halves of the output ring gears) to adjust the backlash in the fixed and output gear meshes, requires that the pinons can be moved outward as a result of the expanding sun ring 318, and that the taper on the inner gears 201 of the pinion 223 (and the output gear 211) be of a greater taper angle. This way the axial adjustment of the output ring gears 211 has more effect on the inner gear mesh between inner teeth 201 and output gears 211 than the outer gear mesh between outer teeth 202 and fixed gears 210. As a result, the relative position of the fixed ring gear 210 on an end and the output ring gear 211 half on that end, do not need to be changed. This allows the bearing races 314 to be molded or machined into the fixed and output gears because there is no change in this relative position required during backlash adjustment. The only thing that must be considered in this adjustment strategy is that the relative position of the two fixed ring gears 210 to each other will need to be shimmed/adjusted at the same time as the two output ring gears 211 are adjusted. This adjustment could, however, be a result of the compliance of the housing 212 which supports and secures, including via connecting portion 296, the two fixed rings 210 together.

(202) Adjustable sun ring pressure via axially spring two-piece sun ring with a mechanical spring (or repelling magnet ring) pushing axially outward will compensate for thermal expansion and gear surface wear while reducing or eliminating backlash. This allows for a greater tolerance range on the diameters of the sun ring and pinion contact races, as well as the tolerance of the gear faces.

(203) An axially expandable sun ring 318, as shown in FIG. 69, provides the capability to adjust the preload force of the sun ring races on the pinion races. This can be done by a number of means including, for example, a magnetic coil 324 on both axial ends of the axially expandable sun ring assembly as shown below. The electromagnetic coils in this example are fixed to the actuator housing. By powering them to a level that is proportional to the output torque of the actuator, the preload of the pinions and ring gears can be adjusted at all times to ensure a zero-backlash gear interface and the lowest possible friction.

(204) In an embodiment, shown in FIG. 70, a power-off safety brake is integrated into the gearbox as follows. A separation spring 326 is strong enough to create a high level of friction between the sun ring 318 and pinion contact face 328. This friction also results in higher friction between the gear mesh surfaces making the gearbox very difficult or impossible to backdrive. This results in a power-off brake that prevents rotation of the actuator when power is lost. To release the brake, an actuation means, such as an electromagnetic coil 324 exerts a force in the opposite direction. The level of this force can then be adjusted to relieve enough of the spring force to eliminate unnecessary friction, but not so much as to cause backlash at any given torque output. For clarity, the greater the EM force on the sun ring assembly, the lower the preloading force on the pinions. When power is lost to the actuator, the EM coils become unpowered and the mechanical spring provides the preload force which is then high enough to make the gearbox less or completely non-backdrivable.

(205) Features of embodiments of this planet driven actuator may include: the fixed ring gears are secured together, such as through the axial center of the device; planet gears would include a number of teeth in the axially outer section to be either a factor of or equal to the number of teeth of the axially inner gears; serpentine air fence causes air to pas circumferentially between cooling fins as it flows from the center axis outward; a non-geared sun ring preloads pinons but allows them to float for equal torque transfer; the sun ring can be geared; the sun ring may also distributes torque between pinions when some pinons are no being pulled along by stator; and the sun ring can be used as a brake member (not shown) by applying braking force to sun ring (whether geared or not) with a brake device (not shown). An alternative brake using a sun ring is shown in FIG. 70.

(206) Planetary Bearing

(207) A rotor can be coupled to a gearbox and make use of the planet gears as a bearing with the sun as the interface. Six non-limiting configurations of gearboxes (71-78) are presented to demonstrate the configuration of gears such that the planets can act as bearings. This can work for any number of planets greater than 3. FIGS. 71-78 cover configurations of symmetric planetary gearboxes with either axially inner or axially outer sun interfaces of many possible gear ratios. This principle works in any planetary system with an input gear and a stationary gear on opposing radial sides (ex. left and right of planet gear in FIGS. 71-78) of a planetary gear.

(208) Each of FIGS. 71-78 shows a 2D section view of a respective embodiment. Gear teeth are not shown for simplification. Each shows a planet 400 interfacing with an input gear 402, a stationary gear 404, and an output gear 406. A dotted line 408 indicates a central axis about which the input and output gears rotate.

(209) FIG. 71 shows an embodiment using a sun input 402 interfacing with axially inner planet gear teeth and outer stationary gear 404 interfacing with axially outer planet gear teeth.

(210) FIG. 72 shows an input ring gear 402 interfacing with the axially inner (or outer) planet gear teeth and a stationary sun gear 404 interfacing with the axially outer planet gear teeth (and curving outward to loop around the input ring gear), and an output sun gear 406 interfacing the axially inner planet gear teeth. FIG. 72 is the same as FIG. 71 but with what is radially inner and what is radially outer inverted.

(211) FIG. 73 shows a sun input 402 interfacing with axially outer planet gear teeth and outer stationary 404 interfacing with axially outer planet gear teeth.

(212) FIG. 74 is the same as FIG. 73 but with what is radially inner and what is radially outer inverted.

(213) FIGS. 75 and 76 have a stationary portion surrounded by a moving part. This would not work for continuous motion, but would be perfectly allowable for a limited range or motion joint, i.e., the moving part would have a slot part of the way around the circumference which allows the stationary part to be grounded. These would also be a speed increaser if the axially inner planet gear is larger than the axially outer planet gear. This could also be reversed to change it to a reducer, although this may make it more difficult to manufacture/assemble the planet gear.

(214) FIG. 75 shows an outer input gear 402 interfacing with axially inner planet gear teeth and stationary sun gear 404 interfacing with axially inner planet gear teeth.

(215) FIG. 76 shows an outer input gear 402 interfacing with axially inner planet gear teeth and stationary sun gear 404 interfacing with axially outer planet gear teeth.

(216) FIG. 77 shows an outer input gear 402 interfacing with axially outer planet gear teeth and a stationary sun gear 404 interfacing with axially inner planet gear teeth.

(217) FIG. 78 shows an outer input gear 402 interfacing with axially outer planet gear teeth and a stationary sun gear 404 interfacing with axially outer planet gear teeth.

(218) Out of Phase Gears

(219) One potential drawback when using the differential gearbox is the additional gear meshes when compared to a three or four planet system. When the planets are all in phase, gears make contact with the next tooth at the same time, and with additional planets, the potential for noise and vibration are increased. By keeping the planets out of phase, the additional initial tooth contacts can be distributed more evenly, significantly reducing the ‘cogging feel’ of an in-phase system. In one exemplary embodiment, there are 14 planets and thus 14 initial contacts for each tooth. In a single phase system, all of these contacts occur at one point in time, while in a 7 phase system, only two contacts occur at a single point in time, but the contacts occur 7× as often.

(220) In one embodiment, shown in FIG. 79, and FIG. 80, there are 14 planets 123 positioned evenly around the sun 114. Each planet is identical and there are 7 unique phases of planet. Opposite planets are in the same phase. The gear diameters and tooth numbers are provided in Table 3.

(221) TABLE-US-00003 TABLE 3 Scaled Diameter Teeth Sun 89.18 114 Outer 129.86 166 Ring Stator 126.47 194 Ring Planet 20.34 26 Large Planet 16.95 26 Small Sun 2 92.57 142

(222) This can be separated into two traditional planetary gearsets: an inner gearset 500 and outer gearset 502, each with a sun gear, planet gear, and ring gear. Each gearset has a constant pitch or module, which may be different from the other gearset. Note that the differential gearset does not make use of a sun gear on the outer gearset. The virtual sun gear would fit into the system, but is not required due to the balanced nature of the system.

(223) TABLE-US-00004 TABLE 4 Inner Gearset Outer Gearset Diameter Teeth Diameter Teeth Sun 89.18 114 92.57 142 Ring 129.86 166 126.47 194 Planet 20.34 26 16.95 26

(224) The two gearsets are designed such that diameters and tooth numbers in the system are compatible in: The number of planets The radial and tangential position of the planets The phase of the planets

(225) Individually, the gearsets follow known rules for planetary geartrains, with the sum of the number of teeth in the sun and ring gears being evenly divisible by the number of planets. This ensures that the planets are evenly spaced around the sun.

(226) $\mathrm{Inner}\mathrm{Gearset}.fwdarw.\frac{114+166}{14}=20$$\mathrm{Outer}\mathrm{Gearset}.fwdarw.\frac{142+194}{14}=24$

(227) The radial position of the planets is controlled by the relative scales of the two gearsets, ensuring that the planet gear axes fall on the same radius.

(228) The phase of the planets is kept compatible by ensuring that the two gearsets have the same number of unique phases. The number of unique phases in the system is calculated by dividing the number of planets by the greatest common factor of the number of teeth on the sun gear, ring gear, and the number of planets.

(229) $\mathrm{Inner}\mathrm{Gearset}.fwdarw.\frac{14}{\mathrm{GCF}\left(114,166,14\right)}=\frac{14}{2}=7\mathrm{Outer}\mathrm{Gearset}.fwdarw.\frac{14}{\mathrm{GCF}\left(142,192,14\right)}=\frac{14}{2}=7$

(230) The phases are organized such that similar planet phases are distributed evenly around the sun. In the example above, there are 2 planets for each unique phase. The two planets in one phase will be located 180° from each other.

(231) With the same number and position of unique gear phases, the system can operate. If only the position were compatible, the system could operate only if there were planet configurations specified for each individual gear position. Each planet configuration would use identical gears, but the rotational alignment between the inner and outer gears would be unique for each phase pair.

(232) In an embodiment, the number of teeth on the planet gears may either be equal, or the number of teeth on one planet may be an integer multiple of the number of teeth of the other planet. This provides a number of advantages.

(233) First, the planet may be more easily manufactured as a single piece using methods including, but not limited to injection molding. It is beneficial to have the planets as a single piece in order to better allow for load sharing mechanisms in the system. One of the load sharing mechanisms that the exemplary system relies on is the radial compression of the planets to ensure gear tooth contact on both the sun and the outer ring. One of the ways to ensure this occurs is to include a large through hole in the planet, allowing for some additional radial flexibility. If the planet were to be constructed of multiple pieces, the method of fastening them together would require significantly more material and thus result in significantly more stiffness.

(234) Second, the system may be assembled with the planets as a single piece. In any planetary gearset, one or more of the gears must be inserted axially. In one process, planets could be placed around the sun radially, and the outer ring may be inserted axially around the planets. For the differential gearbox, two planetary gearsets are joined axially and if the planet is a single piece, there are limitations to the assembly method. By constraining the number of teeth on the planet gears, there are significantly more configurations that may be assembled. Without this constraint, some configurations cannot be assembled, as the outer planet gear teeth would prevent the axial insertion of a gear into the inner gearset. This is applicable for spur and helical gear teeth. See the additional specification filed herewith for images of the different configurations (sun input, ring input, etc.).

(235) For most reasonable gear ratios, the two planet diameters must be similar. If the addendum of the smaller planet gear is larger than the dedendum of the larger gear, an undercut exists, meaning that a gear could not be axially inserted into position onto the inner gearset.

(236) In FIG. 81, it is clear that the two planets shown are out of phase. The respective lines 504 running between the gear center axes and the center axis of the device intersects the gear teeth 506 at a different point on the nearest tooth, falling near the center of the sun tooth on the left gear, and falling to one side of the sun tooth on the right gear.

(237) By using the principles described above, there are a number of unique solutions that may be used in a differential gearbox. A list of these solutions is shown below, but the scope of the claims is not limited to these specific solutions. Additional solutions exist with different numbers of gear teeth and each solution may be geometrically scaled to suit any diameter, keeping the number of teeth constant. Specific configurations can be determined by solution of known equations applied following the principles in this disclosure.

(238) TABLE-US-00005 TABLE 5 Number Outer Stator Planet Planet Outer Stator Planet Planet Gear of Sun Ring Ring Large Small Sun 2 Sun Ring Ring Large Small Sun 2 Ratio Planets Diameter Diameter Diameter Diameter Diameter Diameter Teeth Teeth Teeth Teeth Teeth Teeth 7.220339 26 137.6667 165.6667 161.6667 14 10 141.6667 118 142 194 12 12 170 3.61017 26 196.6667 236.6667 226.6667 20 10 206.6667 118 142 272 12 12 248 2.707627 26 255.6667 307.6667 291.6667 26 10 271.6667 118 142 350 12 12 326 13.23729 26 118 142 140 12 10 120 118 142 168 12 12 144 4.211864 26 177 213 205 18 10 185 118 142 246 12 12 222 2.922518 26 236 284 270 24 10 250 118 142 324 12 12 300 2.54049 26 275.3333 331.3333 313.3333 28 10 293.3333 118 142 376 12 12 352 3.20904 26 216.3333 260.3333 248.3333 22 10 228.3333 118 142 298 12 12 274 5.214689 26 157.3333 189.3333 183.3333 16 10 163.3333 118 142 220 12 12 196 5.253687 25 150.6667 182.6667 176.6667 16 10 156.6667 113 137 212 12 12 188 3.233038 25 207.1667 251.1667 239.1667 22 10 219.1667 113 137 287 12 12 263 2.559489 25 263.6667 319.6667 301.6667 28 10 281.6667 113 137 362 12 12 338 13.33628 25 113 137 135 12 10 115 113 137 162 12 12 138 4.243363 25 169.5 205.5 197.5 18 10 177.5 113 137 237 12 12 213 2.944374 25 226 274 260 24 10 240 113 137 312 12 12 288 2.727876 25 244.8333 296.8333 280.8333 26 10 260.8333 113 137 337 12 12 313 3.637168 25 188.3333 228.3333 218.3333 20 10 198.3333 113 137 262 12 12 238 7.274336 25 131.8333 159.8333 155.8333 14 10 135.8333 113 137 187 12 12 163 4.569328 24 173.9231 211.9231 203.9231 19 11 181.9231 119 145 241 13 13 215 2.893908 24 247.1539 301.1539 285.1539 27 11 263.1539 119 145 337 13 13 311 2.70775 24 265.4615 323.4615 305.4615 29 11 283.4615 119 145 361 13 13 335 3.89916 24 192.2308 234.2308 224.2308 21 11 202.2308 119 145 265 13 13 239 14.62185 24 119 145 143 13 11 121 119 145 169 13 13 143 3.452381 24 210.5385 256.5385 244.5385 23 11 222.5385 119 145 289 13 13 263 7.920168 24 137.3077 167.3077 163.3077 15 11 141.3077 119 145 193 13 13 167 3.133253 24 228.8462 278.8462 264.8462 25 11 242.8462 119 145 313 13 13 287 5.686275 24 155.6154 189.6154 183.6154 17 11 161.6154 119 145 217 13 13 191 13.44444 24 108 132 130 12 10 110 108 132 156 12 12 132 7.333333 24 126 154 150 14 10 130 108 132 180 12 12 156 5.296296 24 144 176 170 16 10 150 108 132 204 12 12 180 4.277778 24 162 198 190 18 10 170 108 132 228 12 12 204 3.666667 24 180 220 210 20 10 190 108 132 252 12 12 228 3.259259 24 198 242 230 22 10 210 108 132 276 12 12 252 2.968254 24 216 264 250 24 10 230 108 132 300 12 12 276 2.75 24 234 286 270 26 10 250 108 132 324 12 12 300 2.580247 24 252 308 290 28 10 270 108 132 348 12 12 324 13.44444 26 108 132 130 12 10 110 117 143 169 13 13 143 7.333333 26 126 154 150 14 10 130 117 143 195 13 13 169 5.296296 26 144 176 170 16 10 150 117 143 221 13 13 195 4.277778 26 162 198 190 18 10 170 117 143 247 13 13 221 3.666667 26 180 220 210 20 10 190 117 143 273 13 13 247 3.259259 26 198 242 230 22 10 210 117 143 299 13 13 273 2.968254 26 216 264 250 24 10 230 117 143 325 13 13 299 2.75 26 234 286 270 26 10 250 117 143 351 13 13 325 2.580247 26 252 308 290 28 10 270 117 143 377 13 13 351 13.55357 25 103.3846 127.3846 125.3846 12 10 105.3846 112 138 163 13 13 137 2.601191 25 241.2308 297.2308 279.2308 28 10 259.2308 112 138 363 13 13 337 2.772321 25 224 276 260 26 10 240 112 138 338 13 13 312 2.992347 25 206.7692 254.7692 240.7692 24 10 220.7692 112 138 313 13 13 287 3.285714 25 189.5385 233.5385 221.5385 22 10 201.5385 112 138 288 13 13 262 3.696429 25 172.3077 212.3077 202.3077 20 10 182.3077 112 138 263 13 13 237 4.3125 25 155.0769 191.0769 183.0769 18 10 163.0769 112 138 238 13 13 212 5.339286 25 137.8462 169.8462 163.8462 16 10 143.8462 112 138 213 13 13 187 7.392857 25 120.6154 148.6154 144.6154 14 10 124.6154 112 138 188 13 13 162 7.398058 23 120.1667 148.1667 144.1667 14 10 124.1667 103 127 173 12 12 149 3.699029 23 171.6667 211.6667 201.6667 20 10 181.6667 103 127 242 12 12 218 2.774272 23 223.1667 275.1667 259.1667 26 10 239.1667 103 127 311 12 12 287 13.56311 23 103 127 125 12 10 105 103 127 150 12 12 126 4.315534 23 154.5 190.5 182.5 18 10 162.5 103 127 219 12 12 195 2.994452 23 206 254 240 24 10 220 103 127 288 12 12 264 2.603021 23 240.3333 296.3333 278.3333 28 10 258.3333 103 127 334 12 12 310 3.288026 23 188.8333 232.8333 220.8333 22 10 200.8333 103 127 265 12 12 241 5.343042 23 137.3333 169.3333 163.3333 16 10 143.3333 103 127 196 12 12 172 3.181598 24 210.7143 260.7143 246.7143 25 11 224.7143 118 146 314 14 14 286 4.639831 24 160.1429 198.1429 190.1429 19 11 168.1429 118 146 242 14 14 214 14.84746 24 109.5714 135.5714 133.5714 13 11 111.5714 118 146 170 14 14 142 2.938559 24 227.5714 281.5714 265.5714 27 11 243.5714 118 146 338 14 14 310 3.959322 24 177 219 209 21 11 187 118 146 266 14 14 238 2.749529 24 244.4286 302.4286 284.4286 29 11 262.4286 118 146 362 14 14 334 8.042373 24 126.4286 156.4286 152.4286 15 11 130.4286 118 146 194 14 14 166 3.50565 24 193.8571 239.8571 227.8571 23 11 205.8571 118 146 290 14 14 262 5.774011 24 143.2857 177.2857 171.2857 17 11 149.2857 118 146 218 14 14 190 2.757202 22 240.9231 298.9231 280.9231 29 11 258.9231 108 134 332 13 13 306 3.190476 22 207.6923 257.6923 243.6923 25 11 221.6923 108 134 288 13 13 262

(239) These parameters for the gearbox, using two sizes of radially outer planets which alternate as you look around the circle (A, B, A, B, A . . . ), while each of the radially inner planets are of the same size, are believed to work: (P=planet, R=ring, in =inner, out=outer).

(240) TABLE-US-00006 TABLE 6 P P # Diameter Outer P Out P Teeth Out P Out P Total Soln Ps Sun R out 2 in Sun R Out 2 in Pitch Ratio Error 1 14 105 168 21.9 18.6 18.6 350 560 73 62 62 3.33 2.67 0.102 2 10 98 161 29.4 23.1 17.5 140 230 42 33 25 1.43 2.56 0.144 3 14 114.8 173.6 12.2 10.4 28 574 868 61 52 140 5 2.95 0.156 4 10 79.9 159.8 27.5 22.3 23.78 215 430 74 60 64 2.69 2 0.193 5 10 86 172 29.6 24 25.6 215 430 74 60 64 2.5 2 0.198 6 16 103.2 163.2 19.8 18.3 16.5 344 544 66 61 55 3.33 2.72 0.202 7 16 103.2 163.2 19.8 18.3 16.5 344 544 66 61 55 3.33 2.72 0.202 8 10 81.35 162.7 28 22.7 24.22 215 430 74 60 64 2.64 2 0.203 9 16 116.8 156.8 15.8 14.4 13.8 584 784 79 72 69 5 3.92 0.227 10 16 116.8 156.8 15.8 14.4 13.8 584 784 79 72 69 5 3.92 0.227 11 12 105.6 172.8 15.4 13.6 30 528 864 77 68 150 5 2.57 0.253 12 18 126.9 189 20.4 18.9 17.4 423 630 68 63 58 3.33 3.04 0.255 13 18 126.9 189 20.4 18.9 17.4 423 630 68 63 58 3.33 3.04 0.255 14 18 126.9 172.8 14.1 12.3 17.4 423 576 47 41 58 3.33 3.76 0.255 15 18 126.9 172.8 14.1 12.3 17.4 423 576 47 41 58 3.33 3.76 0.255 16 18 132.75 180 14 12.5 18.5 531 720 56 50 74 4 3.81 0.265 17 18 132.75 180 14 12.5 18.5 531 720 56 50 74 4 3.81 0.265 18 24 150.6 194.4 16.5 9.9 15 502 648 55 33 50 3.33 4.44 0.267 19 24 150.6 194.4 16.5 9.9 15 502 648 55 33 50 3.33 4.44 0.267 20 14 119 173.6 15.8 11.6 24.2 595 868 79 58 121 5 3.18 0.273 21 10 104 196 24.4 20.8 36.4 260 490 61 52 91 2.5 2.13 0.273 22 22 116.8 158.4 13.2 9.4 14.4 584 792 66 47 72 5 3.81 0.281 23 12 104.4 183.6 21.3 20.1 28.2 348 612 71 67 94 3.33 2.32 0.31 24 26 121.2 156 11.4 9.9 10.8 404 520 38 33 36 3.33 4.48 0.324 25 26 121.2 156 11.4 9.9 10.8 404 520 38 33 36 3.33 4.48 0.324 26 20 146.02 189 18.9 12.5 14.02 479 620 62 41 46 3.28 4.4 0.327 27 20 146.02 189 18.9 12.5 14.02 479 620 62 41 46 3.28 4.4 0.327 28 20 143.7 186 18.6 12.3 13.8 479 620 62 41 46 3.33 4.4 0.332 29 20 143.7 186 18.6 12.3 13.8 479 620 62 41 46 3.33 4.4 0.332 30 20 141.38 183 18.3 12.1 13.58 479 620 62 41 46 3.39 4.4 0.336 31 20 141.38 183 18.3 12.1 13.58 479 620 62 41 46 3.39 4.4 0.336 32 12 100.56 161.5 24.3 17.2 19.44 269 432 65 46 52 2.67 2.65 0.342 33 24 118.2 158.4 13.5 12 11.4 394 528 45 40 38 3.33 3.94 0.343 34 24 118.2 158.4 13.5 12 11.4 394 528 45 40 38 3.33 3.94 0.343 35 12 99.47 160 13.6 11.2 28.53 373 600 51 42 107 3.75 2.64 0.344 36 12 111.9 180 15.3 12.6 32.1 373 600 51 42 107 3.33 2.64 0.344 37 12 124.33 200 17 14 35.66 373 600 51 42 107 3 2.64 0.344 38 12 113.05 180.6 24.5 16.8 24.5 323 516 70 48 70 2.86 2.67 0.347 39 12 107.6 172.8 26 18.4 20.8 269 432 65 46 52 2.5 2.65 0.348 40 10 120 195 21 15.5 37.5 240 390 42 31 75 2 2.6 0.353 41 10 96 156 16.8 12.4 30 240 390 42 31 75 2.5 2.6 0.353 42 20 127.08 169 20.8 11.7 11.7 391 520 64 36 36 3.08 4.03 0.358 43 20 127.08 169 20.8 11.7 11.7 391 520 64 36 36 3.08 4.03 0.358 44 20 146.63 195 24 13.5 13.5 391 520 64 36 36 2.67 4.03 0.358 45 20 146.63 195 24 13.5 13.5 391 520 64 36 36 2.67 4.03 0.358 46 20 136.85 182 22.4 12.6 12.6 391 520 64 36 36 2.86 4.03 0.358 47 20 136.85 182 22.4 12.6 12.6 391 520 64 36 36 2.86 4.03 0.358 48 20 117.3 156 19.2 10.8 10.8 391 520 64 36 36 3.33 4.03 0.358 49 20 117.3 156 19.2 10.8 10.8 391 520 64 36 36 3.33 4.03 0.358 50 12 106.56 183.4 22.5 20.8 26.32 251 432 53 49 62 2.36 2.39 0.367 51 14 101.2 162.4 21.2 16.8 18.8 253 406 53 42 47 2.5 2.65 0.369 52 12 100.4 172.8 21.2 19.6 24.8 251 432 53 49 62 2.5 2.39 0.371 53 12 117 180 18.3 13.2 28.8 390 600 61 44 96 3.33 2.86 0.379 54 8 87.96 158.9 22.7 18.8 32.63 248 448 64 53 92 2.82 2.24 0.38 55 16 124.8 163.2 17.7 14.7 13.2 416 544 59 49 44 3.33 4.25 0.381 56 16 124.8 163.2 17.7 14.7 13.2 416 544 59 49 44 3.33 4.25 0.381 57 8 101.53 183.4 26.2 21.7 37.66 248 448 64 53 92 2.44 2.24 0.381 58 12 107.45 155.4 22.4 14.7 17.85 307 444 64 42 51 2.86 3.24 0.389 59 12 122.8 177.6 25.6 16.8 20.4 307 444 64 42 51 2.5 3.24 0.389 60 12 138.15 199.8 28.8 18.9 22.95 307 444 64 42 51 2.22 3.24 0.389 61 20 116.68 167 16.7 15.6 13.84 531 760 76 71 63 4.55 3.32 0.389 62 20 116.68 167 16.7 15.6 13.84 531 760 76 71 63 4.55 3.32 0.389 63 12 91.8 158.4 21.3 18.3 21.6 306 528 71 61 72 3.33 2.38 0.391 64 12 104.7 169.2 15 10.8 30.6 349 564 50 36 102 3.33 2.62 0.401 65 12 122.15 197.4 17.5 12.6 35.7 349 564 50 36 102 2.86 2.62 0.401 66 20 125 161 16.1 12.3 10.73 559 720 72 55 48 4.47 4.47 0.401 67 20 125 161 16.1 12.3 10.73 559 720 72 55 48 4.47 4.47 0.401 68 12 117 180 24.5 21 20.5 234 360 49 42 41 2 2.86 0.409 69 12 122.77 187.7 23.7 10.9 29.39 259 396 50 23 62 2.11 2.89 0.409 70 12 129.85 193.2 23.8 13.3 28.35 371 552 68 38 81 2.86 3.05 0.41 71 12 111.3 165.6 20.4 11.4 24.3 371 552 68 38 81 3.33 3.05 0.41 72 12 103.6 158.4 20 9.2 24.8 259 396 50 23 62 2.5 2.89 0.41 73 12 129.5 198 25 11.5 31 259 396 50 23 62 2 2.89 0.41 74 12 110.33 168.7 21.3 9.8 26.41 259 396 50 23 62 2.35 2.89 0.411 75 20 154.5 199 19.9 15.2 13.27 559 720 72 55 48 3.62 4.47 0.411 76 20 154.5 199 19.9 15.2 13.27 559 720 72 55 48 3.62 4.47 0.411 77 24 133.5 165.6 12.9 8.7 11.4 445 552 43 29 38 3.33 5.16 0.414 78 24 133.5 165.6 12.9 8.7 11.4 445 552 43 29 38 3.33 5.16 0.414 79 12 86.1 162 21 19.8 24.6 287 540 70 66 82 3.33 2.13 0.414 80 12 100.45 189 24.5 23.1 28.7 287 540 70 66 82 2.86 2.13 0.414 81 12 131.2 198.4 24 17.6 27.21 246 372 45 33 51 1.88 2.95 0.415 82 12 114.8 173.6 21 15.4 23.8 246 372 45 33 51 2.14 2.95 0.415 83 12 123 186 22.5 16.5 25.5 246 372 45 33 51 2 2.95 0.415 84 12 106.6 161.2 19.5 14.3 22.1 246 372 45 33 51 2.31 2.95 0.415 85 12 105.2 177.6 20.4 18.8 26.4 263 444 51 47 66 2.5 2.45 0.417 86 12 130 187.2 27.6 11.2 25.6 325 468 69 28 64 2.5 3.27 0.419 87 20 137.5 185 20 15 13 550 740 80 60 52 4 3.89 0.419 88 20 137.5 185 20 15 13 550 740 80 60 52 4 3.89 0.419 89 20 129.25 173.9 18.8 14.1 12.22 550 740 80 60 52 4.26 3.89 0.419 90 20 129.25 173.9 18.8 14.1 12.22 550 740 80 60 52 4.26 3.89 0.419 91 20 134.75 181.3 19.6 14.7 12.74 550 740 80 60 52 4.08 3.89 0.419 92 20 134.75 181.3 19.6 14.7 12.74 550 740 80 60 52 4.08 3.89 0.419 93 20 126.5 170.2 18.4 13.8 11.96 550 740 80 60 52 4.35 3.89 0.419 94 20 126.5 170.2 18.4 13.8 11.96 550 740 80 60 52 4.35 3.89 0.419 95 20 148.5 199.8 21.6 16.2 14.04 550 740 80 60 52 3.7 3.89 0.419 96 20 148.5 199.8 21.6 16.2 14.04 550 740 80 60 52 3.7 3.89 0.419 97 20 123.75 166.5 18 13.5 11.7 550 740 80 60 52 4.44 3.89 0.419 98 20 123.75 166.5 18 13.5 11.7 550 740 80 60 52 4.44 3.89 0.419 99 20 143 192.4 20.8 15.6 13.52 550 740 80 60 52 3.85 3.89 0.419 100 20 143 192.4 20.8 15.6 13.52 550 740 80 60 52 3.85 3.89 0.419

(241) These parameters for the gearbox, where the radially inner planets are all the same size and the radially outer planets are all the same size, but not necessarily the same as the inner, are believed to work:

(242) TABLE-US-00007 TABLE 7 Diameter # Outer Planet Planet Teeth Outer Planet Planet Total Solution Planets Sun Ring Outer Inner Sun Ring Outer Inner Pitch Ratio Error 1 25 165.00 195.00 9.90 13.80 550 650 33 46 3.33 6.50 0.028 2 22 137.18 184.90 12.20 17.35 506 682 45 64 3.69 3.87 0.028 3 18 115.20 172.80 18.40 15.73 432 648 69 59 3.75 3.00 0.030 4 18 129.60 194.40 20.70 17.70 432 648 69 59 3.33 3.00 0.030 5 25 144.00 180.00 8.40 15.60 600 750 35 65 4.17 5.00 0.031 6 25 156.00 195.00 9.10 16.90 600 750 35 65 3.85 5.00 0.031 7 22 115.82 156.10 10.30 14.65 506 682 45 64 4.37 3.88 0.036 8 22 110.00 167.20 15.80 16.20 550 836 79 81 5.00 2.92 0.038 9 22 118.35 179.90 17.00 17.43 550 836 79 81 4.65 2.92 0.040 10 19 142.50 180.50 13.00 15.50 570 722 52 62 4.00 4.75 0.056 11 22 118.80 167.20 9.20 19.60 594 836 46 98 5.00 3.45 0.058 12 39 129.62 168.50 11.30 9.97 390 507 34 30 3.01 4.33 0.063 13 39 143.38 186.40 12.50 11.03 390 507 34 30 2.72 4.33 0.066 14 38 159.60 199.50 9.80 12.95 456 570 28 37 2.86 5.00 0.068 15 38 136.80 171.00 8.40 11.10 456 570 28 37 3.33 5.00 0.068 16 42 123.20 156.80 10.40 8.00 462 588 39 30 3.75 4.67 0.072 17 42 138.60 176.40 11.70 9.00 462 588 39 30 3.33 4.67 0.072 18 42 154.00 196.00 13.00 10.00 462 588 39 30 3.00 4.67 0.072 19 34 142.80 163.20 9.00 6.00 476 544 30 20 3.33 8.00 0.073 20 34 166.60 190.40 10.50 7.00 476 544 30 20 2.86 8.00 0.073 21 32 136.00 184.00 15.00 11.50 544 736 60 46 4.00 3.83 0.081 22 32 122.40 165.60 13.50 10.35 544 736 60 46 4.44 3.83 0.081 23 17 132.60 198.90 15.60 24.97 170 255 20 32 1.28 3.00 0.083 24 17 129.20 193.80 15.20 24.33 170 255 20 32 1.32 3.00 0.083 25 17 115.60 173.40 13.60 21.77 170 255 20 32 1.47 3.00 0.083 26 17 119.00 178.50 14.00 22.41 170 255 20 32 1.43 3.00 0.083 27 17 122.40 183.60 14.40 23.05 170 255 20 32 1.39 3.00 0.083 28 17 125.80 188.70 14.80 23.69 170 255 20 32 1.35 3.00 0.083 29 17 108.80 163.20 12.80 20.49 170 255 20 32 1.56 3.00 0.083 30 17 112.20 168.30 13.20 21.13 170 255 20 32 1.52 3.00 0.083 31 17 105.40 158.10 12.40 19.85 170 255 20 32 1.61 3.00 0.083 32 30 132.00 180.00 12.40 14.40 330 450 31 36 2.50 3.75 0.086 33 30 129.87 177.10 12.20 14.17 330 450 31 36 2.54 3.75 0.088 34 22 130.90 161.70 11.90 10.50 374 462 34 30 2.86 5.25 0.089 35 22 149.60 184.80 13.60 12.00 374 462 34 30 2.50 5.25 0.089 36 18 132.30 182.70 10.50 22.75 378 522 30 65 2.86 3.63 0.089 37 18 113.40 156.60 9.00 19.50 378 522 30 65 3.33 3.63 0.089 38 18 119.70 165.30 9.50 20.58 378 522 30 65 3.16 3.63 0.089 39 18 138.60 191.40 11.00 23.83 378 522 30 65 2.73 3.63 0.089 40 18 126.00 174.00 10.00 21.66 378 522 30 65 3.00 3.63 0.089 41 30 134.13 182.90 12.60 14.63 330 450 31 36 2.46 3.75 0.089 42 19 117.93 179.70 13.30 22.76 399 608 45 77 3.38 2.91 0.096 43 23 138.00 172.50 15.90 7.50 460 575 53 25 3.33 5.00 0.097 44 23 155.36 194.20 17.90 8.45 460 575 53 25 2.96 5.00 0.098 45 17 107.93 166.80 20.20 14.42 187 289 35 25 1.73 2.83 0.184 46 17 126.63 195.70 23.70 16.92 187 289 35 25 1.48 2.83 0.185 47 22 126.50 187.00 14.50 20.00 506 748 58 80 4.00 3.09 0.105 48 22 143.00 176.00 15.50 8.50 286 352 31 17 2.00 5.33 0.107 49 22 158.68 195.30 17.20 9.43 286 352 31 17 1.80 5.33 0.109 50 22 155.92 191.90 16.90 9.27 286 352 31 17 1.83 5.33 0.109 51 22 130.08 160.10 14.10 7.73 286 352 31 17 2.20 5.33 0.109 52 22 127.32 156.70 13.80 7.57 286 352 31 17 2.25 5.33 0.109 53 25 137.20 176.40 9.80 14.90 350 450 25 38 2.55 4.50 0.112 54 25 140.00 180.00 10.00 15.20 350 450 25 38 2.50 4.50 0.112 55 25 138.60 178.20 9.90 15.05 350 450 25 38 2.53 4.50 0.112 56 25 135.80 174.60 9.70 14.75 350 450 25 38 2.58 4.50 0.112 57 25 134.40 172.80 9.60 14.59 350 450 25 38 2.60 4.50 0.112 58 25 154.00 198.00 11.00 16.72 350 450 25 38 2.27 4.50 0.112 59 25 155.40 199.80 11.10 16.87 350 450 25 38 2.25 4.50 0.112 60 25 126.00 162.00 9.00 13.68 350 450 25 38 2.78 4.50 0.112 61 25 148.40 190.80 10.60 16.11 350 450 25 38 2.36 4.50 0.112 62 25 151.20 194.40 10.80 16.42 350 450 25 38 2.31 4.50 0.112 63 25 152.60 196.20 10.90 16.57 350 450 25 38 2.29 4.50 0.112 64 25 149.80 192.60 10.70 16.27 350 450 25 38 2.34 4.50 0.112 65 25 133.00 171.00 9.50 14.44 350 450 25 38 2.63 4.50 0.112 66 25 124.60 160.20 8.90 13.53 350 450 25 38 2.81 4.50 0.112 67 25 123.20 158.40 8.80 13.38 350 450 25 38 2.84 4.50 0.112 68 25 121.80 156.60 8.70 13.23 350 450 25 38 2.87 4.50 0.112 69 25 127.40 163.80 9.10 13.83 350 450 25 38 2.75 4.50 0.112 70 25 128.80 165.60 9.20 13.99 350 450 25 38 2.72 4.50 0.112 71 25 131.60 169.20 9.40 14.29 350 450 25 38 2.66 4.50 0.112 72 25 130.20 167.40 9.30 14.14 350 450 25 38 2.69 4.50 0.112 73 25 141.40 181.80 10.10 15.35 350 450 25 38 2.48 4.50 0.112 74 25 142.80 183.60 10.20 15.51 350 450 25 38 2.45 4.50 0.112 75 25 144.20 185.40 10.30 15.66 350 450 25 38 2.43 4.50 0.112 76 25 145.60 187.20 10.40 15.81 350 450 25 38 2.40 4.50 0.112 77 25 147.00 189.00 10.50 15.96 350 450 25 38 2.38 4.50 0.112 78 25 142.50 187.50 12.90 14.40 475 625 43 48 3.33 4.17 0.113 79 25 125.93 165.70 11.40 12.73 475 625 43 48 3.77 4.17 0.115 80 21 130.13 185.90 18.00 14.76 441 630 61 50 3.39 3.33 0.116 81 19 140.18 185.40 11.90 19.04 589 779 50 80 4.20 4.10 0.119 82 35 175.00 192.50 8.50 8.00 350 385 17 16 2.00 11.00 0.119 83 34 150.09 180.10 10.30 8.54 510 612 35 29 3.40 6.00 0.121 84 19 117.80 155.80 10.00 16.00 589 779 50 80 5.00 4.10 0.122 85 20 117.59 170.30 14.80 16.42 580 840 73 81 4.93 3.23 0.124 86 34 153.00 183.60 10.50 8.70 510 612 35 29 3.33 6.00 0.124 87 20 116.00 168.00 14.60 16.20 580 840 73 81 5.00 3.23 0.125 88 32 172.80 192.00 8.40 9.60 576 640 28 32 3.33 10.00 0.125 89 23 138.67 184.90 10.30 18.34 552 736 41 73 3.98 4.00 0.126 90 24 116.72 158.40 13.20 11.46 336 456 38 33 2.88 3.80 0.127 91 24 124.67 169.20 14.10 12.24 336 456 38 33 2.70 3.80 0.127 92 24 125.56 170.40 14.20 12.33 336 456 38 33 2.68 3.80 0.127 93 24 126.44 171.60 14.30 12.42 336 456 38 33 2.66 3.80 0.127 94 24 120.25 163.20 13.60 11.81 336 456 38 33 2.79 3.80 0.127 95 24 122.91 166.80 13.90 12.07 336 456 38 33 2.73 3.80 0.127 96 24 117.60 159.60 13.30 11.55 336 456 38 33 2.86 3.80 0.127 97 24 115.83 157.20 13.10 11.38 336 456 38 33 2.90 3.80 0.127 98 24 114.95 156.00 13.00 11.29 336 456 38 33 2.92 3.80 0.127 99 24 123.79 168.00 14.00 12.16 336 456 38 33 2.71 3.80 0.127 100 24 121.14 164.40 13.70 11.90 336 456 38 33 2.77 3.80 0.127

(243) Whether by material choice, stiffness reducing geometric features, or both, the planet gear should have a torsional stiffness such that the inner and outer gears may flex torsionally enough to take up any manufacturing tolerance in the gears and ensure proper gear tooth contact on both the inner and outer gearsets, while retaining enough torsional stiffness to keep the inner and outer planet gears axially aligned in the system and able to transmit a local torque of a magnitude correlating to the intended maximum torque of the gear system. In addition, the bending stiffness of the planet gear should be sufficient to prevent slipping of the gear teeth due to planet bending deflection.

(244) In the claims, the word “comprising” is used in its inclusive sense and does not exclude other elements being present. The indefinite articles “a” and “an” before a claim feature do not exclude more than one of the feature being present. Each one of the individual features described here may be used in one or more embodiments and is not, by virtue only of being described here, to be construed as essential to all embodiments as defined by the claims.

(245) The various embodiments described above can be combined to provide further embodiments. These and other changes can be made to the embodiments in light of the above-detailed description. In general, in the following claims, the terms used should not be construed to limit the claims to the specific embodiments disclosed in the specification and the claims, but should be construed to include all possible embodiments along with the full scope of equivalents to which such claims are entitled. Accordingly, the claims are not limited by the disclosure.