Patent Publication Number: US-2020278017-A1

Title: Rounded Strain Wave Gear Flexspline Utilizing Bulk Metallic Glass-Based Materials and Methods of Manufacture Thereof

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     The current application claims the benefit of and priority under 35 U.S.C. § 119(e) to U.S. Provisional Patent Application No. 62/811,798 entitled “Design for a Rounded Strain Wave Gear Flexspline Utilizing Bulk Metallic Glass-Based Materials” filed Feb. 28, 2019. The disclosure of U.S. Provisional Patent Application No. 62/811,798 is hereby incorporated by reference in its entirety for all purposes. 
    
    
     GOVERNMENT SPONSORED RESEARCH 
     This invention was made with government support under Grant Number 80NM0018D004, awarded by NASA (JPL). The government has certain rights in the invention. 
    
    
     FIELD OF THE INVENTION 
     The present invention generally relates to apparatus and systems for a rounded strain wave gear flexspline utilizing bulk metallic glass-based materials; and more particularly to a change of the flexspline geometry that reduces low cycle fatigue failure. 
     BACKGROUND OF THE INVENTION 
     Harmonic drives (HDs) are used widely in robotics as a method for achieving high gear reductions and for driving force transmissions. HDs were developed to take advantage of the elastic dynamics of metals, particularly the expansion of a metal ring to engage gear teeth without exceeding the elastic limit of the ring, which would cause permanent (i.e. plastic) deformation. The HD is made of three components: a wave generator, a flexspline (a.k.a. an inner race), and a circular spline (a.k.a. an outer race) ( FIG. 1 ). The wave generator is an elliptical cam with small ball-bearings built into the outer circumference and is usually attached to the input shaft. The flexspline, is a thin metal cup with external gear teeth and contains a diaphragm at the bottom of the cup for connecting to an output shaft. The circular spline is a steel ring with internal teeth and is usually fixed to a casing. The circular spline has two more teeth than the flexspline and the diameter of the circular spline is slightly larger than the flexspline such that if they were put together without the wave generator, they would be concentric and their teeth wouldn&#39;t touch. 
     In operation, the flexspline is deflected by the motion of the elliptical wave generator, which forces the teeth at the major axis of the ellipse to engage with the circular spline (while the teeth at the minor axis are completely disengaged). When the wave generator completes 180 degrees of motion, the flexspline has moved by one tooth relative to the circular spline. The movement of the flexspline is the output power. 
     HDs have many characteristics that make their use critical in robotics applications. They have high-speed reduction ratios of 1/30 to 1/320, which provides high efficiency gearing without using complex mechanisms. HDs operate with nearly zero backlash and have extremely high precision. They have small numbers of components and assemble easily and they can generally be small-sized and lightweight. HDs have high torque capacity due to the use of fatigue resistance steel in the flexspline and they have high efficiency. 
     BRIEF SUMMARY OF THE INVENTION 
     Methods and systems for designing low cost wave generator for metal strain wave gearing are illustrated. 
     Many embodiments are directed to a cup-type flexspline for a metal strain wave gear comprising, a base, and a vertical wall, where the vertical wall transitions through a curvature to the base, where an input shaft is disposed at the base; wherein the vertical wall is circular with an outer wall diameter, where the flexspline maintains circularity along the rotational axis of the vertical wall; where the maximum radius of curvature at the base of the cup is at least 10% of the diameter of the flexspline in accordance with the equation: 
     
       
         
           
             
               
                 
                   
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     In many other embodiments, the radius of curvature is between about 15% to about 20% of the diameter of the flexspline. 
     In still many other embodiments, the flexspline has a flush input base. 
     In yet many other embodiments, the flexspline has a hemispherical base curvature. 
     In still yet many other embodiments, the flexspline has an elliptical base curvature. 
     In still yet many other embodiments, the flexspline comprises a bulk metallic glass-based material. 
     In further embodiments, the bulk metallic glass-based material is a bulk metallic glass. 
     In yet many embodiments, the bulk metallic glass-based material is a bulk metallic glass matrix composite. 
     In still yet many other embodiments, the flexspline has a fatigue life of at least 10% longer than a flexspline with the radius of curvature between about 1% to about 2% when run at the same torque. 
     In still yet other embodiments, the flexspline is formed using a net shape process. 
     In still yet many other embodiments, the flexspline forming technique is one of: an injection molding technique; a die casting technique; a 3D printing technique; a thermoplastic forming technique; a blow molding technique; a discharge forming technique; a metal injection molding technique; a pressing with powder technique; a suction casting technique; and a forming from sheet metal technique. 
     In still yet many other embodiments, the flexspline comprises a brittle material, wherein the brittle material has a fracture toughness less than about 50 MPa m 1/2 . 
     In still yet many other embodiments, the flexspline comprises a metal alloy, wherein the metal alloy has less than about 10% ductility in a tension test. 
     In still yet many other embodiments, the flexspline comprises at least one of tool steel, nanocrystalline metals, nanograined metals, ceramics, and metal matrix composites. 
     In still yet many other embodiments, the flexspline comprises a laminate of at least two materials. 
     In still yet many other embodiments, the laminate material comprises at least one of metal, and carbon fiber with a metal coating. 
     Additional embodiments and features are set forth in part in the description that follows, and in part will become apparent to those skilled in the art upon examination of the specification or may be learned by the practice of the disclosure. A further understanding of the nature and advantages of the present disclosure may be realized by reference to the remaining portions of the specification and the drawings, which forms a part of this disclosure. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The description will be more fully understood with reference to the following figures, which are presented as exemplary embodiments of the invention and should not be construed as a complete recitation of the scope of the invention, wherein: 
         FIG. 1  illustrates a strain wave in accordance with the prior art. 
         FIG. 2  conceptually illustrates a flexspline geometry configured to reduce low cycle fatigue failure when the flexspline is made from a brittle metal in accordance with embodiments. 
         FIGS. 3A-3B  illustrate flexsplines manufactured from solid billets or castings using conventional machining processes, such as lathing, milling, or grinding in accordance with the prior art. 
         FIG. 4  illustrates three common sizes of strain wave gear flexsplines made from machined steel, where the flexspline has a flat input that interfaces with a component to transmit torque in accordance with the prior art. 
         FIG. 5  illustrates the cross-section of a machined steel size CSF-20 flexspline showing a radius of curvature in accordance with the prior art. 
         FIGS. 6A-6D  illustrate a stress concentration is created when replicating a machined steel flexspline during injection molding of bulk metallic glass (BMG) in accordance with embodiments. 
         FIG. 7  illustrates injection molded bulk metallic glass flexsplines, where these parts are cast to replicate the shape of the machined steel versions, which are designed to maximize torque due to the straight walls in accordance with embodiments. 
         FIGS. 8A-8C  illustrate a blow molding process that thermoplastically forms BMGs into flexsplines, where replicating the steel version creates sharp edges in accordance with embodiments. 
         FIGS. 9A-9B  illustrate a BMG flexspline loaded and the subsequent low cycle fatigue failure due to the low toughness of the BMG in accordance with embodiments. 
         FIG. 10  illustrates a BMG flexspline connected to an input shaft and then to an outer spline to drive torque, where sharp corners are removed in accordance with embodiments. 
         FIG. 11  illustrates a low cycle fatigue crack in a CSF-20-50 BMG flexspline after approximately 20,000 cycles at 30 Nm of torque, where the crack originates from the stress concentration at a small radius of curvature in accordance with embodiments. 
         FIG. 12  illustrates a BMG flexspline sheared off under load at the location of a stress concentration in accordance with embodiments. 
         FIG. 13  illustrates the maximum possible radius of curvature at the edge of the cup based on the fixed diameters of the flexspline wall and the input base in accordance with embodiments. 
         FIGS. 14A-14D  illustrate stress concentration reduction by rounding the bottom of the cup in accordance with embodiments. 
         FIGS. 15A-15D  illustrate a modified blow molding process that allows a curve to form at the edges of the flexspline in accordance with embodiments. 
         FIG. 16  illustrates a flexspline geometry that has a hemispherical base with a protruding flat input base in accordance with embodiments. 
         FIG. 17  illustrates a flexspline geometry that has an elliptical radius of curvature in accordance with embodiments. 
         FIG. 18  illustrates a flexspline geometry that has an input base flush to the flexspline, eliminating another sharp stress concentration in accordance with embodiments. 
         FIG. 19  illustrates a flexspline geometry that has two different spherical radii of curvature that make up the rounded corners of the flexspline in accordance with embodiments. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     Turning now to the drawings, cup-type flexsplines for metal strain wave gears, and systems and methods for their design and manufacture, are described. In many embodiments, the cup-type flexspline has a base and a vertical wall, where the vertical wall transitions through a curvature to the base. An input shaft locates at the base of the flexspline and has a diameter. The vertical wall is in a circular shape with an outer wall diameter, and the flexspline maintains circularity along the rotational axis of the vertical wall. Many embodiments of the invention describe a flexspline that the cup of the flexspline is free from sharp edges and with a rounded bottom with curvature maximized based on the geometry of the flexspline. Many embodiments describe the maximum radius of curvature at the base of the cup is at least 10% of the diameter of the flexspline. Many other embodiments highlight that the radius of curvature is between about 15% to about 20% of the diameter of the flexspline. Flexsplines according to such embodiments demonstrate improved fatigue life of at least about 10% over designs with sharp angles between the base and the wall when run at the same torque. 
     In many embodiments, the flexspline has a hemispherical base curvature. In some other embodiments, the flexspline has an elliptical base curvature. In some embodiments, the flexspline has a flush input base. In some other embodiments, the flexspline has two different spherical radii of curvature. Many embodiments describe that the flexspline is made of bulk metallic glass-based material. Many embodiments reveal that the bulk metallic glass-based material can be made from near or net-shaped processes, such as injection molding, die casting, 3D printing, thermoplastic forming, blow molding, discharge forming, metal injection molding, pressing with powder, suction casting, forming from sheet metal or a variety of other processes whereby feedstock is formed into the flexspline in a single step without significant machining. In many embodiments, the flexspline is made from a brittle material with a fracture toughness of less than about 50 MPa m 1/2 . In some other embodiments, the flexspline is made from a metal alloy with less than about 10% ductility in a tension test. In some other embodiments, the flexspline is made from tool steel, nanocrystalline metals, nanograined metals, ceramics, or metal matrix composites. 
     Harmonic drives are one of the driving factors in the early formulation of spacecraft design because they limit the size of the spacecraft. Harmonic drives are also used very heavily on Jet Propulsion Lab rovers, including many that were integrated into the Mars Exploration Rovers (MER). Developing low cost harmonic drives or high performance drives is game-changing for future NASA missions and for terrestrial robotics. 
     Harmonic drives were developed to take advantage of the elastic dynamics of metals, particularly the expansion of a metal ring to engage gear teeth without exceeding the elastic limit of the ring, which would cause permanent (i.e. plastic) deformation. The harmonic drive is made of three components: a wave generator, a flexspline (a.k.a. an inner race), and a circular spline (a.k.a. an outer race). 
       FIG. 1  illustrates an exploded view of a typical strain wave gear that can be fabricated from BMG-based materials in accordance with embodiments of the invention. In particular, the strain wave gear  100  includes a wave generator  102 , a flexspline  108 , and a circular spline  112 . The illustrated wave generator  102  includes a wave generator plug  104  and a ball bearing  106 . Importantly, the wave generator plug  104  is elliptical in shape, and is disposed within the ball bearing  106  so that the ball bearing  106  conforms to the elliptical shape. In this arrangement, the outer race of the ball bearing  106  can rotate relative to the wave generator plug  104 . 
     In the illustrated embodiment, the flexspline  108  is depicted as being in the shape of a cup; notably, the outer rim of the cup includes a set of gear teeth  110 . In the illustration, the flexspline is fitted over the ball bearing, such that the outer rim of the flexspline conforms to the aforementioned elliptical shape. Note that in this arrangement, the ball bearing allows the flexspline to rotate relative to the wave generator plug. The circular spline,  112  is in the shape of a ring; importantly, the inner perimeter of the ring includes a set of gear teeth. Normally, there are more gear teeth on the circular spline  114  than on the flexspline  110 . In many instances there are two more gear teeth on the circular spline  112  than on the flexspline  108 . Typically, the flexspline  108  is fitted within the circular spline  112  such that the gear teeth of the flexspline  110  engage the gear teeth of the circular spline  114 . Notably, because the gear teeth of the flexspline  110  conform to an elliptical shape, only the gear teeth proximate the major axis of the elliptical shape engage the gear teeth of the circular spline  114  in the usual case. Conversely, the gear teeth of the flex spline  110  that are proximate the minor axis of the elliptical shape are disengaged from the gear teeth of the circular spline  114 . In many instances, 30% of the gear teeth of the flexspline  110  are engaged with the gear teeth of the circular spline  114 . With this arrangement, the wave generator plug  104  can rotate in a first direction about the central axis of the elliptical shape, and thereby cause the flexspline  108  to rotate in a second opposite direction and at a different rate of rotation (generally slower) about the central axis of the elliptical shape. This can be achieved as the flexspline  108  is made of a flexible material that can accommodate the deflections that may result from the rotation of the wave generator plug  104 . 
     The primary method by which strain wave gear flexsplines are manufactured is through the machining of steel.  FIGS. 3A-3B  illustrate methods where flexsplines are manufactured from solid billets or castings using conventional machining processes, such as lathing, milling, or grinding. A lathe  301  rotates a flexspline about an axis of rotation to perform cutting by the cutting tool  302 . A straight edge  303  of the flexspline is shown in  FIG. 3B . In this method, machining a large radius of curvature is challenging compared to a straight edge. 
     The vast majority of current commercial flexsplines are made of steel, which is known for its combination of high toughness and wear resistance. Typical cup-type flexsplines are made with a vertical wall that transitions through a 90 degree angle to a base where an input shaft is located.  FIG. 4  depicts three common sizes of strain wave gear flexspline:  401  is CSF-32 flexspline,  402  is the CSF-20 flexspline, and  403  is CSF-8 flexspline. Each flexspline is made from machined steel, and has a radius of curvature  404  between the base of the cup  405  and the wall  406  of about 1% to about 2% of the diameter of the wall. The flexspline has a flat input that interfaces with a component to transmit torque. The base  405  is preferably to be flat to make a mating interface. Due to the high toughness of steel, the small radius of curvature  404  is sufficient to prevent fracture. 
     The torque that the flexspline can support is a function of the size of the flexspline cup, its length and the number of teeth on the flexspline outer wall. Due to the very high toughness of steel and the limitations of conventional machining, a very small radius of curvature is added to the bottom of the flexspline cup, typically about 1% to about 2% of the diameter of the flexspline.  FIG. 5  shows the cross-section of a typical machined steel size CSF-20 flexspline with a radius of curvature  501  of about 1 millimeter, which is about 1% to 2% of the diameter of the flexspline. Machining larger radii of curvature is more difficult due to the necessity of keeping the flexspline perfectly symmetric along its rotational axes. Due to the high toughness of steel, the small radius of curvature is not a normal location of failure of the flexspline, which normally fails due to buckling of the flexspline wall or the degradation of the flexspline teeth. In operation, a steel flexspline is rarely expected to crack or fail due to a stress concentration. 
     Despite the high performance of steel in the flexspline, it is expensive to manufacture due to the difficulty with machining steel, the high-tolerance features, and the very thin wall. Bulk metallic glasses (BMGs) have been demonstrated to be ideal candidates for flexsplines because they can be manufactured using near or net-shaped processes, such as injection molding, die casting, thermoplastic forming, metal injection molding or a variety of other processes whereby feedstock is formed into the flexspline in a single step without significant machining. (See e.g., U.S. Pat. No. 9,328,813 B2 to Hofmann et al., U.S. Pat. No. 10,151,377 B2 to Hofmann et al., U.S. patent application Ser. No. 15/918,831 to Hofmann et al., U.S. patent application Ser. No. 62/811,765 to Hofmann et al.; the disclosures of which are hereby incorporated by reference.) 
     BMG-based material flexsplines have been manufactured to mimic the shape of the steel flexsplines, which contain several locations of stress concentrations. As an example,  FIGS. 6A-6D  illustrate an injection molding technique that can be implemented to form a flexspline of a strain wave gear in accordance with embodiments of the invention. In particular,  FIG. 6A  depicts that a molten BMG-based material  601  that has been heated to a molten state and is thereby ready to be inserted into a mold  602 . The mold  602  helps define the shape of the flexspline to be formed.  FIG. 6B  depicts that the molten BMG-based material  601  is pressed into the mold  602 .  FIG. 6C  depicts that the mold  602  is released after the BMG-based material has cooled.  FIG. 6D  depicts that any excess flash  603  is removed. Thus, it is depicted that a strain wave gear component is fabricated using direct casting techniques in conjunction with a BMG-based material in accordance with embodiments of the invention. Note that the straight edge of the flexspline  604  from replicating the steel flexspline models creates stress concentration.  FIG. 7  shows the BMG-based material flexsplines made with injection molding technique. The flexsplines have been cast to replicate the shape of the machined steel versions, which are designed to maximize torque due to the straight walls. 
       FIGS. 8A-8C  illustrate the forming of a flexspline using blow molding techniques. In particular,  FIG. 8A  depicts that a BMG-based material  801  is placed within a mold  802 .  FIG. 8B  depicts that the BMG-based material  801  is exposed to pressurized gas or liquid that forces the BMG-based material to conform to the shape of the mold  802 . Typically, a pressurized inert gas is used. The BMG-based material  801  is usually heated so that it is sufficiently pliable and can be influenced by the pressurized gas or liquid. Again, any suitable heating technique can be implemented in accordance with embodiments of the invention.  FIG. 8C  depicts that due to the force of the pressurized gas or liquid, the BMG-based material conforms to the shape of the mold  802 . Replicating the steel flexspline creates sharp edges  803  in the BMG-based flexspline. 
     However, unlike steel, BMG-based materials are known for having much lower fracture toughness and fatigue life. In fact, BMG flexsplines tend to fail via cracking or shearing at much lower number of cycles than their steel counterparts. BMG-based materials are typically associated with fracture toughness less than about 50 MPa m 1/2  whereas steel is normally greater than about 100 MPa m 1/2 . Fatigue strengths of steel are typically greater than about 20% of their yield strength whereas BMG-based materials normally fail at less than about 10% of their yield strengths at about 107 cycles. 
     As an example,  FIGS. 9A-9B  illustrate schematically a BMG flexspline fatigue failure due to the low toughness of the BMG-based material.  FIG. 9A  depicts the outer spline  901  rotates counter clockwise along the axis of rotation of the flexspline, while the input shaft  903  rotates clockwise along the axis of rotation. The brittle BMG-based material flexspline  902  is loaded. The straight edge of the flexspline creates the stress concentration  904 .  FIG. 9B  depicts the low cycle fatigue failure  905  due to the low toughness of the BMG-based material. For brittle materials, like BMG, stress concentration creates premature failure under loading. 
       FIG. 10  illustrates the stress concentration in a BMG-based material flexspline. A BMG flexspline  1001  is connected to an input shaft  1003 , and then to an outer spline  1004  to drive torque. Due to the brittle nature of the BMG, sharp corners  1002  are locations of failure.  FIG. 11  shows a fatigue crack in a CSF-20-50 BMG flexspline. The low cycle fatigue crack  1101  appears in the flexspline after approximately 20,000 cycles at 30 Nm of torque. The crack originates from the stress concentration at the small radius of curvature  1102 .  FIG. 12  shows a BMG flexspline that has been sheared off under load at the location of a stress concentration. These types of failure do not occur in steel flexsplines. 
     Although BMGs can be cast for potentially much lower cost than steel, their brittle nature makes them perform worse, despite their higher strength (about 2000 MPa compared to about 500 MPa for steel), higher wear resistance, lower elastic modulus (about 90 GPa compared to about 215 GPa for steel), higher elasticity (about 2% compared to about 0.1% for steel), and corrosion resistance. Improving the design of the flexspline could simultaneously improve performance and reduce the difficulty with net-shaped casting. 
     Embodiments Implementing Rounded Bulk Metallic Glass-Based Materials Flexsplines 
     Many embodiments of the invention describe a strain wave gear flexspline where the cup of the flexspline is free from sharp edges and with a rounded bottom with curvature maximized based on the geometry of the flexspline ( FIG. 2 ). Compared to a steel flexspline, the new design will have the same outer diameter, the same number of teeth and profile, the length of the flexspline, the same size and shape of the input shaft/base, the same wall thickness near the teeth, but will have a rounded bottom where the input shaft/base transitions to the straight wall of the flexspline. Embodiments demonstrate that the large radius of curvature of the flexspline improves the performance of a BMG-based material flexspline by reducing low cycle fatigue failures due to stress concentrations. 
     Many embodiments of the invention refer to bulk metallic glass (BMG) as an alloy which can be quenched into a vitreous state at a relatively large casting thickness (generally over 1 mm). BMGs can also be referred to as amorphous metals (AMs) and their composites as amorphous metal composites (AMCs). Many other embodiments of the invention refer to in-situ composite or bulk metallic glass matrix composite (BMGMC) as an alloy which, upon rapid cooling (cooling rate from about 1K/s to about 1000 K/s), chemically partitions into two or more phases, one being an amorphous matrix and the other(s) being crystalline inclusions. The term “bulk metallic glass-based materials” (BMG-based materials) includes both BMGs and BMGMCs. 
     Given that shearing and cracking is not a normal mode of failure for steel, changing the radius of curvature of the flexspline cup as described in many of the embodiments is not a conventional approach. Moreover, almost all flexsplines are machined from steel and small radii of curvatures are far easier to machine than large ones, especially when circularity must be maintained to high tolerances. In addition, flexspline cups having small radii of curvature maximize the operating torque of the strain wave gear. Nevertheless, embodiments implementing rounded edges are shown to improve the fatigue life of a BMG flexspline as compared to a straight wall cup. Moreover, the rounded shape reduces the net shaped manufacturing, as inserts normally used for casting around release much easier from the mold when they are round, as opposed to sharp. Accordingly, embodiments implementing brittle materials, like BMGs and others, simultaneously improve castability and fatigue life by increasing the curvature of the flexspline cup. 
     Rounded flexsplines according to embodiments decrease the performance of the strain wave gears, because rounded corners do not take as much load as straight walls. The performance of rounded flexsplines is compensated by the use of brittle materials in the flexsplines, which would otherwise crack in straight wall structures. In some embodiments, the brittle materials provide better performance in rounded flexsplines. In some other embodiments, the brittle materials are easier to manufacture. BMGs, according to such embodiments, can be cast into the flexsplines, which lowers the manufacturing cost of flexsplines. 
     Many embodiments of the invention remove stress concentrations at the base of the flexspline by adding a large radius of curvature to the base of the cup. Many embodiments increase the radius of curvature at the base of the flexspline cup from about 1% to about 2% of the flexspline diameter to at least 10% of the diameter of a standard flexspline while maintaining circularity along the rotational axis. Many other embodiments implement configurations that reduce other sharp edges in the apparatus. In various embodiments, cup-type flexsplines have a maximum radius of curvature of about 15% to about 20% based on the ratio of the input base diameter to the flexspline diameter. In many such embodiments, the maximum radius of curvature can be calculated with Equation 1: 
     
       
         
           
             
               
                 
                   
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       FIG. 13  illustrates a cup-type flexspline with a rounded edge according to many embodiments. Based on the fixed diameter of the flexspline wall and the input base, the maximum possible radius of curvature  1301  at the edge of the cup is 8 millimeter for a size CFS-20 flexspline. Without changing the diameter of the flexspline  1302  or the diameter of the input base  1303 , the BMG flexspline can support a radius of curvature between about 15% to about 20% of the diameter of the flexspline. As a comparison, a conventional steel cup-type CFS-20 flexspline as depicted in  FIG. 5  has a radius of curvature  501  of about 1 millimeter, which is about 1% to about 2% of the flexspline diameter. 
     Table 1 lists measurements of the diameter of the flexspline, the diameter of the input shaft/base, the approximate radius of curvature of the machined steel, the maximum radius of curvature possible and the maximum radius of curvature as a percentage of the diameter for three standard sizes of flexsplines. Overall, the radius of curvature of the machined steel is about 1% to about 2% of the diameter of the flexspline. By contrast, embodiments implement radius of curvature between about 15% to about 20% of the flexspline diameter, based on standard sizes. Embodiments demonstrate that the larger curvatures decrease the possible torque on the strain wave gear but reduces the stress concentrations of the BMG, resulting in longer life. Moreover, the rounded shape is easier to cast through near or net-shaped processes, such an injection molding, die casting, blow molding or metal injection molding. 
     
       
         
           
               
               
               
               
               
               
             
               
                 TABLE 1 
               
               
                   
               
               
                   
                   
                   
                   
                   
                 Maximum 
               
               
                   
                 Diameter  
                 Diameter 
                 Machined 
                 Maximum 
                 Radius of 
               
               
                   
                 of 
                 of 
                 Radius of 
                 Radius of 
                 Curvature  
               
               
                 Gear 
                 input shaft 
                 flexspline 
                 Curvature 
                 Curvature 
                 as % of  
               
               
                 size 
                 (mm) 
                 (mm) 
                 (mm) 
                 (mm) 
                 Diameter 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 CSF-8 
                 12.25 
                 20 
                 0.25 
                 3.875 
                 19% 
               
               
                 CSF-20 
                 48 
                 32 
                 1 
                 8 
                 17% 
               
               
                 CSF-32 
                 81 
                 52 
                 2 
                 14.5 
                 18% 
               
               
                   
               
            
           
         
       
     
     In various embodiments, rounded edge BMG-based material flexsplines are manufactured with direct casting techniques in accordance with embodiments of the invention. Rounded edges are easier to cast than sharp edges. As an example,  FIGS. 14A-14D  illustrate a modified injection molding process that can be implemented to form a round edge flexspline in accordance with embodiments of the invention. In particular,  FIG. 14A  depicts a molten BMG-based material  1402  that has been heated to a molten state and is thereby ready to be inserted into a mold  1403 . The mold  1403  helps define the shape of the flexspline to be formed to have rounded edges  1401 .  FIG. 14B  depicts that the molten BMG-based material  1402  is pressed into the rounded edge  1401  mold  1403 .  FIG. 14C  depicts that the mold  1403  is released after the BMG-based material has cooled.  FIG. 14D  depicts that any excess flash  1404  is removed. Note that the rounded edge of the cup of the flexspline  1401  reduces the stress concentration while simultaneously reduces the difficulty with manufacturing. 
       FIGS. 15A-15D  illustrate the forming a rounded flexspline using blow molding techniques. In particular,  FIG. 15A  depicts that a BMG-based material  1501  is placed within a mold  1502  with rounded edges  1503 .  FIG. 15B  depicts that the BMG-based material  1501  is exposed to pressurized gas or liquid that forces the BMG-based material to conform to the shape of the mold  1502 . Typically, a pressurized inert gas is used. The BMG-based material  1501  is usually heated so that it is sufficiently pliable and can be influenced by the pressurized gas or liquid. Again, any suitable heating technique can be implemented in accordance with embodiments of the invention.  FIG. 15C  depicts that due to the force of the pressurized gas or liquid, the BMG-based material conforms to the shape of the mold  1502  with rounded edges  1503 . The modified blow molding process allows a curve  1503  to form at the edges of the flexspline.  FIG. 15D  shows a prototype blow molded flexspline showing the natural tendency to form a hemisphere when expanding. This shape has the largest radius of curvature possible for the given diameter and thus the lowest stress concentration. 
     Many embodiments describe the flexspline is made at least in part of a bulk metallic glass-based material that has been manufactured into a near or net-shaped flexspline. The fatigue life of the flexspline is improved by at least 10% when run at the same torque as a flexspline made from the same material but with a standard flexspline design created for steel. Many embodiments describe that the BMG can be injection molded, die cast, 3D printed, thermoplastically formed, blow molded, discharge formed, metal injection molded, pressed with powder, suction cast, or formed from sheet metal. In other embodiments, the flexspline has an elliptical base curvature. Many other embodiments describe that the cracking during operation of the flexspline can be suppressed compared to a similar cup with a radius of curvature of about 1% to about 2% of the flexspline diameter. 
     Many other embodiments describe a flexspline of a cup-type strain wave gear that the radius of curvature at the base of the cup is at least 10% of the diameter of the flexspline. In some embodiments, the flexspline is made from a brittle material with a fracture toughness of less than 50 MPa m 1/2 . In some other embodiments, the flexspline is made from a metal alloy with less than 10% ductility in a tension test. In some other embodiments, the flexspline is made from tool steel, nanocrystalline or nanograined metals, ceramics, metal matrix composites. 
     Embodiments Implementing BMG-Based Material Flexsplines With A Spherical Radius Of Curvature 
     To accommodate BMG properties and manufacturing, many embodiments implement flexspline cups with features having reduced sharp edges.  FIG. 16  illustrates embodiments where the BMG-based material flexspline has a hemispherical base with a protruding flat input base. In such embodiments, the flexspline has a wall  1605  with a diameter, an input base  1602  with a diameter, and a hemispherical base  1604 . More particularly, the flexspline has a flat input base  1602  to connect to the input shaft. The radius of curvature of the hemisphere, according to such embodiments, depends on the diameter of the flexspline and the diameter of the input shaft. Many embodiments describe a radius of curvature of at least 10% of the diameter of the flexspline. Many other embodiments include the flexspline has a spherical radius of curvature. In some embodiments, the rounded base of the flexspline has axial symmetry around the rotational axis of the flexspline. Many other embodiments describe increasing the wall thickness to decrease stress concentrators. In many such embodiments, the diameter at the teeth  1601  of the flexspline and the thickness of the wall near the teeth do not change from the standard flexspline such that the flexspline will fit into a standard outer spline and wave generator. In many embodiments, the BMG flexspline can be used with a standard outer spline and wave generator based on the required size. However, the fatigue life and the manufacturing will be greatly enhanced through the rounding of the base. 
     Embodiments Implementing BMG-Based Material Flexsplines With An Elliptical Radius Of Curvature 
     Many other embodiments describe another design of the flexspline cup base that does not maintain the standard input base sizes and shapes.  FIG. 17  illustrates a BMG-based material flexspline, according to embodiments, having a hemispherical base with a protruding flat input base. In such embodiments, the flexspline has a wall  1705  with a diameter, an input base  1702  with a diameter, and a hemispherical base  1704 . The flexspline has a flat input base  1702  to connect to the input shaft. The radius of curvature of the rounded edge depends on the diameter of the flexspline and the diameter of the input shaft. Many embodiments describe the radius of curvature is at least 10% of the diameter of the flexspline. Many other embodiments include the flexspline has an elliptical radius of curvature. In some embodiments, the rounded base of the flexspline has axial symmetry around the rotational axis of the flexspline. In many such embodiments, the diameter at the teeth  1701  of the flexspline and the thickness of the wall near the teeth do not change from the standard flexspline such that the flexspline fits into a standard outer spline and wave generator. In many embodiments, the BMG flexspline can be used with a standard outer spline and wave generator based on the required size. However, the fatigue life and the manufacturing will be greatly enhanced through the rounding of the base. 
     Embodiments Implementing BMG-Based Material Flexsplines With A Flush Input Base 
     Many other embodiments describe embodiments including a flush input base such that when the flexspline is cast from BMG, it has an improved fatigue life of at least 10% over a BMG with a steel design when run at the same torque.  FIG. 18  illustrates embodiments of a BMG-based material flexspline with a flush input base. The flexspline has a wall  1805  with a diameter, an input base  1802  with a diameter, and a hemispherical base  1804 . The input shaft or base  1802  of the flexspline cup where connections are made is flush with the flexspline, to eliminate sharp stress concentration. The flush input base  1802  connects to the input shaft. The radius of curvature depends on the diameter of the flexspline and the diameter of the input shaft. Many embodiments describe the radius of curvature is at least 10% of the diameter of the flexspline. In some embodiments, the hemispherical base of the flexspline has axial symmetry around the rotational axis of the flexspline. In many such embodiments the diameter at the teeth  1801  of the flexspline and the thickness of the wall near the teeth do not change from the standard flexspline such that the flexspline will fit into a standard outer spline and wave generator. In many embodiments, the BMG flexspline can be used with a standard outer spline and wave generator based on the required size. However, the fatigue life and the manufacturing will be greatly enhanced through the rounding of the base. 
     Embodiments Implementing BMG-Based Material Flexsplines With Two Different Spherical Radii Of Curvature 
     In some other embodiments, the flexspline has two different spherical radii of curvature that make up the rounded corners of the flexspline.  FIG. 19  illustrates the BMG-based material flexspline has a rounded base with a flush input base. The flexspline has a wall  1905  with a diameter, an input base  1902  with a diameter, and a rounded base  1904 . The input base  1902  flushes to the flexspline and connects to the input shaft. The radius of curvature depends on the diameter of the flexspline and the diameter of the input shaft. Many embodiments describe two different spherical radii of curvature  1903  and  1903 ′ that comprise the rounded corners of the flexspline. Many embodiments describe the radius of curvature is at least 10% of the diameter of the flexspline. In many such embodiments the diameter at the teeth  1901  of the flexspline and the thickness of the wall near the teeth do not change from the standard flexspline such that the flexspline will fit into a standard outer spline and wave generator. In many embodiments, the BMG flexspline can still be used with a standard outer spline and wave generator based on the required size. However, the fatigue life and the manufacturing will be greatly enhanced through the rounding of the base. 
     DOCTRINE OF EQUIVALENTS 
     As can be inferred from the above discussion, the above-mentioned concepts can be implemented in a variety of arrangements in accordance with embodiments of the invention. Accordingly, although the present invention has been described in certain specific aspects, many additional modifications and variations would be apparent to those skilled in the art. It is therefore to be understood that the present invention may be practiced otherwise than specifically described. Thus, embodiments of the present invention should be considered in all respects as illustrative and not restrictive.