Patent Publication Number: US-2021190148-A1

Title: Pdm transmission with sliding contact between convex shaft pins and concave bearings surfaces

Description:
RELATED APPLICATIONS 
     This application is a continuation-in-part of, commonly-assigned U.S. Nonprovisional patent application Ser. No. 15/721,959, filed Oct. 1, 2017, shortly to be U.S. Pat. No. 10,934,778. Ser. No. 15/721,959 claims the benefit of, and priority to, commonly-assigned U.S. Provisional Patent Application Ser. No. 62/402,686, filed Sep. 30, 2016 (now expired). The disclosures of U.S. Pat. No. 10,934,778, and of application Ser. Nos. 15/721,959 and 62/402,686 are incorporated herein by reference in their entirety. 
    
    
     FIELD OF THE DISCLOSURE 
     This disclosure is directed generally to rotary power transmission assemblies particularly adapted for use in bottom hole assemblies (“BHAs”) in order to transfer torque generated by a subterranean positive displacement motor (“PDM”) to, for example, a rotary drill bit. In some embodiments, this disclosure is directed more specifically to such a transmission assembly using laminated rubber (or other elastomer) bearings elements having a “bridge”-style geometry in which a planar face opposes a generally concave curved face. In other embodiments, this disclosure is directed to transmission assembly embodiments using unlaminated or “monolithic” bearings elements (made of materials such as metal) that preferably also have the ‘bridge”-style geometry. 
     BACKGROUND OF THE DISCLOSED TECHNOLOGY 
     It is well understood that bottom hole assemblies (“BHAs”) include rotating power shafts that are necessarily misaligned by virtue of the BHA&#39;s design. For example, the rotation of the rotor in the PDM is eccentric and not concentric. This eccentric rotation of the rotor must be resolved into concentric rotation that will ultimately rotate the bit. Further, directional drilling in deviated wellbores necessarily causes misalignment of rotating power shafts in interconnected BHA components. 
     Specialized transmission sections designed for downhole applications transfer torque between such misaligned shafts. Conventionally, PDM transmission designs resolve the misalignment between input/output shafts via contact between cooperating components on each of the input and output shafts, and torque is transferred from input shaft to output shaft through internal bearings contact. Conventionally, such internal bearings contact is typically metal-to-metal. The metal-to-metal contact surfaces can deteriorate rapidly on some conventional designs, and in some downhole work environments. Deterioration can be a particular problem under heavy torque load. Such deterioration may shorten the service life of the transmission. Notable effects causing such shortened service life include galling of the metal-to-metal contact surfaces and resulting fretting and general erosion of the metal. 
     There are several types of PDM transmission designs known in the art. Constant Velocity (or CV) joint styles include: (1) ball bearing designs, in which torque is transferred via a pre-designed number of mating ball and socket couplings (typically 6 to 8); (2) spline designs, in which the cooperating metal surfaces have interlocking splines and receptacles; (3) woodruff key designs, in which torque is transferred via wedges, semicircles or other shapes; and (4) elliptical roller bearing designs, which are similar to ball bearing designs except with elongated ball and socket couplings (i.e. elliptical shapes) in order to provide more contact length in each coupling for better torque load distribution and transfer. 
     Other PDM transmission styles known in the art include: (1) flex shaft designs, in which an elongated input shaft resolves eccentric rotation into concentric rotation by flexing over its length; (2) flex shaft/CV joint combination and hybrid designs; and (3) knuckle joint designs, in which opposing tabs and slots interlock in a bending “knuckle” configuration to transfer torque with high sliding force contact and drilling mud exposure. 
     Even small amounts of fretting and other erosion can also cause loss of design kinematics in conventional transmission designs with metal/metal contact. Such loss in design kinematics can compromise the original design intent to transfer torque by distributed contact between multiple elements in the bearing surfaces provided in the conventional designs described above. The loss in distributed bearing contact manifests itself as a corresponding loss in torque transfer efficiency, caused by such effects as a change of transmission angle and erratic torque transfer through the bearing surfaces. In such cases, conventional transmissions may perform differently from specification over time (and usually not as well). More specifically, the surfaces of the bearings contacts in such designs become recessed away from the optimum 90-degree transmission angle and do not engage sliding surfaces at the same offset location or angle at which they were designed to operate. This causes irregular engagement between bearings surfaces and leads to stress concentrations not anticipated by original design considerations. Eventually, over time, the non-uniform wear of the bearings surfaces can cause transmission designs with two, three, four or more contacts to be driven by only one or two bearing surfaces, especially during instantaneous dynamic movement. This leads to accelerated wear and lateral misalignment. The lateral misalignment will also cause an increased orbiting lateral or transverse force during transmission rotation for which the bearing arrangement may not be designed. 
     As noted, all of the foregoing existing styles of transmission have service life issues caused, at least in part, by deterioration of the bearings contact interface(s). Abaco&#39;s U.S. patent application Ser. No. 15/721,959 (now U.S. Pat. No. 10,934,778) (hereafter “Parent Application”) discloses laminated “bridge”-style bearings designs and embodiments addressing some of the above-described problems and needs in the prior art with laminated torsional bearings that flex rather than slide in providing torque transfer during misaligned (articulated) rotation. The present disclosure enlarges upon the Parent Application with description of unlaminated “bridge”-style bearings embodiments. In such embodiments, curve bearing surfaces (and preferably convex curved bearing surfaces) on transmission shaft pins are allowed to slidably rotate against corresponding curved surfaces (and preferably concave curved bearing surfaces) on the unlaminated bearing elements as the shaft “tilts” during misaligned rotation with respect to a housing. The unlaminated “bridge”-style bearings of the present disclosure are further free to slidably displace within receptacles provided in the periphery of the housing. 
     SUMMARY AND TECHNICAL ADVANTAGES 
     These and other drawbacks in the prior art are addressed in the Parent Application by a transmission providing laminated bearing embodiments including a contact interface between an input shaft and output shaft, in which the input and output shafts are misaligned. It will be appreciated that in a BHA application, the input shaft may typically be connected to the rotor of a PDM, and the output shaft to a flex shaft/constant velocity (CV) joint as part of the linkage ultimately connecting to a rotating bit. The transmission in the Parent Application provides an interlocking mechanism in which an input shaft adapter, on the end of the input shaft, is received into a recess in an output shaft adapter on the end of the output shaft. More specifically, shaped pins provided on the outer periphery of the input shaft adapter are received into shaped receptacles provided in the recess in the output shaft adapter. Shaped laminated torsional bearings are also placed within the confines of the receptacle, interposed between the input shaft adapter pins and the side walls of the receptacle. 
     Embodiments of the laminated torsional bearings disclosed in the Parent Application provide (1) a curved rubber/metal laminate portion to mate with a corresponding curved bearing surface of the input shaft adapter pins, and (2) a flat rubber/metal laminate portion to bear on the side walls of the receptacle. Specifically, the input shaft adapter pins bear upon the curved laminate portions of the torsional bearings, and the flat laminate portions of the torsional bearings bear on the side walls of the output shaft adapter receptacles. Thus, when torque is applied to the input shaft, torque is transmitted to the output shaft via flex in the torsional bearings rather than via sliding of contact surfaces. 
     The curved and flat laminate portions of the torsional bearings embodiments disclosed in the Parent Application are preferably made of alternating metal layer and rubber layer construction. The deployment of the torsional bearings between input shaft adapter pins and output shaft adapter receptacles is designed to avoid, or at least to minimize, relative sliding contact between bearing surfaces during transmission of torque. That is, the laminate design described in the Parent Application is such that transmission of torque, at least primarily, is via flex: (1) between the contact surfaces of the input shaft adapter pins and the curved laminate portions on the torsional bearings, and (2) between the contact surfaces of the flat laminate portions on the torsional bearings and the side walls of the output shaft adapter receptacles. Advantageously, adhesive may be used on the contact surfaces during assembly and service to inhibit sliding movement. In this way, according to laminated bearings embodiments described in the Parent Application, misalignment of input and output shafts during articulated shaft rotation is taken up by flex of the elastomeric layers in the curved and flat laminate portions of the torsional bearings, obviating sliding bearings contact and its associated drawbacks as described above in the Background section. 
     As noted above, the present disclosure enlarges upon the Parent Application with description of unlaminated “bridge”-style bearings embodiments. Dissimilar from the laminated bridge-style bearings embodiments described in the Parent Application (which are designed to flex rather than slide against shaft pins when taking up misaligned rotation), the unlaminated “bridge”-style bearings of the present application are designed so that the unlaminated bridge-shaped bearing elements (also referred to herein as “torque transfer elements” or “TTEs”) promote sliding contact between curved surfaces on pins on the shaft and curved surfaces on the TTEs. Preferably, convex bearing surfaces provided on the transmission shaft pins are configured to slidably rotate against corresponding concave bearing surfaces on the unlaminated TTEs. In preferred embodiments, rotation of the shaft pins about the TTEs is about a generally radial axis centered on the shaft pins and orthogonal to the shaft&#39;s longitudinal axis. 
     With reference now to the “Background” section above, unlaminated bearings embodiments set forth in this disclosure address contact surface erosion and degradation problems described in the “Background” section in different ways than addressed by the laminated bearings embodiments described in the Parent Application. Unlaminated bearings embodiments as set forth in this disclosure are not configured to flex in order to limit sliding contact between transmission components. Unlaminated bearings designs as set forth in this disclosure necessarily require sliding contact between transmission components (such sliding contact preferably primarily comprising sliding rotation contact between convex bearing surfaces provided on the shaft pins and corresponding concave bearing surfaces on the unlaminated TTEs). However, unlaminated bearings embodiments as set forth in this disclosure are configured to optimize sliding contact between transmission components so that the prior art&#39;s contact surface deterioration problems are addressed and contact surface deterioration typically seen in conventional designs is reduced. 
     In a first aspect, therefore, this disclosure describes embodiments of a torque transmission comprising: an input shaft adapter having first and second ends, the first end of the input shaft adapter configured to mate with an input shaft, the second end of the input shaft adapter providing a plurality of pins disposed on an outer surface of the input shaft adapter, each pin providing a curved pin portion; an output shaft adapter having first and second ends, the second end of the output shaft adapter configured to mate with an output shaft, the first end of the output shaft adapter providing a recess formed therein; a plurality of notches formed in a recess periphery of the recess, one notch for each pin disposed on the input shaft adapter, wherein the recess is shaped and sized to receive the second end of the input shaft adapter such that when the second end of the input shaft adapter is received inside the recess, each pin on the input shaft adapter is received into a corresponding notch on the recess; a plurality of torsional bearings, a curved laminate portion provided on each torsional bearing; and wherein one torsional bearing is interposed between one pin and one corresponding notch when the pins are received into their corresponding notches, such that the curved laminate portion contacts the curved pin portion; and wherein selected torsional bearings each further comprise a flat portion, each flat portion contacting the notch when the pins are received into their corresponding notches. 
     In some embodiments according to the first aspect, selected flat portions of the torsional bearings are laminated. 
     In some embodiments according to the first aspect, each pin has a maximum pin nose diameter, and in which selected pin nose diameters are on a locus that coincides with an outer diameter of the output shaft. 
     In some embodiments according to the first aspect, the torque transmission further comprises a spherical bearing, the spherical bearing including a spherical bearing laminate portion; and a tip, the tip provided on second end of the input shaft adapter; wherein, when the second end of the input shaft adapter is received inside the recess, the spherical bearing laminate portion is interposed between the tip and the recess. 
     In some embodiments according to the first aspect, selected curved laminate portions include metal and elastomer layers. 
     In some embodiments according to the first aspect, selected flat portions of the torsional bearings include a laminate comprising metal and elastomer layers. 
     In some embodiments according to the first aspect, the spherical bearing laminate portion includes metal and elastomer layers. 
     In some embodiments according to the first aspect, the torque transmission further comprises a boot retainer, the boot retainer having first and second boot retainer ends; and an outer input shaft adapter periphery on the second end of the input shaft adapter and an outer output shaft adapter periphery on the first end of the output shaft adapter; wherein, when the second end of the input shaft adapter is received inside the recess, the boot retainer is received over the input shaft adapter and the output shaft adapter such that the first end of the boot retainer is affixed to the outer input shaft adapter periphery and the second end of the boot retainer is affixed to the outer output shaft adapter periphery. 
     In some embodiments according to the first aspect, the torque transmission further comprises an outer output shaft adapter periphery on the first end of the output shaft adapter; a fill port connecting the outer output shaft adapter periphery to the recess; and an evacuate port connecting the outer output shaft adapter periphery to the recess. 
     In some embodiments according to the first aspect, the torque transmission further comprises adhesive bonding between curved pin portions and curved laminate portions. 
     In some embodiments according to the first aspect, the torque transmission further comprises adhesive bonding between flat portions and notches. 
     In some embodiments according to the first aspect, the torque transmission further comprises adhesive bonding between the spherical bearing laminate portion and at least one of the tip and the recess. 
     In some embodiments according to the first aspect, selected pins each have a midpoint, and in which the curved pin portions on said selected pins each have a radius whose centerpoint coincides with the midpoint. 
     In a second aspect, this disclosure describes embodiments of a double knuckle transmission coupling, comprising: an input shaft having a first input shaft end and a second input shaft end, the second input shaft end having an input shaft slot defining an input shaft tongue and groove configuration; an output shaft having a first output shaft end and a second output shaft end, the first output shaft end having an output shaft slot defining an output shaft tongue and groove configuration; a plurality of arcuate tongue recesses, one arcuate recess formed in each tongue in the input and output shaft tongue and groove configurations; a center coupling element, the center coupling element including two pairs of knuckles, each knuckle providing an arcuate knuckle surface configured to be received within a corresponding arcuate tongue recess; a plurality of receptacles, one receptacle formed in each arcuate tongue recess; a plurality of torsional bearings, a curved laminate portion provided on each torsional bearing; wherein one torsional bearing is received into each receptacle, such that the curved laminate portions contact the arcuate knuckle surfaces when the knuckles are received within their corresponding arcuate tongue recesses. 
     The second aspect may include embodiments in which selected torsional bearings each further comprise a flat laminate portion, each flat laminate portion contacting the receptacle when the selected torsional bearings are received into their corresponding receptacles. 
     In a third aspect, this disclosure describes embodiments of a torque transmission, comprising: an input shaft adapter having first and second ends, the first end of the input shaft adapter configured to mate with an input shaft, the second end of the input shaft adapter providing a plurality of pins disposed on an outer surface of the input shaft adapter, each pin providing a curved pin portion; an output shaft adapter having first and second ends, the second end of the output shaft adapter configured to mate with an output shaft, the first end of the output shaft adapter providing a recess formed therein; a plurality of notches formed in a recess periphery of the recess, one notch for each pin disposed on the input shaft adapter, wherein the recess is shaped and sized to receive the second end of the input shaft adapter such that when the second end of the input shaft adapter is received inside the recess, each pin on the input shaft adapter is received into a corresponding notch on the recess; a plurality of bearings, a curved portion provided on each bearing; and wherein one bearing is interposed between one pin and one corresponding notch when the pins are received into their corresponding notches, such that the curved portion of the bearing contacts the curved pin portion; and wherein selected bearings each further comprise a flat portion, each flat portion contacting the notch when the pins are received into their corresponding notches. 
     The third aspect may include embodiments in which selected ones of the curved portions of the bearings and the flat portions of the bearings include a laminate. In such embodiments, the laminate may comprise metal and elastomer layers. 
     The third aspect may also include embodiments further comprising: a boot retainer, the boot retainer having first and second boot retainer ends; and an outer input shaft adapter periphery on the second end of the input shaft adapter and an outer output shaft adapter periphery on the first end of the output shaft adapter; wherein, when the second end of the input shaft adapter is received inside the recess, the boot retainer is received over the input shaft adapter and the output shaft adapter such that the first end of the boot retainer is affixed to the outer input shaft adapter periphery and the second end of the boot retainer is affixed to the outer output shaft adapter periphery. 
     The third aspect may also include embodiments further comprising: an outer output shaft adapter periphery on the first end of the output shaft adapter; a fill port connecting the outer output shaft adapter periphery to the recess; and an evacuate port connecting the outer output shaft adapter periphery to the recess. 
     The third aspect may also include embodiments in which selected pins each have a midpoint, and in which the curved pin portions on said selected pins each have a radius whose centerpoint coincides with the midpoint. 
     The third aspect may also include embodiments in which each pin has a maximum pin nose diameter, and in which selected pin nose diameters are on a locus that coincides with an outer diameter of the output shaft. 
     In a fourth aspect, this disclosure describes embodiments of an articulated transmission disposed to transmit torque via misaligned rotation, the transmission comprising: a shaft having an axial shaft centerline about which the shaft is disposed to rotate; a plurality of shaft pins, each shaft pin extending radially from the shaft centerline, each shaft pin further providing a curved shaft pin bearing surface thereon; a generally cylindrical housing having an axial housing centerline about which the housing is disposed to rotate, the housing having a plurality of housing cavity receptacles formed therein, each housing cavity receptacle for receiving a corresponding shaft pin; and a plurality of torque transfer elements (TTEs), each TTE providing a curved TTE pin bearing surface and a TTE housing bearing surface; wherein each housing cavity receptacle provides a housing bearing surface; wherein a shaft pin and a TTE are received into each housing cavity receptacle such that within each housing cavity receptacle, the shaft pin bearing surface is received onto the TTE pin bearing surface and the TTE housing bearing surface opposes the housing bearing surface; wherein, responsive to misaligned rotation of the shaft centerline with respect to the housing centerline and regardless of angular deflection of the shaft centerline with respect to the housing centerline experienced within each housing receptacle during an articulated revolution of the shaft: (1) the shaft pins are free to slidably rotate about the TTEs; and (2) the TTE housing bearing surfaces are free to slidably displace against corresponding housing bearing surfaces. 
     The fourth aspect may include embodiments in which shaft pins further provide a convex shaft pin bearing surface thereon and TTEs provide a concave TTE pin bearing surface. 
     The fourth aspect may also include embodiments in which the TTEs float at least generally parallel to an untilted shaft centerline when the TTE housing bearing surfaces slidably displace against corresponding housing bearing surfaces. 
     The fourth aspect may also include embodiments in which: each shaft pin further provides a shaft backlash surface; and each housing cavity receptacle further provides a housing backlash surface to oppose a corresponding shaft backlash surface; wherein the transmission further includes a backlash energizer assembly interposed between at least one opposing shaft backlash surface and housing backlash surface. In some embodiments, the backlash energizer assembly includes a puck. In some embodiments, the puck may separate a set screw and a Belleville washer. In some embodiments, the puck may include a laminate of metal and elastomer layers. In some embodiments, the backlash energizer assembly may include a plate, and in which the plate separates a set screw and a ball. 
     The fourth aspect may also include embodiments in which selected ones of the TTE pin bearing surfaces and the TTE housing bearing surfaces include a laminate. In some embodiments, the laminate may comprise metal and elastomer layers. In some embodiments, selected TTE pin bearing surfaces may include a hard facing. In some embodiments, selected TTE housing bearing surfaces may include curvature. In some embodiments, selected TTE housing bearing surfaces may include angled faces. 
     It is therefore a technical advantage of the disclosed laminated bearings to extend the service life of transmissions in which such laminated bearings are deployed. As noted above, relative sliding contact between bearing surfaces during torque transmission is minimized and ideally eliminated. Flex in the curved and flat laminate portions of the torsional bearings takes up and absorbs substantially all input/output shaft displacement due to shaft misalignment. The above-described disadvantages associated with galling and subsequent fretting/erosion of metal-to-metal bearings are thus substantially reduced, if not eliminated completely. Further, “constant velocity” contact in the torsional bearing surfaces in CV transmission style designs can be maintained over a more sustained period via flex in the disclosed torsional bearings, thereby extending the service life of such CV-style transmission designs over a conventionally expected service life. 
     Another technical advantage of the disclosed transmission with laminated bearings is that flex in the laminated bearings (both torsional and spherical) maintains design kinematics for the transmission, promoting efficient torque transfer per design through all torsional bearings during service, and efficient transfer of thrust loads through the misaligned input and output transmission shafts. 
     Another technical advantage of the disclosed transmission with laminated bearings is that periodic maintenance and refurbishment of the transmission is optimized. In prior designs with metal-to-metal contact, fretting, erosion and other service wear on and around the bearings cause larger metal components also to become periodically no longer serviceable, requiring their refurbishment or replacement along with the bearings themselves. Such larger metal components (such as housings, splined connections, etc.) are often expensive and time consuming to repair and replace. Serious deterioration of such larger metal components may even require the entire transmission to be retired from service prematurely. In the laminated bearings transmission described in this disclosure, however, absent extraordinary service events, only the torsional bearings will require periodic replacement. The avoidance of metal-to-metal contact in the disclosed transmission with laminated bearings means that larger metal components in the input shaft adapter and the output shaft adapter should remain substantially less worn over an extended service life. 
     It is a technical advantage of the disclosed transmission with unlaminated bearings to enable transfer of high torque loads as compared to some conventional CV-ball transmission designs. Unlaminated bearings embodiments as set forth in this disclosure preferably provide a shall with shaft pins formed integrally with the shaft on the shaft head. The resulting one-piece shaft head further transfers applied torque into unlaminated bearings at or near the maximum radius of the shaft head as received into the housing. In any proposed transmission deployment, the resulting potential for high torque load capability has to be weighed with the kinematics of a “bridge”-style bearings design as compared to conventional CV-ball transmission designs. The “bridge”-style design provides one less degree of freedom of movement in articulated torque transfer than can be offered by a CV-ball design. Also, the “bridge”-style bearing itself is more limited in its movement in housing pockets during articulated torque transfer than in a corresponding CV-ball design in that the “bridge”-style bearing is configured to slide generally longitudinally only relative to the shaft axis. 
     It is a further technical advantage of the disclosed transmission with unlaminated bearings to offer improved stability over conventional woodruff key designs. The disclosed designs have a comparatively longer circumferential aspect ratio at the shaft head than comparable woodruff key designs. The longer circumferential aspect ratio tends to stabilize the shaft better in the housing during misaligned rotation. 
     A further technical advantage of the disclosed “bridge”-style transmissions (laminated and unlaminated embodiments) is stability offered over comparable conventional designs in which the shaft pins are concave and the “bridge”-style bearings are convex. The geometry of a concave shaft pin is loaded along one of the long dimensions, resulting in “thin strip” contact area and a longer tilting “arm”. The concave shaft pin design is thus more likely to tilt and the stress caused by contact loading on the thin strip contact area is high. In contrast, convex shaft pin embodiments according to the disclosed transmission designs are loaded along the short dimension, resulting in wider/larger contact area and shorter tilting arm. The convex shaft pin geometry thus allows the shaft pins to sit more stably in the housing receptacles. The convex shaft pins also tend to experience less stress since contact loading is on wider contact surfaces than provided on comparable concave shaft pins. 
     The foregoing has rather broadly outlined some features and technical advantages of the disclosed transmission designs, in order that the following detailed description may be better understood. Additional features and advantages of the disclosed technology may be described. It should be appreciated by those skilled in the art that the conception and the specific embodiments disclosed may be readily utilized as a basis for modifying or designing other structures for carrying out the same inventive purposes of the disclosed technology, and that these equivalent constructions do not depart from the spirit and scope of the technology as described. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       For a more complete understanding of the embodiments described in this disclosure, and their advantages, reference is made to the following detailed description taken in conjunction with the accompanying drawings, in which: 
         FIGS. 1A through 12  illustrate various embodiments described in this disclosure including laminated torsional bearings, and in which further: 
         FIG. 1A  is a perspective cutaway view of input shaft assembly  100  shown operationally engaged with output shaft adapter  205 ; 
         FIG. 1B  is a perspective view of output shaft assembly  200 ; 
         FIG. 1C  is a section as shown on  FIG. 1B ; 
         FIG. 2A  is section view as shown on  FIG. 1A ; 
         FIG. 2B  is an enlarged section view as shown on  FIG. 2A ; 
         FIG. 3  is a perspective view of a torsional bearing  300 ; 
         FIG. 4  is an enlargement as shown on  FIG. 3 ; 
         FIG. 5  is a perspective view of spherical bearing  350 ; 
         FIG. 6  is a section as shown on  FIG. 5 ; 
         FIG. 7  is an enlargement as shown on  FIG. 5 ; 
         FIG. 8  is a partially exploded view of input shaft assembly  100  in isolation; 
         FIG. 9  is a partially exploded view of  FIG. 1A  (without the cutaway on  FIG. 1A ); 
         FIG. 10  is an elevation view of  FIG. 1A  (without the cutaway on  FIG. 1A ); 
         FIG. 11  is a section as shown on  FIG. 10 ; and 
         FIG. 12  is a modified version of  FIG. 11  showing transmission misalignment. 
         FIGS. 13A through 20H  illustrate various embodiments described in this disclosure including unlaminated embodiments with sliding contact between convex shaft pins and concave bearings surfaces, and in which further; 
         FIG. 13A  is a partial cutaway and exploded view of an exemplary transmission embodiment according to this disclosure in which upper housing assembly  1200 U is rotatably connected to lower housing assembly  1200 L via misaligned (articulated) rotation of shaft assembly  1100 ; 
         FIG. 13B  is a perspective view of lower housing  1205 L on  FIG. 13A  in isolation; 
         FIG. 13C  is a section as shown on  FIG. 13B ; 
         FIG. 14A  is a section as shown on  FIG. 13A ; 
         FIG. 14B  is a section as shown on  FIG. 14A ; 
         FIG. 15A  illustrates Torque Transfer Element (TTE)  1300 A, which for reference is the same TTE embodiment as TTE  1300  depicted on  FIGS. 13A and 17 ; 
         FIGS. 15B through 15G  illustrate TTEs  1300 B through  1300 G respectively (in which TTE  1300 B through  1300 G are alternative embodiments to TTE assembly  1300 A on  FIG. 15A ); 
         FIG. 16  is an enlargement as shown on  FIG. 15B ; 
         FIG. 17  is a fully exploded view of the exemplary transmission embodiment shown on  FIG. 13A ; 
         FIG. 18  is a further partial cutaway view of lower housing assembly  1200 L as also illustrated on  FIG. 13A ; 
         FIG. 19A  is a section as shown on  FIG. 18 ; 
         FIGS. 19B and 19C  are “faux section” views as shown  FIG. 19A , depicting shaft assembly  1100  substantially assembled at lower housing assembly  1200 L per  FIGS. 13A, 14A and 14B , in which  FIGS. 19B and 19C  combine to schematically depict articulation during misaligned rotation; 
         FIG. 20A  is a section similar to  FIG. 14A , except depicting an alternative embodiment including backlash energizer assembly  1400 ; 
         FIG. 20B  is an exploded view of backlash energizer assembly  1400  from  FIG. 20A  in isolation; and 
         FIGS. 20C and 20D ,  FIGS. 20E and 20F , and  FIGS. 20G and 20H  are matched pairs of cutaway section views and corresponding exploded isolation views of alternative backlash energizer embodiments. 
     
    
    
     DETAILED DESCRIPTION 
     The following description of embodiments provides non-limiting representative examples using Figures, diagrams, schematics, flow charts, etc. with part numbers and other notation to describe features and teachings of different aspects of the disclosed technology in more detail. The embodiments described should be recognized as capable of implementation separately, or in combination, with other embodiments from the description of the embodiments. A person of ordinary skill in the art reviewing the description of embodiments will be capable of learning and understanding the different described aspects of the technology. The description of embodiments should facilitate understanding of the technology to such an extent that other implementations and embodiments, although not specifically covered but within the understanding of a person of skill in the art having read the description of embodiments, would be understood to be consistent with an application of the disclosed technology. 
     Laminated Bearings Embodiments 
     Reference is now made to  FIGS. 1A through 12  in describing currently preferred transmission embodiments including laminated torsional bearings. For the purposes of the following disclosure,  FIGS. 1A through 12  should be viewed together. Any part, item, or feature that is identified by part number on one of  FIGS. 1A through 12  will have the same part number when illustrated on another of  FIGS. 1A through 12 . It will be understood that the embodiments as illustrated and described with respect to  FIGS. 1A through 12  are exemplary, and the scope of the inventive material set forth in this disclosure is not limited to such illustrated and described embodiments. 
     The scope of the inventive material set forth in this disclosure is further not limited to specific deployments of the described embodiments. For example, the following description directed to laminated embodiments makes reference to input shaft  101  operationally engaged with output shaft  201  via connection of input shaft assembly  100  to output shaft assembly  200 . It will be appreciated that in a typical BHA deployment, input shaft  101  may be connected to the rotor in a PDM, and output shaft  201  may be connected to the flex shaft/CV joint above the rotary bit. The description below is not limited to such an exemplary deployment, however, and for this reason input and output shafts  101  and  201  are referred to generically throughout. 
       FIG. 1A  is a perspective cutaway view of input shaft assembly  100  operationally engaged with output shaft adapter  205  according to an exemplary embodiment of the transmission described in this disclosure. With momentary reference to  FIG. 8 , and continuing reference to  FIG. 1A , it will be seen that input shaft assembly  100  comprises input shaft  101  conventionally connected to input shaft adapter  105  via, for example a threaded connection. Input shaft adapter  105  provides a plurality of shaped pins  107  on a distal end thereof. 
     With reference now to  FIGS. 1B and 1C , output shaft assembly  200  comprises output shaft  201  conventionally connected to output shaft adapter  205  via, for example a threaded connection. Output shaft adapter  205  provides a plurality of shaped receptacles  207  in an internal cylindrical recess  206 . [Shaped receptacles  207  may also be referred to as “notches’ in this disclosure.] Cylindrical recess  206  is formed on a distal end of output shaft adapter  205 . With additional reference to  FIGS. 1A and 2A , for example, it will be seen that cylindrical recess  206  is provided in output shaft adapter  205  to receive input shaft adapter  105 . Further, as shown on  FIG. 2A , and as will be described in detail further on this disclosure, receptacles  207 /notches on output shaft adapter  205  are shaped to receive pins  107  on input shaft adapter  105  when torsional bearings  300  are interposed between pins  107  and side walls of receptacles  207 .  FIG. 1C  also depicts spherical bearing receptacle  209  formed on the inside end of cylindrical recess  206 . As will be discussed in greater detail with reference to  FIGS. 5 through 7 , spherical bearing receptacle  209  is shaped to receive spherical bearing  350  illustrated on, for example,  FIGS. 1A, 5, 8 and 9 . 
     With reference to  FIG. 1A  again, and with further reference to  FIG. 11 , it will be seen that the connection between input and output shaft adapters  105  and  205  is protected by boot  210 . Boot retainer  215  maintains and protects boot  210 . Boot retainer  215  attaches to output shaft adapter  215  via threads  217 . Metal strap  214  maintains one end of boot  210  in close contact with input shaft adapter  105 . Seal lip  212  holds the other end of boot  210  to output shaft adapter  205 . It will be therefore seen with reference to embodiments illustrated on  FIGS. 1A and 11  that boot retainer  215  has first and second boot retainer ends, the first end towards input shaft  101  and the second end towards output shaft adapter  205 . Input shaft adapter  105  has an outer input shaft adapter periphery on the second end thereof (towards output shaft adapter  205 ). Output shaft adapter  205  has an outer output shaft adapter periphery on the first end thereof (towards input shaft  101 ). When the second end of input shaft adapter  105  is received inside the recess provided by spherical bearing receptacle  209  in output adapter shaft  205 , boot retainer  215  is received over input shaft adapter  105  and output shaft adapter  205  such that the first end of boot retainer  215  is affixed to the outer input shaft adapter periphery and the second end of boot retainer  215  is affixed to the outer output shaft adapter periphery. [Refer to description immediately above associated with  FIG. 1C  for further understanding of the recess provided by spherical bearing receptacle  209  in output adapter shaft  205 ]. 
       FIG. 2A  is a section as shown on  FIG. 1A . When torque is provided to rotate input shaft adapter  105  in the direction of arrow T, input shaft adapter  105  engages torsional bearings  300  onto the side walls of the receptacles  207  provided in output shaft adapter  205 . Torques is thus transferred to output shaft adapter  205 . 
     While the embodiment illustrated on  FIG. 2A  has six (6) torsional bearings  300 , it will be appreciated that this number is exemplary only. The scope of this disclosure is not limited as to the number of torsional bearings provided in any embodiment. The number will be determined by user design factors such as, without limitation, size of input and output shafts  101  and  201 , and amounts of torque to be transferred in view of stress performance of various constructions of torsional bearings  300 .  FIGS. 2A and 2B  also depict that in some embodiments, adhesive bonding  318  may be provided between some or all of the flat laminate portions  320  of torsional bearings  300  and the shaped receptacles/“notches”  207  on output shaft adapter  205  (although the scope of this disclosure is not limited in this regard). Refer to description below associated with  FIG. 3  for further understanding of flat laminate portions  320 . 
       FIG. 2B  is a section as shown on  FIG. 2A .  FIG. 2B  shows that the engagement of torsional bearings  300  by input shaft adapter  105  is via curved portions of pins  107 . With momentary reference to  FIG. 3  (in which an exemplary torsional bearing  300  is depicted in more detail), it will be seen that the curved portions of pins  107  engage curved laminate portions  310  of torsional bearings  300 . Returning now to embodiments illustrated on  FIG. 2B , it will be seen that in some embodiments, adhesive bonding  317  may be provided between some or all of the curved portions of pins  107  and the curved laminate portions  310  of torsional bearings  300  (although the scope of this disclosure in not limited in this regard). Also, with further reference to  FIG. 2B , it will be seen that torsional bearing  300  has a midpoint  330  which coincides with a corresponding midpoint on selected pins  107 . As shown on  FIG. 2B , the curved portions on said selected pins  107  each have a radius  111  whose centerpoint  113  coincides with the midpoint  330 . 
     With further reference now to  FIGS. 2A and 2B , it will be appreciated that in currently preferred embodiments, the geometries illustrated are designed so that the maximum pin nose diameters  109  on pins  107  are on a locus  409  whose diameter coincides with the external diameter of output shaft  201  (such external diameter also illustrated on  FIG. 2A  as dotted line  409 ). In this way, in such currently preferred embodiments, torque is directly transferred through the full cross-section of output shaft  201 , substantially unifying the torque stress gradients across output shaft  201  near the connection with output shaft adapter  205 . It will nonetheless be appreciated, however, that the scope of this disclosure is not limited to deployments in which locus  409  of maximum pin nose diameters  109  coincides with the external diameter of output shaft  201 . 
       FIG. 3  is a perspective view of a currently preferred embodiment of a torsional bearing  300  (also shown in situ on, for example,  FIGS. 1A, 2A and 2B ). Torsional bearings  300  are shaped to be received in an interposed relationship between pins  107  on input shaft adapter  105 , and the side walls of receptacles  207  on output shaft adapter  205 . In this interposed relationship, pins  107  contact a curved laminate portion  310  on torsional bearings  300 . Curved laminate portion  310  is described in more detail below with reference to  FIG. 4 . The side walls of receptacles  207  contact a flat laminate portion  320  on torsional bearings  300 . Curved laminate portion  310  and flat laminate portion  320  are separated by metal portion  302 . 
       FIG. 4  is an enlargement as shown on  FIG. 3 .  FIG. 4  illustrates curved laminate portion comprising alternating metal layers  312  and rubber layer  314 . Although  FIGS. 3 and 4  have been illustrated with a metal layer  312  as the immediate contact interface with pins  107  on input shaft adapter  105 , this disclosure is not limited in this regard. Other embodiments may provide a rubber layer  314  as the immediate contact interface with pins  107 . It has been found advantageous to provide a rubber layer  314  as the immediate contact interface with pins  107  in deployments where adhesive is used to adhere torsional bearings  300  to pins  107  during assembly. 
     Referring particularly to rubber layers  314  on  FIG. 4 , each rubber layer  314  is preferably less than 0.030″ thick, and more preferably in the range of 0.015 to 0.002″ thick, in order to maintain a beneficial compressive stress field throughout nearly the entire rubber layer during service. Although the scope of this disclosure is not limited to particular thicknesses of rubber layers  314 , it has been found that thicknesses in the above guidelines tend to reduce the tendency of the rubber to extrude from the edge of curved laminate portion  310  when placed under load (compression, shear and some bending). The preferred layer thicknesses for rubber layer  314  may be obtained by highly precise calendaring operations during manufacture, using extremely stiff rolling cylinders to extrude the strip form of uncured “green” rubber. The preferred layer thicknesses may also be obtained by extrusion through a highly accurate and sharp strip die. The strip of “green” rubber may also be cured or semi-cured in the strip form prior to bearing assembly. This may be accomplished with an oven, autoclave or microwave heating. A microwave heating source is more preferred and can offer a continuous cure cycle. The strip may be cut to size and assembled into layers with the metal components. 
     Currently preferred embodiments customize rubber material selections for rubber layers  314 . The selection of material for rubber layer will also dictate the exact preferred method of forming rubber layer  314  and bonding them to metal surfaces such as on metal layers  312 . A high temperature rubber material such as fluorinated silicone rubber (FSR) is advantageous for extended use in transmissions whose service includes elevated bottom hole temperatures. In other embodiments, rubber material selections may be made from, for example, natural rubber (NR), nitrile butadiene rubber (NBR), hydrogenated nitrile butadiene rubber (HNBR), fluoroelastomers (FKM), perfluoroelastomers (FFKM), or ethylene propylene diene monomer (EPDM) rubber formulations. 
     Referring now to metal layers  312  on  FIG. 4 , each metal layer  312  is preferably a high strength carbon alloy steel or stainless steel, preferably with a yield strength in a range of 140 ksi to 230 ksi (higher strengths preferred for highly stressed metal layers  312 ). Metal layer thicknesses are preferably in a range of 0.001″ to 0.030″, and more preferably in a range of  0 . 002 ″ to 0.015″, although this disclosure is not limited in this regard. Further, the ratio of thicknesses of rubber layers  314  to metal layers  312  within curved laminate portion  310  is preferably in a range of 1.0 to 2.0, although again this disclosure is not limited in this regard. A currently preferred embodiment of curved laminate portion  310  has rubber layers  314  that are 0.002″ thick, and metal layers  312  that are 0.002″ thick. 
     Preferred thicknesses of metal layers  312  may be initially obtained from sheet rolling operations or thin film deposition techniques. Final forming of the metal layers  312  may be accomplished pressing with a suitable die. Metal layers  312  having thicknesses in the above preferred ranges will typically take the form of high strength foils. Examples of commercially available high strength foils that may be used for metal layers  312  include Integran Armor Foil, Integran Nickel-Cobalt Nano Foil, as well as traditional high-strength, heat-treated stainless steel 301 or 420 grade foil, all available from specialty suppliers such as Nikken Steel, Comet Metals, or Ulbrich Stainless Steels for example. 
     Curved laminate portion  310  on  FIG. 4  may be formed by any conventional method, such as pressing metal layers  312  and rubber layers  314  together at elevated temperatures, and/or by bonding metal layers  312  and rubber layers  314  together with a suitable adhesive. Suitable conventional high temperature adhesives are commercially available from suppliers such as Cilbond, Lord (Chemlok brand), and Dow Chemicals (Thixon and Megiun brands). A suitable adhesive product may be chosen to suit the characteristics of the rubber/elastomeric material selected for rubber layers  314 . For example, Chemlok  607  is a suitable adhesive for FSR material, while Chemlok  207  primer and Chemlok  6450  top coat is a suitable adhesive for NBR or HNBR. Optimized chemical formulas for such products coincide with the polymer families and compounding mixtures typically found for each category of rubber/elastomer material. The consistency of the adhesive bonding is optimized through heating and pressing steps in manufacture. 
     As noted above, curved laminate portion  310  on  FIGS. 3 and 4  is shaped to mate with pins  107  on input shaft adapter  105 . A series of conventional cylindrical press dies may be used to shape metal layers  314  to the designed curvatures. Dies with less curvature must be used for metal layers  314  further away from the interface with pins  107  in order to maintain an overall uniform radial thickness of the finished curved laminate portion  310 . The total overall radial thickness of finished curved laminate portion  310  will advantageously be optimized for the operating parameters of the transmission being designed. However, it is expected that curved laminate portions  310  deployed in many applications will have overall radial thicknesses in a range from 0.030″ to 0.250″. 
     Construction of curved laminate portion  310  is conventional. Calendared rubber layers  314 , in strip form, are interposed between calendared metal layers  312 , each rubber layer  314  having initially been cut to a suitable length and width to cover the interface between each adjacent metal layer  312 . The length of rubber layers  314  may be the same or slightly longer than the arc length of the adjacent metal layers  312 . The assembled metal and rubber layers  312  and  314  may be held together with adhesive, if desired, and then placed into a forming mold. An adhesive may be particularly desirable if rubber layers  314  were pre-cured prior to assembly. The assembly is then heated and cured in the mold, under pressure, to activate the final rubber curing and bonding reactions of the rubber and adhesive systems. 
     Referring now to  FIG. 3 , torsional bearing  300  also provides flat laminate portion  320 . As noted above, torsional bearings  300  are shaped to be received in an interposed relationship between pins  107  on input shaft adapter  105 , and the side walls of receptacles  207  on output shaft adapter  205 . In this interposed relationship, the side walls of receptacles  207  contact flat laminate portion  320 . It will be appreciated from  FIG. 3  that flat laminate portion  320  is comprised of metal layers and rubber layers similar to metal layers  312  and rubber layers  314  within curved laminate portion  310 . 
     The disclosure immediately above describing currently preferred materials and construction of curved laminate portion  310  applies similarly to the corresponding currently preferred materials and construction of flat laminate  320 . Rectangular metal layers can be cut from metal foils using cutting dies, laser or other conventional foil cutting techniques. Calendared rubber in strip form is cut to size to give optimum coverage and overlap of the metal layers. An adhesive may be used to assemble alternating rubber and metal layers. The assembly is loaded into a mold and cured under heat and pressure. 
     Regarding thicknesses in flat laminate  320 , the disclosure above describing currently preferred thicknesses of metal layers  312  and rubber layers  314  in curved laminate portion  310  applies equally to the currently preferred thicknesses of corresponding metal and rubber layers in flat laminate  320 . As to overall laminate thickness of flat laminate  310 , thicknesses in the range of 0.020″ to 0.250″ are preferred, although the scope of this disclosure is not limited in this regard. 
     Referring again to  FIG. 3 , metal portion  302  on torsional bearing  300  separates curved laminate portion  310  and flat laminate portion  320 . Metal portion  302  is made from a conventional high strength plain carbon steel such as high strength grade  4340 , or a high strength low alloy steel such as 300M. Alternatively, a high strength martensitic alloy steel may be used, such as Aermet 100. 
     It will be seen from  FIGS. 3 and 2A  that the side elevation of torsional bearing  300  is shaped to be received into output shaft adapter receptacles  207  by virtue of a generally asymmetric trapezoidal profile that includes flat laminate portion  320 . Such asymmetric trapezoidal profile achieves several advantages, including (1) maximizing the cross-sectional area of flat laminate portion  320  so as to transmit and distribute torque through torsional bearing  300  with reduced compressive stress and shear stress on the materials in the construction of flat laminate portion  320 , and (2) creating a self-immobilizing “dovetail” shape when retained in output shaft adapter receptacles  207  by input shaft adapter pins  107  (see  FIGS. 2A and 2B ). 
     As noted above in the “Summary” section, and with reference to  FIGS. 1A and 1B , even though the input shaft  101  and output shaft  201  are misaligned in service, there is no relative movement during torque transmission between (1) contact surfaces between pins  107  and curved laminate portions  310 , and (2) contact surfaces between flat laminate portions  320  and receptacles  207 . Flex in the curved and flat laminate portions  310  and  320  of torsional bearings  300  takes up and absorbs substantially all relative displacement of input shaft  101  and output shaft  201  due to shaft misalignment. To that end, embodiments may provide curved and flat laminate portions  310  and  320  that are bonded with adhesive to their corresponding bearing surfaces on pins  107  and receptacles  207 . Suitable adhesives are described above in the discussion of the construction of torsional bearings  300 . 
       FIG. 5  is a perspective view of spherical bearing  350 . With momentary reference to  FIGS. 1A through 1C , it will be seen that spherical bearing  350  acts as thrust bearing, absorbing compressive and shear forces at the point at which the tip of input shaft adapter  105  contacts output shaft adapter  205  inside cylindrical recess  206 . Spherical bearing receptacle  209  is provided inside output shaft adapter  205 , and is positioned and shaped to mate with spherical bearing  350  when input shaft adapter pins  107  and torsional bearings  300  are fully received and operationally engaged within output shaft adapter receptacles  207 . 
       FIG. 5  depicts spherical bearing  350  as a dome-shaped laminate of alternating metal and rubber layers. More colloquially, preferred embodiments of spherical bearing  350  have a general “contact lens” shape. With momentary reference to  FIGS. 1A and 1B , for example, spherical bearing  350  allows a large thrust load to be transmitted through from input shaft assembly  100  to output shaft assembly  200  while also allowing a small angle of deflection. It will be appreciated that spherical bearing  350  obviates metal-to-metal contact between the tip of input shaft adapter  105  and output shaft adapter  250  responsive to the thrust load. 
     Spherical bearing  350  is similar in materials and construction to curved and flat laminate portions  310  and  320  on torsional bearings  300 , as described above.  FIG. 6  is a section as shown on  FIG. 5 , and illustrates preferred embodiments of spherical bearing  350  to be of substantially uniform laminate thickness.  FIG. 7  is an enlargement as shown on  FIG. 5 , and depicts spherical bearing  350  to comprise alternating metal layers  352  and rubber layers  354 . As described above with respect to metal layers  312  and rubber layers  314  on torsional bearings  300 ,  FIG. 7  depicts a metal layer  352  as the immediate contact interface with input shaft adapter  105  on one side, and with spherical bearing receptacle  209  on the other side. Other embodiments may provide a rubber layer  354  as the immediate contact interface on either or both sides. It has been found advantageous to provide rubber layer  314  as the immediate contact interface with pins  107  in deployments where adhesive is used to adhere spherical bearing  350  to input shaft adapter  105  and/or spherical bearing receptacle  209  during assembly. 
     Currently preferred embodiments of individual metal layers  352  and rubber layers  354  on spherical bearing  350  may preferably have individual thicknesses consistent with the thickness ranges described above with respect to metal layers  312  and rubber layers  314  on torsional bearings  300 , although the scope of this disclosure is not limited in this regard. Currently preferred embodiments of overall laminate thicknesses of spherical bearing  350  are in the range of 0.040″ to 0.500″. 
     Currently preferred embodiments of individual metal layers  352  and rubber layers  354  on spherical bearing  350  may preferably be made of materials consistent with the materials and constructions described above with respect to metal layers  312  and rubber layers  314  on torsional bearings  300 , although the scope of this disclosure is not limited in this regard. In currently preferred embodiments, fabrication of spherical bearings  350  utilizes a series of spherical dies where each individual metal layer  352  is pressed to a custom curvature in register with its neighboring metal layers  352 , so that a uniform thickness of rubber layers  354  and a constant overall thickness can be maintained throughout spherical bearings  350 . Rubber layers  354  can be pre-formed in a die press with suitable spherical curvature, or cut to a geometrical shape that avoids overlapping material folds during assembly. 
     It will be appreciated that similar to the discussion above with respect to torsional bearings  300 , and with reference to  FIGS. 1A and 1B , there is no relative movement during torque transmission between (1) contact surfaces between the tip of input shaft adapter  105  and spherical bearing  350 , and (2) contact surfaces between spherical bearing  350  and spherical bearing receptacle  209 , even though the input shaft  101  and output shaft  201  are misaligned in service. Flex in spherical bearing  350  takes up and absorbs substantially all relative displacement of input shaft  101  and output shaft  201  due to shaft misalignment and/or thrust load during service. To that end, embodiments may provide a spherical bearing  350  that is bonded with adhesive to its corresponding bearing surfaces on the tip of input shaft adapter  105  and spherical bearing receptacle  209 . Suitable adhesives are described above in the discussion of the construction of torsional bearings  300 . 
       FIG. 8  is a partially exploded view of input shaft assembly  100 , torsional bearings  300  and spherical bearing  350  immediately before (with reference to  FIG. 1A ) insertion into output shaft adapter  205  during assembly. 
       FIG. 9  is a partially exploded view of  FIG. 1A  (without the cutout shown on  FIG. 1A ).  FIG. 10  is an elevation view of  FIG. 1A  (without the cutout shown on  FIG. 1A ).  FIG. 11  is a section as shown on  FIG. 10 , and  FIG. 12  is a modified version of  FIG. 11  showing transmission misalignment. 
       FIGS. 9 and 11  are useful to describe aspects of currently preferred assembly methods of the components shown on  FIGS. 1A through 1C  (and  FIGS. 9 and 11 ). Boot retainer  215  and boot  214  are received over input shaft adapter  105 . Note the smallest inside diameter of boot retainer  215  should be greater than max pin nose diameter  109  in order for boot retainer  215  to slide over. Boot retainer  215  and boot  210  are then moved temporarily down/along input shaft  101  while assembly continues. Alternatively, boot retainer  215  may be provided in two halves and assembled over input shaft  101  if the smallest inside diameter of boot retainer  215  is designed to be less than max pin nose diameter  109 . Adhesive is applied as desired to the bearing surfaces of pins  107 , curved laminate portions  310  of torsional bearings  300 , receptacles  207 , flat laminate portions  320  of torsional bearings  300 , tip of input shaft adapter  105 , spherical bearing  350  and spherical bearing receptacle  209 . Input shaft assembly  100  is assembled (refer  FIG. 8 ) and inserted into output shaft assembly  200 . Pressure is applied before heating the assembled pieces to 300 deg F for 30-90 mins to cure the adhesive. 
     With reference now to  FIGS. 1A  though  1 C and  FIGS. 9 and 11  again, boot  210  and boot retainer  215  are slid into position where seal lip  212  locks into its groove on boot retainer  215  and metal strap  214  is tightened down to hold boot  210  to input shaft adapter  105 . Boot retainer  215  is screwed down onto output shaft adapter  205  via threads  217 . It will be appreciated from  FIG. 11  that when fully screwed down, boot retainer  215  forces the distal end of boot  210  (near seal lip  212 ) onto input shaft adapter  105 . A suitable adhesive and/or an additional metal strap may also be used to secure the distal end of boot  210  to input shaft adapter  105 . A suitable adhesive may also be applied to secure seal lip  212  to boot retainer  215 . 
       FIG. 11  also illustrates radius “r” of spherical bearing  350 . In currently preferred embodiments, “r” is selected to have a center point that coincides with the midpoint of pins  107  as deployed on input shaft adapter  105 .  FIG. 11  further illustrates fill port  221  and evacuate port  223  for lubricant in alternative embodiments in which input shaft assembly  100  and output shaft assembly are a sealed unit. See discussion of “variations” immediately below regarding such sealed unit embodiments. It will be therefore seen with reference to embodiments illustrated on  FIG. 11  that output shaft adapter  205  has an outer output shaft adapter periphery on the first end thereof (towards input shaft  101 ). Fill port  221  connects the outer output shaft adapter periphery to the recess provided by spherical bearing receptacle  209  in output adapter shaft  205 . [Refer to description above associated with  FIG. 1C  for further understanding of the recess provided by spherical bearing receptacle  209  in output adapter shaft  205 .] Evacuate port  223  also connects the outer output shaft adapter periphery to the recess provided by spherical bearing receptacle  209  in output adapter shaft  205 . Fill port  221  and evacuate port  223  may be sealed as required with suitable tapered pipe plugs. Evacuate port  223  may be used in conjunction with a conventional vacuum pump: (1) during filling through fill port  221 , to evacuate lubricant chamber in order to vacuum-assist distribution of lubricant throughout the chamber, and (2) to remove lubricant from throughout the chamber during lubricant purge.  FIG. 11  further illustrates that in some embodiments, adhesive bonding  357 ,  358  may be provided between at least one of: (1) the laminate portion of spherical bearing  350  and the tip provided by shaft adapter  105 ; and/or (2) the laminate portion of spherical bearing  350  and the recess provided by spherical bearing receptacle  209  in output adapter shaft  205  (although the scope of this disclosure is not limited in either of these regards). 
       FIG. 12  illustrates the flex of torsional bearings  300  and spherical bearing  350  during transmission misalignment. 
     Variations on Laminated Bearings Embodiments 
     Currently preferred embodiments envisage three (3) to eight (8) torsional bearings  300  equally spaced around input shaft adapter  105 . This disclosure is not limited in this regard, however, and any number of bearings could be deployed. Within currently preferred embodiments, four (4) to eight (8) pins are more preferred, with four (4) to six (6) pins used on 4.75″ to 6.75″ shaft sizes, and eight (8) pins used on larger sizes. 
     Embodiments of the disclosed transmission may run as a sealed assembly with grease or oil lubrication. Refer to disclosure above with reference to  FIG. 11 . Because the internal components in the laminated bearings embodiments described herein are configured to avoid metal-to-metal sliding contact, however, other embodiments may be left unsealed, and may be further optimized for mud compatibility in such unsealed state. 
     Embodiments of the disclosed transmission may be combined with several types of thrust and tension socket devices to control the thrust load of the rotor. The scope of this disclosure is not limited in this regard. For example, and without limitation, a thrust surface and tension rod coupling could be provided instead of the spherical bearing  350  as received into spherical bearing receptacle  209  as described above. 
     Embodiments of the disclosed torsional bearings  300  may also be combined with other, alternative transmission designs transmitting torque between misaligned or angularly displaced shafts, such as, for example, universal joint designs, CV joint designs, claw joint designs or knuckle joint designs. Deployment of embodiments of the disclosed torsional bearings  300  on such alternative transmission design may provide advantages as described above in this disclosure, including improving the operational torque transfer efficiency and life cycle in such alterative designs. 
     In particular, without limiting the preceding paragraph, the double knuckle transmission coupling disclosed in U.S. Published Patent Application 2017/0045090 (applicant Lord Corporation of Cary, N.C., U.S.A) is considered highly suitable for modification to include embodiments of torsional bearings  300  as described in this disclosure. In this regard, the following Figures and paragraphs of the written specification of 2017/0045090 are incorporated into this disclosure by reference as if fully set forth herein: (1)  FIGS. 2 through 21B  of 2017/0045090; and (2) paragraphs 0004 through 0028, paragraphs 0038 through 0050, and paragraphs 0053 and 0054 of 2017/0045090. 
     For example, referring to  FIGS. 6, 7, 8, 9, 11 and 12  in 2017/0045090 and associated narrative, the interfaces between couple center element  404  and input yoke  402 /output yoke  406  may be adapted to receive embodiments of torsional bearings  300  as described in this disclosure. In more detail, arcuate recesses  432  on input yoke  402  and arcuate recesses  443  on output yoke  406  in 2017/0045090 may be adapted to provide shaped receptacles, and then torsional bearings  300  may be provided in such shaped receptacles. The curvatures on curved laminate portions  312  on torsional bearings  300  (referring to  FIG. 3  herein) may preferably be selected to match corresponding curvatures on arcuate recesses  432 ,  443  on input yoke  402 /output yoke  406  in 2017/0045090. Knuckles  411  on couple center element  404  will then bear on curved laminate portions  312  of torsional bearing  300  (referring to  FIG. 3  herein) when input yoke  402 , output yoke  406  and couple center element  404  are assembled. Resilient bearing contact could thereby be provided at the interfaces between couple center element  404  and input yoke  402 /output yoke  406 . Such an adaptation may thus provide many of the same advantages described above in this disclosure to the double knuckle coupling described in 2017/0045090. Further, the shaped receptacles provided in arcuate recesses  432 ,  443  in 2017/0045090 may receive torsional bearings  300  snugly such that flat laminate portions  320  on torsional bearings  300  (again referring to  FIG. 3  herein) provide further resilient bearing contact between couple center element  404  and input yoke  402 /output yoke  406 . 
     Alternatively and/or additionally, laminated bearings may be provided at torque transfer interfaces between faces  416  on couple center element  404  in 2017/0045090 when couple center element  404  is received within slots  436 ,  439  on input yoke  402 /output yoke  406 . 
     Some embodiments of the adaptation described in the preceding paragraph (hereafter, “double knuckle coupling adaptation”) may have contact surfaces adhesively bonded as described above in this disclosure. Some embodiments of the double knuckle coupling adaptation may be open to mud flow, and others may be protected from mud flow. Some embodiments of torsional bearings  300  deployed in the double knuckle coupling adaptation may have curved faces provided thereon, so that when received in the shaped receptacles, torsional bearings  300  are flush with the outer surfaces of input yoke  402  and output yoke  406 . In some embodiments of the double knuckle coupling adaptation, torsional bearings  300  may be provided in all occurrences of the interfaces between couple center element  404  and input yoke  402 /output yoke  406 . In other embodiments, torsional bearings  300  may be provided in selected ones of such interfaces. 
     Unlaminated Bearings Embodiments 
     The scope of this disclosure is not limited to laminated bearings embodiments such as torsional bearings  300  and spherical bearings  350  described above with reference to  FIGS. 1 through 12 . Selected bearings may be unlaminated (or “monolithic”) bearings. Selected unlaminated bearing materials could also include, without limitation, polymer, plastic or metals. Preferably, unlaminated bearings described in this disclosure have the “bridge”-style shape. However, selected unlaminated bearing shapes could also include, without limitation, flat, spherical, cylindrical or chevron shapes. 
     The unlaminated bearings embodiments described below with reference to  FIGS. 13A and 20A  are referred to as “Torque Transfer Elements” (TTEs) in order to provide a different nomenclature in this disclosure from the laminated bearings embodiments described above with reference to  FIGS. 1 through 12 . As described above, laminations in laminated bearings embodiments (such as torsional bearings  300  and spherical bearings  350  on  FIGS. 1 through 12 ) are disposed to “flex” during misaligned (articulated) shaft rotation. By contrast, unlaminated bearings (or TTEs), embodiments of which are described below with reference to  FIGS. 13A  though  20 H, are disposed to slide and displace within pockets (or “housing cavity receptacles”) provided in the internal periphery of the housing in which the articulating shaft is received. As the shaft “tilts” about its untilted axial centerline during misaligned (articulated) rotation, curved bearing surfaces on shaft pins slidably rotate against corresponding curved bearings surfaces on the TTEs as received in the housing cavity receptacles. Further, substantially flat surfaces on the TTEs are disposed to slidably displace against corresponding bearing surfaces on the housing cavity receptacles as the shaft tilts and the curved bearing surfaces on the shaft pins slidably rotate against curved bearing surfaces on the TTEs. The sliding displacement of TTEs with respect to the housing cavity receptacles during articulated rotation is in a direction generally parallel to the shaft&#39;s untilted axial centerline. Preferably, the curved bearing surfaces on the shaft pins are convex, and the curved bearing surfaces on the TTEs are concave, although the scope of this disclosure is not limited in this regard. 
     Reference is now made to  FIGS. 13A through 20H  in describing currently preferred transmission embodiments including unlaminated torsional bearings. For the purposes of the following disclosure,  FIGS. 13A through 20H  should be viewed together. Any part, item, or feature that is identified by part number on one of  FIGS. 13A through 20H  will have the same part number when illustrated on another of  FIGS. 13A through 20H . It will be understood that the embodiments as illustrated and described with respect to  FIGS. 13A through 20H  are exemplary, and the scope of the inventive material set forth in this disclosure is not limited to such illustrated and described embodiments. 
     As noted above, the scope of the inventive material set forth in this disclosure is not limited to specific deployments of the described embodiments. For example, the following description directed to unlaminated embodiments makes reference to upper and lower housing assemblies  1200 U,  1200 L each operationally engaged with shaft assembly  1100  at opposing ends thereof. These embodiments reflect a typical BHA deployment. The description below is not limited to such an exemplary deployment, however. 
       FIG. 13A  is a partial cutaway and exploded view of an exemplary transmission embodiment according to this disclosure in which upper housing assembly  1200 U is rotatably connected to lower housing assembly  1200 L via misaligned (articulated) rotation of shaft assembly  1100 .  FIG. 17  is a fully exploded view of the transmission embodiment shown on  FIG. 13A . Generally on  FIGS. 13A and 17 , applied torque is shown transmitted from upper housing assembly  1200 U into shaft assembly  1100 , and then into lower housing assembly  1200 L. A general convention is followed throughout the embodiments illustrated on  FIGS. 13A through 20H , in which applied torque is disposed to follow shaft rotation in a clockwise direction looking downhole from an illustrated “high side” (see notation near upper housing assembly  1200 U on  FIGS. 13A and 17 ) to an illustrated “low side” (see notation near lower housing assembly  1200 L). This convention follows the generally accepted subterranean drilling convention of “clockwise rotation looking downhole”. In particular, this convention follows the general convention of configuring the rotor of a positive displacement motor (“PDM” or “mud motor”) to rotate a shaft in a clockwise direction looking downhole. 
     It will be understood, however, that the scope of this disclosure is not limited to embodiments following the “clockwise rotation looking downhole” convention for rotation and torque. Alternative embodiments, not illustrated, configured to transmit applied torque in a counterclockwise direction looking downhole are within the scope of this disclosure. Persons of ordinary skill in this art will require very little experimentation to adapt the embodiments illustrated on  FIGS. 13A through 20H  of this disclosure to transfer applied torque in the opposite direction from the direction illustrated. In many cases, it will require no more than reversing orientations of illustrated components or creating “minor images” of illustrated assemblies. 
       FIGS. 13A and 17  should be viewed together for a more detailed understanding of applied torque transmission from upper housing assembly  1200 U into shaft assembly  1100 , and then into lower housing assembly  1200 L. Upper housing assembly  1200 U includes upper housing  1205 U, which in turn includes upper housing threads  1201 U provided on one end thereof. Upper housing threads  1201 U are preferably configured to mate with an adapter ultimately connected rotatably to a PDM rotor, although the scope of this disclosure is not limited any particular component with which upper housing threads  1201 U may be configured to mate. Shaft rotation direction R on  FIGS. 13A and 17  illustrates clockwise rotation of upper housing assembly  1200 U looking downhole, consistent with the corresponding general convention of configuring a PDM rotor to rotate clockwise looking downhole, as described above. 
     Lower housing assembly  1200 L includes lower housing  1205 L, which in turn includes lower housing threads  1201 L provided on one end thereof. Lower housing threads  1201 L are preferably configured to mate with a motor bearing mandrel or drive shaft ultimately connected to a rotary bit, although the scope of this disclosure is not limited any particular component with which lower housing threads  1201 L may be configured to mate. Shaft rotation direction R on  FIGS. 13A and 17  further illustrates clockwise rotation of lower housing assembly  1200 L looking downhole, consistent with the corresponding general convention of configuring a PDM rotor to rotate clockwise looking downhole, as described above. 
       FIGS. 13A and 17  show upper and lower housings  1205 U,  1205 L as hollow, with internal receptacles and surfaces formed therein according to Figures and detailed description set forth below.  FIGS. 13A and 17  further show that shaft assembly  1100  provides a shall head  1102  at each end of shaft  1101 . As will be described in more detail further below, each shaft head  1102  is configured to be received into a corresponding one of upper and lower housings  1205 U,  1205 L and, when received therein, to interface with receptacles and surfaces formed internally on upper and lower housings  1205 U,  1205 L. As seen on  FIGS. 13A and 17 , each shaft head  1102  provides a preselected number of shaft pins  1106 . Shaft pins  1106  are preferably spaced equally in radial disposition around shaft head  1102 , although the scope of this disclosure is not limited to equi-spaced radial disposition. Five (5) shaft pins  1106  are provided on each shaft head  1102  in the embodiments illustrated on  FIGS. 13A through 20H , although again the scope of this disclosure is not limited to any particular number of shaft pins  1106  per shaft head  1102 . Other embodiments (not illustrated) may provide shaft heads with other numbers of shaft pins, and/or with other than equi-spaced radial disposition. Other embodiments (not illustrated) may also provide a number and spacing configuration of shaft pins on a shaft head at one end of a shaft that differs from the number and spacing configuration of shaft pins at the other end of the shaft. 
       FIG. 17  illustrates each shaft pin  1106  preferably providing a curved shaft pin bearing surface  1109  and a shaft backlash surface  1105 . The curved shaft pin bearing surface  1109  on one shaft pin  1106  generally faces the shaft backlash surface  1105  of a neighboring shaft pin  1106 . 
       FIGS. 13A and 17  further illustrate Torque Transfer Elements (“TTEs”)  1300  interposed between shaft pins  1106  and upper and lower housings  1205 U,  1205 L when shaft heads  1102  are received into upper and lower housings  1205 U,  1205 L. Preferably, one (1) TTE  1300  is provided for each shaft pin  1106 , as depicted in the embodiments illustrated throughout  FIGS. 13A through 20H  in this disclosure. It will nonetheless be appreciated that the scope of this disclosure is not limited in this regard, and other embodiments may provide some shaft pins without TTEs, or some shaft pins with laminated torsional bearings (embodiments of which are described above in this disclosure with reference to  FIGS. 1 through 12 ). 
       FIGS. 13A and 17  further illustrate: Upper and lower boots  1210 U,  1210 L; upper and lower boot retaining rings  1211 U,  1211 L; and upper and lower split rings  1212 U,  1212 L. Boots  1210 U/L, boot retaining rings  1211 U/L and split rings  1212 U/L advantageously seal the connection between shaft  1101  and upper and lower housings  1205 U,  1205 L at either end of shaft  1101 . Boots  1210 U/L are preferably made of a rubber or elastomer material in order to provide seals while at the same time permitting independent articulation between shaft  1101  and upper housing  1205 U at one end of shaft  1101 , and between shaft  1101  and lower housing  1205 L at the other end of shaft  1101 . 
     From this point forward in the discussion of  FIGS. 13A through 20H , the Figures and associated disclosure will describe features, aspects and alternative embodiments with reference to assemblies at the “low side” as drawn on  FIGS. 13A and 17 . That is, the Figures and associated disclosure will describe features, aspects and alternative embodiments in and around and associated with lower housing assembly  1200 L as depicted on  FIGS. 13A and 17 . Persons of ordinary skill in this art will require very little experimentation to reverse the orientation of embodiments illustrated with reference to the “low side” on  FIGS. 13A and 17  in order to understand corresponding assemblies and features on the “high side”. 
       FIG. 13B  is a perspective view of lower housing  1205 L on  FIG. 13A  in isolation.  FIG. 13C  is a section as shown on  FIG. 13B .  FIG. 13B  shows that lower housing  1205 L is generally hollow, providing housing cavity  1206  formed therein.  FIG. 13C  shows housing cavity receptacles  1207  provided in lower housing  1205 L generally at a periphery of housing cavity  1206 . With momentary reference to  FIGS. 13A and 17 , it will be appreciated that lower housing  1205 L provides one (1) housing cavity receptacle  1207  each for receiving a corresponding shaft pin  1106  on shaft head  1102 . Thus, five (5) housing cavity receptacles  1207  are illustrated on  FIG. 13C , one each for receiving a corresponding one of the five (5) shaft pins  1106  shown on  FIG. 17 . 
       FIG. 13C  further illustrates that each housing cavity receptacle  1207  provides a housing bearing surface  1203  and a housing backlash surface  1202 .  FIG. 13B  illustrates housing bearing surfaces  1203  and housing backlash surfaces  1202  in perspective view. 
       FIGS. 13B and 13C  further illustrate optional hard facing  1209  inside lower housing  1205 L. In embodiments where provided, hard facing  1209  assists reducing thrust wear between shaft head  1102  and lower housing  1205 L during articulated/misaligned rotation of shaft head  1102  as received in lower housing  1205 L. It will be understood that hard facing  1209  may optionally also be provided in upper housing  1205 U. In other non-illustrated embodiments, hard facing may be provided on the tip of shaft head  1102 , or a thrust bearing may be provided instead of hard facing  1209 . 
       FIG. 14A  is a section as shown on  FIG. 13A .  FIG. 14B  is a section as shown on  FIG. 14A .  FIGS. 14A and 14B  show shaft pins  1106  engaged with TTEs  1300  in housing cavity receptacles  1207 . Curved shaft pin bearing surfaces  1109  on shaft pins  1106  slidably engage with curved TTE pin bearing surfaces  1301 . TTE housing bearing surfaces  1302  further slidably engage with housing bearing surfaces  1203 . Following the convention of clockwise shaft rotation R looking downhole per  FIG. 13A ,  FIG. 14A  illustrates applied torque transfer in a clockwise direction in the following sequence: (A) from shaft pins  1106  on shaft head  1102  into TTEs  1300 ; and then (B) through TTEs  1300  and into lower housing  1205 L via housing bearing surfaces  1203 .  FIGS. 14A and 14B  further illustrate that during such applied clockwise torque transfer, TTE housing bearing surface  1302  bears upon housing bearing surface  1203 .  FIG. 14B  also shows that during such applied clockwise torque transfer, curved shaft pin bearing surfaces  1109  provided on shaft pins  1106  bear upon curved TTE pin bearing surfaces  1301 . 
     With reference now to  FIG. 17 , it will be understood that a reverse transfer sequence enables “applied clockwise torque transfer looking downhole” at upper housing assembly  1200 U, in which torque is transferred in the following sequence: (A) from upper housing  1205 U into TTEs  1300 ; and then (B) into shaft pins  1106  on shaft head  1102 . This reverse sequence is like imagining torque transfer on  FIG. 14A  in the opposite direction (counterclockwise) to rotation direction R as illustrated on  FIG. 14A . 
     With further reference now to  FIGS. 14A and 14B , it will be appreciated that in currently preferred embodiments, the illustrated geometries are designed so that the maximum shaft pin diameters  1110  on shaft pins  1106  are on a locus  1409  whose diameter coincides with the external diameter of lower housing assembly  1200 L at lower housing threads  1201 L (such external diameter also illustrated on  FIG. 14A  as dotted line  1409 ). In this way, in such currently preferred embodiments, torque is directly transferred through the full cross-section of lower housing assembly  1200 L at lower housing threads  1201 L, substantially unifying the torque stress gradients across lower housing assembly  1200 L at that threaded connection. It will nonetheless be appreciated, however, that the scope of this disclosure is not limited to deployments in which locus  1409  of maximum shaft pin diameters  1110  coincides with the external diameter of lower housing assembly  1200 L at lower housing threads  1201 L. 
     Additionally, as further shown on  FIGS. 14A and 14B , shaft pins  1106  are free to slidably rotate about TTEs  1300  during misaligned (articulated) rotation of shaft  1101 . Likewise, TTEs  1300  are free to slidably displace within housing cavity receptacles  1207  during misaligned (articulated) rotation of shaft  1101 . Shaft pins  1106  are disposed to rotate about TTEs  1300  at the interface between curved shaft pin surfaces  1109  and curved TTE pin bearing surfaces  1301 . TTEs  1300  are disposed to slidably displace within housing cavity receptacles  1207  at the interface between TTE housing bearing surfaces  1302  and housing bearing surfaces  1203 .  FIG. 14B  illustrates that rotation of shaft pins  1106  about TTEs  1300  is about shaft pin centerlines  1107 , and that the interface between curved shaft pin surfaces  1109  and TTE pin bearing surfaces  1301  is at shaft pin radius  1111  from shaft pin centerline  1107 .  FIG. 14B  further shows that shaft pin radius  1111  defines the maximum shaft pin diameter  1110  for shaft pins  1106 .  FIGS. 13A and 14B  illustrate that sliding displacement of TTEs  1300  within housing cavity receptacles  1207  is in a direction generally parallel to the shaft&#39;s untilted (undeflected) axial centerline  1103 , such that the TTEs  1300  float at least generally parallel to an untilted axial shaft centerline  1103  when the  11 B housing bearing surfaces  1302  slidably displace against corresponding housing bearing surfaces  1203 . [Undeflected (or untilted) shaft centerline  1103  is also shown on  FIG. 19B ]. 
       FIG. 18  is a further partial cutaway view of lower housing assembly  1200 L as also illustrated on  FIG. 13A .  FIG. 19A  is a section as shown on  FIG. 18 .  FIGS. 19B and 19C  are “faux section” views as shown  FIG. 19A , depicting shaft assembly  1100  substantially assembled at lower housing assembly  1200 L per  FIGS. 13A, 14A and 14B , in which  FIGS. 19B and 19C  combine to schematically depict articulation during misaligned rotation. By “faux section” views, it will be understood from  FIG. 14A , for example, that since the illustrated embodiments depict five (5) shaft pins  1106  and associated TTEs  1300  distributed evenly around the periphery of shaft head  1102 , a true straight line section through the assembly of shaft assembly  1100  at lower housing assembly  1200 L does not allow shaft pins  1106  on opposite sides of shaft head  1102  to be seen on one view. Thus,  FIGS. 19B and 19C  depict more of a “pie-shaped” or “offset” section through the assembly of shaft assembly  1100  at lower housing assembly  1200 L, so that shaft pins  1106  on opposite sides of shaft head  1102  can be seen on each of  FIGS. 19B and 19C . 
       FIG. 18  illustrates parts and features also described above with reference to  FIGS. 13A, 14A and 14B , including shaft  1101 , shaft pins  1106 , lower housing  1205 L and TTEs  1300 .  FIG. 18  also illustrates shaft pin centerline  1107  and shaft pin radius  1111  as previously described above with reference to  FIG. 14B . 
       FIGS. 18, 19B and 19C  should now be viewed together.  FIG. 18  illustrates shaft deflection angle α disposed about shaft pin centerline  1107 . Although shown disposed about shaft pin centerline  1107  on  FIG. 18 ,  FIG. 19C  illustrates that shaft deflection angle α actually represents an angle of shaft deflection (or tilt, or articulation) either side of undeflected shaft centerline  1103  during misaligned rotation of shaft  1101 .  FIG. 19C  shows that at the illustrated moment, deflected shaft centerline  1104  is angularly displaced (or “tilted”) from undeflected shaft centerline  1103  by α/2, where such angular displacement (tilt) is in a first angular direction of shaft misalignment. It will be further understood that although not specifically illustrated, shaft  1101  will also be angularly deflected (tilted) by α/2 in a second angular direction of shaft misalignment during one full revolution of misaligned rotation by shaft  1101 , where the first and second angular directions oppose one another either side of undeflected shaft centerline  1103 . Shaft deflection angle α thus represents the combined angular deflection (tilt) of shaft  1101  in both the first and second angular directions either side of undeflected shaft centerline  1103  during one full revolution of misaligned shaft rotation. 
     Now comparing  FIG. 19B  with  FIG. 19C , it will be seen on  FIG. 19B  that shaft  1101  is in an undeflected condition such that undeflected shaft centerline  1103  is continuous through shaft  1101  and lower housing  1205 L. Shaft pin  1106  on  FIG. 19B  is in a “neutral” position with respect to TTE  1103 . In contrast, shaft  1101  on  FIG. 19C  is shown in a deflected condition as described immediately above, such that deflected shaft centerline  1104  on  FIG. 19C  is angularly displaced (tilted) from undeflected shaft centerline  1103  by α/2. Shaft pin  1106  on  FIG. 19C  is also shown in a deflected condition with respect to TTE  1300 . Shaft pin  1106  has rotated an angle of α/2 about shaft pin centerline  1107  with respect to TTE  1300 . Likewise, curved shaft pin bearing surface  1109  on shaft pin  1106  has slidably rotated an angle of α/2 about shaft pin centerline  1107  with respect to curved TTE pin bearing surface  1301  on TTE  1300 .  FIG. 18  further illustrates the potential for such rotation of shaft pins  1106  about shaft pin centerline  1107  with respect to TTE  1300 .  FIG. 18  shows such potential for rotation by α/2 either side of an undeflected condition (as shown on  FIG. 19B ) for a total overall potential shaft deflection angle α. 
       FIGS. 19B and 19C  further illustrate that TTEs  1300  remain in a generally stationary angular position while shaft pins  1106  rotate about shaft pin centerlines  1107  during misaligned rotation (tilt) of shaft  1101 . However, with additional reference to  FIG. 14B , it will be appreciated that TTEs  1300  are disposed (and are free) to slidably displace within housing cavity receptacles  1207  during misaligned rotation (tilt) of shaft  1101 . As shaft pins  1106  rotate with respect to TTEs  1300  during tilt, TTEs  1300  are disposed (and are free) to displace within housing cavity receptacles  1207  via sliding contact between TTE housing bearing surfaces  1302  and housing bearing surfaces  1203 . As described above,  FIGS. 13A and 14B  illustrate that such sliding displacement of TTEs  1300  within housing cavity receptacles  1207  is in a direction generally parallel to the shaft&#39;s unfilled (undeflected) axial centerline  1103 , such that the TTEs  1300  float at least generally parallel to an untilted axial shaft centerline  1103  when the TTE housing bearing surfaces  1302  slidably displace against corresponding housing bearing surfaces  1203 . 
     The foregoing description of torque transfer via unlaminated bearings (TTEs) has been made with reference to illustrated embodiments in which two housing assemblies  1200 U and  1200 L are provided, one at each end of shaft  1101 . The scope of this disclosure is not limited, however, to two housing assemblies on shaft  1101 . Other embodiments (not illustrated) may provide only one housing assembly on shaft  1101 , on a selected end thereof. In such other embodiments, the scope of this disclosure is further not limited as to the selected end of shaft  1101  (high side or low side on  FIG. 13A ) on which the single housing assembly is to be provided. 
     The foregoing description of torque transfer via both laminated bearings and unlaminated bearings (TTEs) has been made with “pure” assemblies in which all bearings in one articulating assembly are either laminated or unlaminated. The scope of this disclosure is not limited, however, to such “pure” embodiments. Other embodiments (not illustrated) may include “hybrid” articulating assemblies, inside which laminated bearings arrangements (such as described herein with reference to  FIGS. 1 through 12 ) are mixed with unlaminated bearings arrangements (such as described herein with reference to  FIGS. 13A through 20H ). 
     Referring now to  FIGS. 13A and 17 , it will be understood that torque backlash will be created in upper and lower housing assemblies  1200 U,  1200 L whenever applied torque through shaft  1101  is reduced, stopped or even reversed. Torque backlash may be momentary or sustained, responsive to corresponding changes in transmitted torque over time through shaft  1101 . Under the above-described “clockwise looking downhole” convention of shaft rotation direction R on  FIGS. 13A and 17 , torque backlash will be in a counterclockwise direction in response to applied clockwise torque looking downhole. Torque backlash thus manifests itself on  FIG. 14A , for example, in the opposite direction (counterclockwise) to the clockwise shaft rotation direction R looking downhole shown on  FIG. 14A . 
       FIG. 14A  illustrates that during torque backlash events in lower housing assembly  1200 L, applied torque is no longer transferred through TTEs  1300 . Instead, counterclockwise torque backlash causes shaft backlash surface  1105  to bear upon housing backlash surface  1202 . Although not specifically illustrated, it will be understood that the corresponding effect occurs in upper housing assembly  1200 U. 
       FIGS. 20A through 20H  illustrate currently preferred embodiments of alternative backlash energizer assemblies, which, when provided, seek to remediate negative effects of torque backlash.  FIG. 20A  is a section similar to  FIG. 14A , except depicting an alternative embodiment including backlash energizer assembly  1400 .  FIG. 20B  is an exploded view of backlash energizer assembly  1400  from  FIG. 20A  in isolation.  FIGS. 20C and 20D ,  FIGS. 20E and 20F , and  FIGS. 20G and 20H  are each matched pairs of cutaway section views and corresponding exploded isolation views of alternative backlash energizer embodiments  1404 ,  1404 A and  1420 . 
     Referring first to  FIGS. 20A and 20B , backlash energizer assemblies  1400  each include set screw  1401 , puck  1402 , and Belleville washer  1403 . Pucks  1402  are preferably of unitary hard material construction, such as metal or ceramic. Each backlash energizer assembly  1400  is shown on  FIG. 20A  interposed between a shaft backlash surface  1105  and a corresponding housing backlash surface  1202 . Each Belleville washer  1403  is configured to contact and provide compression bias against shaft backlash surface  1105  such that torque backlash will act against Belleville washer  1403 &#39;s bias during backlash events. Each Belleville washer  1403  is further positioned to react against puck  1402  as received into a corresponding recess in housing backlash surface  1202 . Set screws  1401  may be inserted from the outside of lower housing  1205 L through openings  1208  provided for such purpose. Set screws  1401  engage threads provided in openings  1208  to set a user-desired compression bias for Belleville washers  1403  against shaft backlash surfaces  1105 . 
     It will thus be appreciated from  FIGS. 20A and 20B  that backlash energizer assemblies  1400  dampen and absorb torque backlash during backlash events. Belleville washers  1403  (and their associated compression bias) receive torque backlash, and may further temporarily store some of the torque backlash energy during backlash events. Several technical advantages are thus provided. Wear between shaft backlash surface  1105  and housing backlash surface  1202  is reduced, Concussive energy loss between shaft backlash surface  1105  and housing backlash surface  1202  is also reduced by removal of a gap between the two. Further, torque energy during backlash events is not completely lost. Referring to  FIG. 20A , any torque backlash energy stored in Belleville washers  1403  during a backlash event will be released when clockwise torque is reestablished (per shaft rotation direction R shown on  FIG. 20A ). Further, compression bias of Belleville washers  1403  tends to keep shaft pins  1106 , TTEs  1300  and housing bearing surfaces  1203  fully engaged by continuous contact during both normal torque transfer periods and torque backlash events. This in turn: (1) reduces wear on contact surfaces on shaft pins  1106 , TTEs  1300  and housing bearing surfaces  1203 ; (2) reduces concussive energy loss during a transition back to normal torque after a torque backlash event; and (3) reduces the chance of TTEs  1300  becoming dislocated between shaft pins  1106  and housing bearing surfaces  1203  during torque backlash events. 
       FIGS. 20C and 20D  illustrate an alternative embodiment to the backlash energizer assembly  1400  of  FIGS. 20A and 20B . On  FIGS. 20C and 20D , torque backlash remediation is provided by a single puck  1404 . Similar to puck  1402  in backlash energizer assembly  1400 , puck  1404  is preferably of unitary hard material construction, such as metal or ceramic. Puck  1404  on  FIGS. 20C and 20D  provides advantages of simplicity of construction and assembly over backlash energizer  1400  on  FIGS. 20A and 20B , at the expense of advantages that may be provided by the compression bias of Belleville washer  1403  in backlash energizer  1400 , described above. 
       FIGS. 20E and 20F  illustrate an alternative embodiment to the backlash energizer embodiment illustrated on  FIGS. 20C and 20D . On  FIGS. 20E and 20F , a laminated puck  1404 A substituted for the plain single puck  1404  of  FIGS. 20C and 20D . Laminated puck  1404 A provides a resilient laminate construct for opposing contact with shaft backlash surface  1105 , in which the laminate preferably includes alternating elastomer layers  1405  and metal layers  1406 . The laminate, however, may be of any suitable materials. The scope of this disclosure is not limited in this regard. The scope of this disclosure is further not limited to the design of laminate, including as to number of layers and their thicknesses. Puck  1404 A on  FIGS. 20E and 20F  provides similar advantages of simplicity of construction and assembly as puck  1404  on  FIGS. 20C and 20D , and the laminar construction of puck  1404 A may also provide some (or all) of the advantages that may be provided by the compression bias of Belleville washer  1403  in backlash energizer  1400 , described above. 
       FIGS. 20G and 20H  illustrate backlash energizer assembly  1420  as a yet further alternative embodiment to backlash energizers previously described with reference to  FIGS. 20A and 20B, 20C and 20D, and 20E and 20F . Backlash energizer assembly  1420  includes set screw  1421 , plate  1422  and ball  1423 . Backlash energizer assembly  1420  on  FIGS. 20G and 20H  is similar in overall design to backlash energizer assembly  1400  on  FIGS. 20A and 20B , except that plate  1422  in assembly  1420  substitutes for puck  1402  in assembly  1400 , and ball  1423  in assembly  1420  substitutes for Belleville washer  1423  in assembly  1400 . Also, comparing  FIGS. 20G and 20A , the recess provided in lower housing  1205 L for plate  1422  and ball  1423  on  FIG. 20G  may have to be adapted dimensionally to suit plate  1422  and ball  1423  as compared to the corresponding recess for puck  1402  and Belleville washer  1403  on  FIG. 20A . Preferably, the recess provided on  FIG. 20G  leaves sufficient clearance from ball  1423  to allow ball  1423  to rotate within such recess. Backlash energizer assembly  1420  on  FIGS. 20G and 20H  thus further facilitates keeping shaft pins  1106 , TTEs  1300  and housing bearing surfaces  1203  fully contact-engaged during both normal torque periods and torque backlash events even when (especially when) there is relative articulating movement between shaft backlash surface  1105  and housing backlash surface  1202 . It will be appreciated that in previously described embodiments ( FIGS. 20A and 20B, 20C and 20D, and 20E and 20F ), keeping shaft pins  1106 , TTEs  1300  and housing bearing surfaces  1203  fully contact-engaged during relative articulating movement between shaft backlash surface  1105  and housing backlash surface  1202  requires sliding contact between shaft backlash surface  1105  and Belleville washer  1403 , and pucks  1404  and  1404 A respectively. Such sliding contact may lead to wear and/or loss of contact between shaft backlash surface  1105  and Belleville washer  1403 , and pucks  1404  and  1404 A respectively. Rolling contact between shaft backlash surface  1105  and ball  1423  on  FIGS. 20G and 20H  remediates any such concerns brought on by corresponding sliding contact in other backlash energizer embodiments. 
     It will be understood that the scope of this disclosure is not limited to the backlash energizer designs described above. The scope of this disclosure is not limited to any specific backlash energizer embodiment or configuration thereof. Some embodiments may provide no backlash energizer at all, or a hybrid including backlash energizers in some locations and not others. Some embodiments may further provide hybrids in which different backlash energizer designs are mixed on one housing assembly, or over two housing assemblies (upper and lower). Such embodiments providing mixed configurations may also include hybrid embodiments in which no backlash energizer is provided at selected locations. 
       FIGS. 15A through 15G  illustrate various alternative Torque Transfer Element (“TTE”) embodiments. Earlier disclosure identified TTEs  1300  included in the illustrated embodiments of upper and lower housing assemblies  1200 U,  1200 L on  FIGS. 13A, 14A, 14B and 17 .  FIG. 15A  illustrates TTE  1300 A, which for reference is the same TTE embodiment as TTE  1300  depicted on  FIGS. 13A and 17 .  FIGS. 15B through 15G  illustrate TTEs  1300 B through  1300 G respectively (in which TTE  1300 B through  1300 G are alternative embodiments to TTE assembly  1300 A on  FIG. 15A ).  FIG. 16  is an enlargement as shown on  FIG. 15B . 
     TTE  1300 A on  FIG. 15A  includes curved TTE pin bearing surface  1301 A and TTE housing bearing surface  1302 A, which correspond to TTE pin bearing surface  1301  and TTE housing bearing surface  1302  on  FIGS. 13A, 14A, 14B and 17 , for example. 
       FIG. 15B  and  FIG. 16  are similar to  FIGS. 3 and 4 .  FIGS. 3 and 4  are described in detail above in this disclosure. TTE  1300 B on  FIG. 15B  includes curved TTE pin bearing surface  1301 B and TTE housing bearing surface  1302 B. Curved TTE pin bearing surface  1301 B and TTE housing bearing surface  1302 B on  FIG. 15B  each include a laminate for opposing contact with curved shaft pin bearing surface  1109  and housing bearing surface  1203  (refer  FIG. 14B , for example). The laminate preferably includes alternating TTE elastomer and metal layers, such as TTE elastomer layers  1314  and TTE metal layers  1312  on curved TTE pin bearing surface  1301 B depicted on  FIG. 16 . The laminate, however, may be of any suitable materials. The scope of this disclosure is not limited in this regard. The scope of this disclosure is further not limited to the design of laminate, including as to number of layers and their thicknesses. TTE  1300 B on  FIG. 15B , with its laminated bearing surfaces, enables resilient contact with curved shaft pin bearing surface  1109  and housing bearing surface  1203  with some compression bias. With further reference to  FIG. 14B , such compression bias assists with keeping shaft pins  1106 , TTEs  1300 B and housing bearing surfaces  1203  fully engaged by continuous contact during both normal torque transfer periods and torque backlash events. In particular, and referring momentarily to  FIG. 14A , it will be understood that compression bias from TTE  1300 B may retain shaft pins  1106 , TTEs  1300 B and housing bearing surfaces  1203  together during misaligned rotation. 
     Referring now to  FIGS. 15C through 15G  together, TTEs  1300 C through  1300 G each include curved TTE pin bearing surfaces  1301 C through  1301 G and TTE housing bearing surfaces  1302 C through  1302 G respectively. TTE housing bearing surfaces  1302 C,  1302 F and  1302 G each differ from curved TTE housing bearing surface  1302 A on  FIG. 15A  in that they have curvature, whereas TTE housing bearing surface  1302 A on  FIG. 15A  is substantially planar. TTE housing bearing surface  1302 C on  FIG. 15C  is curved in a longitudinal transmission assembly direction (i.e. parallel to undeflected shaft centerline  1103  shown on  FIGS. 19B and 19C ). TTE housing bearing surface  1302 F on  FIG. 15F  is curved in a transverse direction  1325 F (i.e. orthogonal to undeflected shaft centerline  1103  shown on  FIGS. 19B and 19C ). TTE housing bearing surface  1302 G on  FIG. 51G  is curved in both longitudinal and transverse directions ( 1325 G). With momentary reference to  FIGS. 14A and 14B , curvature on TTE housing bearing surfaces  1302 C,  1302 F and  1302 G further assists with continuous contact between housing bearing surfaces  1203  and TTE housing bearing surfaces  1302 C,  1302 F and  1302 G during misaligned rotation. 
     Referring now to  FIG. 15D , TTE  1300 D includes curved TTE pin bearing surface  1301 D and TTE housing bearing surface  1302 D. TTE  1300 D on  FIG. 15D  is a further alternative embodiment to TTE  1300 A on  FIG. 15A . TTE housing bearing surface  1302 D on  FIG. 15D  differs from TTE housing bearing surface  1302 A on  FIG. 15A  in that TTE housing bearing surface  1302 D includes angled faces at the periphery, whereas TTE housing bearing surface  1302 A on  FIG. 15A  is substantially planar. Embodiments according to  FIG. 15D  are useful to provide clearance at the edges of TTE housing bearing surface  1302 D in limited space deployments where the corners of TTE  1300 D might interfere with corners in housing cavity receptacle  1207  (refer to  FIG. 14B , for example). 
     Referring now to  FIG. 15E , TTE  1300 E includes curved TTE pin bearing surface  1301 E and TTE housing bearing surface  1302 E. TTE  1300 E on  FIG. 15E  is a further alternative embodiment to TTE  1300 A on  FIG. 15A . Curved TTE pin bearing surface  1301 E on  FIG. 15E  differs from curved TTE pin bearing surface  1301 A on  FIG. 15A  in that curved TTE pin bearing surface  1301 E provides hard facing  1330 E. (It will be understood that hard facing  1330 E is actually integral with curved TTE pin bearing surface  1301 E although illustrated as a separate item for clarity). It will be further appreciated that internal hard facing  1300 E on curved TTE pin bearing surface  1301 E, per  FIG. 15E , reduces contact wear on curved TTE pin bearing surface  1301 E during misaligned shaft rotation. 
     It will be understood that the scope of this disclosure is not limited to the various TTE designs described above. The scope of this disclosure is not limited to any specific TTE embodiment or configuration thereof. Some embodiments may provide hybrids in which different TTE designs are mixed on one housing assembly, or over two housing assemblies (upper and lower). Further, TTE designs as described above may be combined into single TTE embodiments (such as, for example, combining the hard facing embodiment of  FIG. 15E  with a curved TTE housing bearing surface embodiment selected from  FIGS. 15C, 15F or 15G  into one hybrid TTE embodiment). 
     Although the inventive material in this disclosure has been described in detail along with some of its technical advantages, it will be understood that various changes, substitutions and alternations may be made to the detailed embodiments without departing from the broader spirit and scope of such inventive material as set forth in the following claims.