Abstract: In a principal section of the flexible external gear of a wave gear drive, a position away from the major axis of an elliptically shaped neutral line of the rim of the flexible external gear is defined as the center position of the teeth meshing, and &thgr; is the angle of inclination of the tangent of that position with a point along the neutral line of the rim. The amount of flexing w of the principal section is defined according to the angle of inclination &thgr;, the number of teeth zF of the flexible external gear, the number of teeth zC of the rigid internal gear, radius ro of the pitch circle of the flexible external gear, and the radius rn of the neutral curve of the rim prior to deformation.

Abstract: The present invention provides an advanced geometry for skew and straight bevel gears having a localized and more stable bearing contact produced by forging. The localization of bearing contact is achieved by substitution of flat tooth surfaces with parabolic tooth surfaces. This is accomplished by either modifying line-contact directly or by using a generating parabolic cylinder during generation of the tooth surfaces. The actual contact area is spread over an ellipse centered around an instantaneous theoretical point of contact at the apex of the parabolic tooth surface. This localized bearing contact reduces the shift of the bearing due to assembly and manufacturing errors, thereby providing a more durable and quieter gear. Furthermore, the geometry of the gear enables creation of dies from which the gear may be forged. Transmission errors are modeled using a pre-designed parabolic function that coincides with the parabolic tooth surface design of the present invention.

Abstract: A rotary positive-displacement pump comprises two gear wheels which mesh with each other without encapsulation. Each gear wheel has a plurality of teeth with a profile which falls within a band of tolerance of ±{fraction (1/20)}th of the depth of the tooth with respect to a theoretical profile similar to a profile defined by a natural spline function passing through a plurality of nodal points having pre-established coordinates {X, Y}.

Abstract: A gear wheel includes multiple helical toothings, each having a different helical angle. A pressing method for molding a gear wheel involves introducing a compactable material into a chamber of a pressing tool, compacting the material, exposing the helical toothings of the gear wheel, and removing the molded body from the pressing tool. A pressing tool for pressing, as one part, a gear wheel, includes a matrix, cylindrical first and second molding tool parts which can be translated along and then rotated about a longitudinal axis, and a driver coupled to the molding tool parts or driving them. The molding tool parts can be moved towards and away from each other and the inner surface of the matrix delimits the chamber and is shaped to allow a linear axial sliding movement of the compactable material relative to the matrix.

Abstract: A kind of gear is provided with shorter teeth, transition teeth and at least one longer tooth. The cross-section of the longer tooth is of a hawk beak shape, and the profile of the longer tooth is smoothly connected in series by a convex section, a tip section, a concave section, and a leading section The two sides of the longer tooth are each provided with a transition tooth which neighbors a shorter tooth on the opposite side of the longer tooth. The pair of engaging gears according to this invention have advantages of reducing the fluid leakage, canceling the inertia of the rotors, and minimizing the vibration and noise. This invention also discloses a fluid machine for conveying, compressing or expanding liquid or gaseous fluids, which includes a casing comprising a housing, an upper end cover and a lower end cover. At least one pair of engaging gears which includes one driving rotor according to this invention and one driven rotor according to this invention is accommodated in the housing.

Abstract: In a sintered sprocket at least the tooth surface layer contains carbon in the range from 0.6 to 1.2 mass % and nitrogen in the range from 0.05 to 0.5 mass %. The structure of the tooth surface layer comprises a tempered martensite structure and a residual austenitic structure, the residual austenitic structure being 10 to 50 volume % of the tooth surface layer. The density of the tooth surface layer is at least 7.4 g/cm3. Metallic elements contained in a base material comprise at least one metal selected from Ni, Cu and Mo in an amount in the range from 0.5 to 5 mass % the balance being Fe and inevitable impurities. The sintered sprocket exhibits high strength and wear resistance and can be manufactured at low cost.

Abstract: This invention is directed to a novel wave tooth gear having a non-circular pitch curve and uniform wave teeth to create a tighter seal between meshing gears. The non-circular wave tooth gear has a major axis and a minor axis disposed perpendicular to the major axis, wherein the major axis is longer than the minor axis and includes a central hub, a plurality of teeth radially extending from the hub at locations surrounding the hub and a plurality of roots, each root positioned between adjacent teeth at locations surrounding the gear. The teeth include a head portion shaped as an arc segment of a first radius and the roots include a recess shaped as an arc segment of a second radius. The teeth heads are joined to adjacent roots by lines of tangency.

Abstract: A gear and method for producing the gear. The gear has a gear tooth profile conjugate to a gear basic-cutter tooth-profile having an addendum with a convex portion having an addendum point proximal to a pitch line and a dedendum with a concave portion having a dedendum point proximal to the pitch line. The convex portion is complementary with a corresponding portion of a mating-gear basic-cutter tooth-profile dedendum. The concave portion is complementary with a corresponding portion of the mating-gear basic-cutter tooth-profile addendum. A transition zone between the addendum point and the dedendum point has a predetermined width. The gear basic-cutter tooth-profile has a predetermined half pitch relief at the pitch line and continuity of profile and continuity of slope at the addendum point.

Abstract: This document discloses a transmission having a roller cam assembly which comprises a pair of drive shafts, one an input shaft and the other an output shaft, wherein one of said shafts is attached to a toothed cam having a trochoidal profile and the other drive shaft is attached to a roller ring having a plurality of cylindrical roller shafts aligned to mesh with said toothed cam and thereby permitting the transfer of torque from one shaft to the other.

Abstract: A gear bearing having a first gear and a second gear, each having a plurality of teeth. Each gear operates on two non-parallel surfaces of the opposing gear teeth to perform both gear and bearing functions simultaneously. The gears are moving at substantially the same speed at their contact points. The gears may be roller gear bearings or phase-shifted gear bearings, and may be arranged in a planet/sun system or used as a transmission.

Abstract: In an involute tooth profile pair structure, a pinion has a smaller pressure angle at its addendum than at its dedendum, and a pressure angle at an addendum of a gear wheel is equal to the pressure angle at the dedendum of the pinion, and a pressure angle at a dedendum of the gear wheel is equal to the pressure angle at the addendum of the pinion.

Abstract: In an involute tooth profile pair structure, a pinion has a smaller pressure angle at its addendum than at its dedendum, and the pressure angle at the addendum of a gear wheel is equal to the pressure angle at the dedendum of the pinion, with the pressure angle at the dedendum of the gear wheel being equal to the pressure angle at the addendum of the pinion.

Abstract: A form of gearing having teeth with different face widths along the tooth height and a method thereof of designing and manufacturing. Different gear tooth face widths are introduced along the tooth height to alter the tooth stiffness characteristic to provide a pair of gears with reduced mesh stiffness variation. The use of variable face widths along the tooth height changes both the geometric properties of the tooth and the load distribution/concentration to reduce the self-excited component of dynamic load, in effect reducing gear noise and increasing power density.

Abstract: The present invention is a gear system generally having a driven gear, rotatably mounted on an axis, having teeth defined by unique geometrical profiles; a driving means contacting the teeth of the driven gear; and round pins or spheres for engaging the teeth of the driven gear rotatably mounted on the driving means, the round pins or spheres for engaging the teeth of the driven gear roll along a profile of the tooth of the driven gear; and the gear system has a variable pressure angle and a variable contact ratio.

Abstract: In a bevel gear pair including a first gear having a plurality of first gear teeth, each defined at least in part by a tooth route and concave and convex flank surfaces, the concave and convex flank surfaces each define a first surface structure formed by grinding. This first surface structure is in turn defined by a plurality of microstriations extending diagonally across the convex and concave flank surfaces. A second gear also includes a plurality of gear teeth adapted to mesh with the gear teeth of the first gear. Each of the second gear teeth is also defined in part by a tooth route and concave and convex flank surfaces. The concave and convex flank surfaces of the second gear define a second surface structure formed by grinding followed by honing. This second surface structure includes a plurality of microstriations; however, unlike the microstriations of the first surface structure, these are parallel to the route of each of the second gear teeth.

Abstract: A flexible meshing type gear device has a rigid internal gear, a flexible external gear disposed inside the internal gear and a wave generator for flexing the external gear into an elliptical shape. One circle of curvature at the point of contact of the involute curve making contact at the meshing center position is made coincident with a tooth profile circle of curvature satisfying the Euler-Savary equation that applies between the tooth profile curvatures at the tooth profile contact points of speed change gears, and the other tooth profile circle of curvature of the equation is defined in the vicinity of the circle of curvature of the other involute curve.

Abstract: Several embodiments of various non-involute gear tooth profiles incorporate relief areas formed across the area of the tooth face generally symmetrically to each side of the pitch circle of the gear. The relief area serves to preclude contact across the areas of meshing or mating gear teeth where convex-to-convex contact would otherwise occur, thus precluding high pressure contact between the two gear teeth at the area of the relief. The remainder of the contact of such non-involute gear tooth profiles provides conformal contact, i. e., convex-to-concave mating faces with correspondingly low pressures developed between the tooth portions. The present invention enables a given gear set to absorb considerably greater torque and force than would otherwise be they case, or alternatively allows gear sets to be made considerably smaller and lighter for a given torque transmission, than would otherwise be the case.

Abstract: A gear assembly includes a first gear including first set of teeth and a first addendum circle, and a second gear having a second set of teeth meshing with the first set of teeth, The shape of the addendum flank of each first tooth and the shape of the addendum flank of each corresponding second tooth are defined by a curve of congruency which passes between the addendum circles and extends between the point of intersection of the addendum circles and the pitch point of the gears.

Abstract: A method for producing gear wheels from blanks obtained by sintering metal powders, comprising the step of coining longitudinal and transverse profiles of the teeth of a sintered blank with a rolling operation by one or more rollers shaped complementarily to the blank with a profile which is adapted to produce modifications of the profiles.

Abstract: In a coupling tooth formation, in particular in a gear box, either on a gear sleeve or on a gear wheel, the teeth are fitted to the base end of a cylindrical base (12) in relation to the rotational axis, elongate in axial direction and provided at their coupling end with a roof outline sloping from the tooth base towards the tooth head, comprising a rounded roof edge (5); the radius of the roof edge rounding increases from the tooth base towards the tooth head according to a pre-set function in order to design the procedure of the tracking process after the initial contact as smoothly running as possible.

Abstract: A toothed gear includes an outer toothed rim 1, a hub 3 and a profiled bridge area 2 connecting the toothed rim 1 and the hub 3 as one piece. The bridge area 2 is connected to the toothed rim and the hub in different planes. The bridge area consists of uniformly spaced, spoke-like bridges 2, which are uniformly distributed over the circumference. The bridges are arranged in an alternating manner on both sides of a center plane extending through the toothed gear.

Abstract: A pivot-hung door drive system with an electro-mechanical or electro-hydraulic drive device that supplies the opening and closing moment required to open and close a connected pivot-hung door panel, whereby an electronic regulation/control system with at least one memory and at least one microprocessor, on the basis of sensor signals, controls the opening or closing moment by means of a gear wheel that is located on an output shaft, which gear wheel is connected by means of a linkage and an actuator arm with the pivot-hung door panel, whereby between the output shaft of the pivot-hung door drive system and the linkage or the actuator arm, there is a device that effects a change in the opening and closing moment over the angle of rotation of the pivot-hung door panel.

Abstract: A method for designing root area geometry of a straight bevel gear providing reduced stress concentration and increased tooth strength. Also, a method for making a forging die for manufacturing gears having improved tooth root geometry. The method includes the steps of designing the straight bevel gear having improved root area geometry, designing an electrode for an electric discharge machining using CAD/CAM device, manufacturing the electrode, and manufacturing the forging die employing the electric discharge machining process.

Abstract: Manufacturing a drive system with a mating gear set with substantially reduced gear axis misalignment drive motion non-uniformity error with half-crowned gear teeth, crowned on only one side, to allow for simple and low cost gear molding, but with the mating gears mounted to oppositely mesh their respectively half-crowned sides. The amount of crowning may be in the range of approximately 75-100 microns.

Abstract: A cycloidal gear with a small number of teeth includes a tooth of cycloid tooth. In the above construction, the number of teeth is four or five; and the cycloidal gear with a small number of teeth meshes with a large gear with cycloid tooth to constitute a gear train.

Abstract: A form of gearing having teeth with different face widths along the tooth height and a method thereof of designing and manufacturing. Different gear tooth face widths are introduced along the tooth height to alter the tooth stiffness characteristic to provide a pair of gears with reduced mesh stiffness variation. The use of variable face widths along the tooth height changes both the geometric properties of the tooth and the load distribution/concentration to reduce the self-excited component of dynamic load, in effect reducing gear noise and increasing power density.

Abstract: Helical or spur gear drive comprising a driven gear and driving gear wherein the driving gear has double crowned teeth defined as (i) an envelope to a family of surfaces generated by a skew or straight rack-cutter having a parabolic tooth profile in normal section and then (ii) as an envelope to a family of tool surfaces that are generated while the tool performs a plunging motion with respect to the driving gear in the direction of the shortest distance between the axes of rotation of the tool and the driving gear and tool plunging motion is varied by a parabolic function, whose variable is displacement of the tool in a direction parallel to the rotational axis of the driving gear. The driven gear has a tooth surface defined as the envelope to a family of surfaces generated by a rack-cutter which surface is parabolic cylinder or a plane.

Abstract: A hydraulic machine with an orbiting displacement element connected unrotatably with an output shaft via an intermediary shaft, the intermediary shaft having at least at one end an external toothing, which engages an internal toothing, which permits a swivel motion of the intermediary shaft. The external toothing has teeth with concavely shaped tooth sides having a smaller curvature at the axial ends than in the area of the axial center.

Abstract: A gear wheel assembly is provided in a sheet material feed mechanism. The gear wheel assembly includes an annular cylindrical gear wheel having an interior surface defining an interior diameter, with a plurality of gear teeth extending from the interior surface. A pinion is mounted for rotation within the gear wheel. The pinion includes an exterior surface defining an outer diameter, the outer diameter of the pinion being less than the inner diameter of the gear wheel. A plurality of gear teeth extend outwardly from the exterior surface of the pinion. The pinion gear teeth have arcuate contact edges adapted to drivingly engage with gear teeth of the gear wheel. The contact edges of the pinion gear teeth can be provided with tapering radii of curvature, preferably tapering outwardly from the respective centers of the gear teeth. In an embodiment, the contact edges of the pinion gear teeth taper from 45 mm at the center to 25 mm at each edge.

Abstract: A gearing system which includes a pair of conjugate gears. The tooth profile of the first gear lies entirely within the pitch circle of the first gear, and the tooth profile of the mating gear lies entirely outside the pitch circle of the mating gear. The profile of the first gear is fully or partially concave, and the tooth profile of the mating gear is fully or partially convex. The profiles of the conjugate gear pair may have constant, or nearly constant, relative curvature. Alternatively, due to the shape of the profiles, constant, or nearly constant, contact stress results when the gears are in mesh.

Abstract: The meshing of the rigid internal gear and the cup-shaped flexible external gear of a flexible meshing type gear device is simulated with racks, similarity transformation is effected on the composite curve consisting of the envelope obtained by axially projecting the movement loci of the rack teeth relative to each other from the tooth trace opening portion to the tooth trace inner extremity in sections perpendicular to the axis and the movement locus in the vicinity of the tooth trace inner extremity, and the resulting curve is adopted as the basic addendum profile of the external teeth and the internal teeth.

Abstract: An internal geared wheel pump that does not have a crescent shaped piece. The pump has an internal geared wheel that meshes with a pinion. The pinion and geared wheel are mounted in a rotatable manner in a housing that has a suction connection and a pressure connection. The geared wheel has passages that produce each time a conductive connection between the base of the tooth and the envelope surface of the geared wheel. Conductive connections are produced between the bearing flanks of the teeth of the geared wheel or the teeth of the pinion and the radial boreholes of the geared wheel.

Abstract: A hybrid gear drive suitable for the transformation of motion and power between an involute worm and a face gear wherein the axis of the face gear and the worm may be crossed or intersected. The gear drive includes a multi-thread involute worm in meshing engagement with a face gear having helical teeth. The multi-thread involute worm threads each have a driving surface and a coasting surface formed in the profiles of the involutes of a pair of base circles having different radii. The gear drive allows practical gear ratios up to about ten for high speed, high load applications such as helicopter or automobile gearboxes.

Abstract: A gear arrangement 10 which comprises a first disc member 12 rotatable about a first axis 14 and carrying rings 16 of teeth 18, the rings 16 being centered on the axis 14 and at respective distances therefrom. A second member 20 is rotatable about a second axis 22 and carries further teeth 24. The second member can move toward and away from the first axis 14. The teeth 18, 24 are so formed as to allow the second teeth 24 to mesh in driving manner with each ring of teeth 18 as the second member 20 moves toward and away from the first axis 14. In this way, the transmission ratio of the gear arrangement can be changed.

Abstract: A curvature of a locus of contact points at a higher torque value is increased such that the torque-dependent characteristic of the working transmission error assumes a minimum value in the vicinity of a working torque value T.sub.1 at the tooth surface position corresponding to the working torque value T.sub.1, in the vicinity of a working torque value T.sub.3 at the tooth surface position corresponding to the working torque value T.sub.3, and in the vicinity of a working torque value T.sub.5 at the tooth surface position corresponding to the working torque value T.sub.5. As a consequence, the change in the working transmission error at the working torque is minimized making it possible to reduce the working transmission error in a wide working torque range.

Abstract: A gearing system which includes a pair of gears. The tooth profile of the first gear has three portions: a concave portion lying within the dedendum of the first gear, a convex portion lying within the addendum of the first gear, and a transition zone disposed between the concave and convex portions. Similarly, the tooth profile of the mating gear has three portions: a concave portion lying within the dedendum of the mating gear, conjugate to the convex portion of the tooth profile of the first gear; a convex portion lying within the addendum of the mating gear, conjugate to the concave portion of the tooth profile of the first gear; and a transition zone disposed between the concave and convex portions. The pair of gears may be designed such that no contact between meshing teeth is made along the transition zones. The tooth profiles of the gear pair have constant, or nearly constant, relative curvature.

Abstract: The tooth shape at around the pitch circle of the outer tooth gear of the pinion to be connected to the prime mover or driven shaft has a tooth surface which is in axial direction at around the central portion of the tooth width and which contacts at around the tooth width end at the allowable displacement angle and the backlash is made small and the outer tooth gear of the pinion is crowned in to an exponential function curve. The precession vibration and the torsional vibration at a high speed rotation can be suppressed because of the small backlash. The crowning curve is exponential function which causes the contacting point to move toward the tooth width end as the displacement increases and the radius of curvature becomes larger as the point on the curve approaches to the tooth width end, so that even when the contacting gear number decreases when displaced, the increase in the contacting stress is suppressed and a larger power can be transmitted as compared to the conventional design.

Abstract: A clockwork wheel (1) including a plate (3) provided with a first series of peripheral teeth (4) and a second series of teeth (5) arranged at right angles to the plate is manufactured in a strip of steel suitable for stamping and by means of a progressive forging die. In order to form the second series of teeth (5), a die perforated with a plurality of openings arranged in a circle is applied onto one face of the strip, and the flat face of a cylinder is pressed onto the other face of the strip to cause the steel to flow inside the openings of the die. The clockwork wheel is used as a setting wheel in a time or date setting mechanism.

Abstract: A rigid internal gear of a wave gear drive is comprise by a tooth-formed member having inner teeth and a circular gear body member, these two members being integrally connected with each other. The tooth-formed member is made of ferrous or copper material having a high strength and wear resistance, while the gear body member is made of lightweight material such as aluminum alloy and the like. These members are connected integrally with each other in a manner that one of these members is formed with baffle means and the other member is made by enveloped casting, or that the member having baffle means is pressed into the other member. These members are therefore surely connected with each other, so that a high torque can be transferred between these members. Also, the lightweight of the rigid internal gear can be achieved without deteriorating strength, wear resistance or the like thereof.

Abstract: Amplitude of transmission error of tooth pair of a gear is obtained in relation to actual contact ratio (.epsilon..sub.r) which is an angular range (.theta..sub.r) of actual contact of the surfaces of the tooth pair divided by an angular pitch (.theta..sub.p) of the gear. The specifications and/or tooth surface modification of the gear is/are are determined so as to reduce the transmission error amplitude under non-load condition in which the actual contact ratio (.epsilon..sub.r) is 1.0. Alternatively, the specifications and/or tooth surface modifications is/are determined so as to increase an effective contact ratio (.epsilon..sub.n) which is an angular range (.theta..sub.n) divided by the angular pitch (.theta..sub.p), the angular range (.theta..sub.n) corresponding to a portion of a path of the tooth contact point in which an edge contact of the tooth pair does not take place at the tooth top or at the ends of the face width of the teeth.

Abstract: A gearset for a gear spindle coupling or the like, and method for forming the same, comprising a sleeve gear and a hub gear which may be ground after surface hardening without the introduction of undesired structural weakening. The sleeve gear includes internal gear teeth and the hub gear includes external gear teeth in mesh with the sleeve gear teeth. Each internal sleeve gear tooth has an internal profile with the tooth height ranging from about 1.9 to about 2.2 divided by the diametral pitch of the sleeve gear, and each external hub gear tooth has a contact height less than the full tooth height. The contact height of the external tooth ranges from about 1.4 to about 1.6 divided by the diametral pitch of the hub gear, with the hub gear tooth region ranging between about 1.4/diametral pitch to about 1.6/diametral pitch. The whole depth of each external gear tooth ranges between about 1.5/diametral pitch to about 1.8/diametral pitch, and the whole depth of each internal gear tooth ranges between about 1.

Abstract: A cogged component, especially a wheel, rack, pinion, spline, or similar structure, intended for the mechanical transmission of force. The body is of a composite reinforced with carbon fibers. The body is, in accordance with the invention, of fiber-reinforced ceramic comprising a lattice of essentially continuous carbon fibers and a matrix that contains carbon. The fibers in the lattice are sheathed in silicon carbide formed essentially by liquid silicon infiltrating the lattice and reacting with the carbon in the matrix. The cogs are constructed either of a similar fiber-reinforced ceramic with a load-accommodating fiber orientation or of a monolithic ceramic.

Abstract: A transmission device for converting a torque from rotary to linear movement includes a rack having a plurality of teeth and a pinion having rollers which mesh with the teeth of the rack, with pressurization provided therebetween. The rack has an arcuate tooth flank diametrically greater than each of the rollers of the pinion. The rack also has a tooth face which has an approach profile progressively moving away from the path of contact of each of the rollers along which each of the rollers would otherwise engage with the tooth face. A plurality of each of the rollers of the pinion concurrently mesh with the corresponding teeth of the rack. Another embodiment converts a torque between rotary and linear movement and comprises a pinion having a plurality of teeth and a rack having a plurality of rollers to mesh with the teeth of the pinion.

Abstract: A manual transmission for use in motor vehicles is disclosed. The transmission includes an input shaft, an output shaft, and a plurality of constant-mesh gearsets that can be selectively engaged for establishing corresponding forward gears therebetween. In addition, a reverse gear assembly is provided for establishing the reverse gear. The reverse gear assembly includes an idler shaft non-rotatably mounted within a housing of the transmission and an idler gear journally supported on the idler shaft. The idler gear is linearly movable into engagement with a reverse input gear and a reverse speed gear. Each tooth of the reverse idler gear includes a pair of intersecting flank radii which intersect at the tooth centerline, creating an included angle therebetween. The teeth of the input and output gears are similarly formed to include a pair of flank radii and included angles.

Abstract: A high addendum tooth for a spur gear that prevents interference upon engagement with other high addendum gear teeth when the engaging gears are not perfectly aligned. The gear tooth design is divided into two portions along the face width of the tooth. The first portion is located at the first end of the tooth and involves having a high tooth height. The sidewall or face surface of this first portion may be involute, flat, or some other profile. The second portion of the gear tooth is situated along the remainder of the length of the tooth extending from the first portion to the second end. The second portion does not have a high tooth height. Instead, the top of the second portion of the tooth is cut and ground to have a flat surface. The second portion is proportionally much longer and occupies a much greater portion of the face width than the first portion.

Abstract: A drive transmitting device having a partly untoothed gear partly having an untoothed portion, and a driven gear capable of meshing which the partly untoothed gear, and transmitting rotation from the partly untoothed gear to the driven gear is characterized in that in the partly untoothed gear, of a predetermined number of continuous teeth positioned on a side on which the partly untoothed gear starts to mesh which the driven gear when it rotates from a state in which the untoothed portion and the driven gear are opposed to each other, the odd teeth from the untoothed portion side are formed with odd tooth inclined surfaces cut away from the tooth top of the front tooth surface in the direction of rotation of the partly untoothed gear toward the root of the rear tooth surface, and the even teeth are formed with even tooth inclined surfaces cut away from the root of the front tooth surface in the direction of rotation toward the tooth top of the rear tooth surface.

Abstract: A strain wave gearing is provided with tooth profiles formed taking into account tooth inclination and change in the movement locus of the origin of the tooth profile coordinates, thereby obtaining proper meshing over a wide range. Specifically, a tooth module is denoted as m; the number of teeth of the rigid internal gear as z.sub.C ; the number of teeth, the deddendum, the thickness of the tooth bottom rim and the radius of the neutral circle of the rim of the flexible external gear as z.sub.F, h.sub.fF, t and r.sub.n, respectively; the coefficient of tooth thickness increase of the rigid internal gear and the coefficient of tooth thickness decrease of the flexible external gear both as .tau.; and an auxiliary angle variable .eta.. The basic addendum profiles of both gears are formed according to two equations, taking an x-axis on a datum line and a y-axis on the tooth center line and taking .+-. of the first equation as positive for the flexible external gear and as negative for the rigid internal gear.

Abstract: A differential apparatus includes a differential casing, a pair of side gears and plural pairs of pinion gears. The pinion gears are accommodated in bores formed in the differential casing, respectively. Each pinion gear has an outer diameter smaller than that of a standard gear to be determined corresponding to predetermined gear specifications. With such a forming of the pinion gears, the tip circular thickness of each pinion gear is increased, so that surface pressure at respective tips of the pinion gears is reduced to improve the seizure resistant capability.

Abstract: A variable-pitch racked bar has a row of rack teeth with a middle fixed pitch region and two end fixed pitch regions. A variable-pitch region is interposed between the middle fixed pitch region and each of the end fixed pitch regions. In the variable-pitch region, the pitch increases from the fixed, small-pitch middle region toward the fixed, large-pitch end regions. In the variable-pitch racked bar, the effective meshing width continuously decreases from the middle of the row of rack teeth toward both ends thereof.

Abstract: In a face gear transmission with a cylindrical pinion and a face gear meshing therewith the toothing of the face gear is derived from a theoretical profile (22) of a pinion with an infinitely small thickness by moving the centre of this pinion along an imaginary axis which the coincides with the axis of rotation of the cylindrical pinion. The teeth of the face gear are crowned so as to achieve the required tooth clearance. The shape of the teeth of the face gear is such that upon the movement of the theoretical pinion profile (22) in the direction of the imaginary axis of rotation, starting from a defined diameter between the maximum and the minimum diameter of the toothing of the face gear, the centre of the theoretical pinion profile undergoes a displacement (P.sub.1, P.sub.2) at the same time at right angles to the imaginary axis of rotation in the direction towards the toothing of the face gear.