12 


12.1 
Gear and tooth geometry 

12.1.1 
CYCLOID Plane curve described by a point on a circle which rolls without slip on a fixed straight line. 

12.1.2 
EPICYCLOID Plane curve described by a point on a circle which rolls without slip on the outside of a fixed circle. 

12.1.3 
HYPOCYCLOID Plane curve described by a point on a circle which rolls without slip on the inside of a fixed circle. 

12.1.4 
EVOLUTE Plane curve, which is the locus of the centres of curvature of a given plane curve. Remark: the given curve can be seen as the involute. 

12.1.5 
INVOLUTE Plane curve, which is the locus of a point of a tangent line as it rolls without slip around a fixed curve. Remark: the fixed curve can be seen as the evolute. 

12.1.6 
INVOLUTE TO A CIRCLE Involute of which its evolute is a circle. 

12.1.7 
SPHERICAL INVOLUTE Spherical curve, described by a point of a cone that rolls without slip by spherical motion around a fixed cone. 

12.1.8 
CONVOLUTE 1. Curve which is a generatrix of a developing surface. 2. Singlecurved surface moving such that it is always tangent to a doublecurved line. 

12.1.9 
HYPERBOLOID, SINGLESPACE ROTATION Surface generated by rotation of a hyperbola about the axis of symmetry that does not intersect with its surface. 

12.1.10 
HELIX Curve that lies on a cylinder and that has a constant angle between any tangent and the axis of the cylinder. 

12.1.11 
HELICOID Surface generated by a plane curve or a twisted curve that is rotated about a linear axis and at the same time is translated in the direction of that axis with constant circular pitch 

12.1.12 
HELICOID, INVOLUTE Surface generated by a straightlinear generatrix inclined at a constant angle to the axis of a cylinder and rolling without slip on the surface of that cylinder. 

12.1.13 
HELICOID, SPHERICAL INVOLUTE Surface generated by a straightlinear generatrix inclined at a constant angle to the axis of a cone and rolling without slip on the surface of that cone. 

12.1.14 
TOROID Surface or body of revolution enclosed by the surface, generated by rotating a circle (generatrix) about an axis that lies in its plane, but outside the circle. 

12.1.15 
GLOBOID Surface or body of revolution, generated by rotating an arc about an axis that lies in its plane, but outside the circle of the arc. 

12.1.16 
GENERATION Process to define or manufacture a predetermined surface, usually single or double curved, as the result of relative motion between a cutting tool and blank material. 

12.1.17 
GENERATRIX Line to be used as an imaginary cutting tool for generation of a surface like a cone, a tooth flank or a thread flank. 

12.1.18 
GENERATRIX, STRAIGHTLINEAR Generatrix that is a straight line. 

12.1.19 
GENERATING SURFACE Surface to be used as a (imaginary) cutting tool for generation of the surface being produced. 

12.1.20 
GENERATING CONE Cone as a generating surface for the thread flanks of a worm. 

12.1.21 
GENERATING GEAR Imaginary gear, comparable to a mating gear, of which the tooth flanks are generating surfaces. 

12.1.22 
GENERATING TORUS Toroidal surface as a generating surface for the thread flanks of a worm. 

12.1.23 
BASIC RACK TOOTH PROFILE [STANDARD PROFILE ] Rack of which the tooth profile is used for defining the tooth proportions of an involute spur gear pair. 

12.1.24 
RACK, BASIC Imaginary rack having the basic rack tooth profile for normal section. 

12.1.25 
COUNTERPART RACK Rack that can be engaged with the basic rack such that its teeth exactly fill the tooth spaces of the basic rack. 

12.1.26 
GEAR BODY Part of a gear which together with gear teeth forms a gear. 

12.1.27 
MATING GEAR [ENGAGING GEAR] The gear with which an another gear forms a gear pair 

12.1.28 
MESHING [GEARING] [TOOTH MESHING] Process of transmission of motion in a gear pair. 

12.1.29 
GEAR TOOTH {WORM THREAD} Shape on a link for transmission of motion by means of interaction with a corresponding shape of another link. 

12.1.30 
DATUM LINE Line of intersection of the datum plane with the plane of the basic rack tooth profile in relation to which the dimensions of the teeth are specified. 

12.1.31 
DATUM PLANE In the basic rack, the plane in which the ratio of tooth thickness and the pitch has a specified standard value (usually 0,5) 

12.1.32 
COAXIAL SURFACE Real or imaginary surface of revolution of a gear or worm about the gear axis or worm axis. 

12.1.33 
ROOT SURFACE Coaxial surface separating the gear teeth from the gear body. 

12.1.34 
TIP SURFACE Coaxial surface, limiting the gear teeth with a side opposite to the gear body. 

12.1.35 
REFERENCE SURFACE Coaxial surface of a gear with reference to which the gear tooth dimensions are defined. 

12.1.36 
COAXIAL SURFACE, SIMILAR TYPE Coaxial surface of a gear, which has a form similar to its reference surface. 

12.1.37 
ADDENDUM Radial distance between the reference surface and the tip surface ( for a bevel gear measured along the back cone). 

12.1.38 
DEDENDUM Radial distance between the reference surface and the root surface (for a bevel gear measured along the back cone). 

12.1.39 
BASE CIRCLE Circle which is the evolute of the tooth profile of an involute cylindrical gear. 

12.1.40 
BASE CYLINDER Coaxial surface of an involute cylindrical gear, whose cross section is the base circle. 

12.1.41 
REFERENCE CIRCLE 1. For a cylindrical gear the cross section of the reference cylinder; 2. For a bevel gear the line of intersection of the reference cone and the reference back cone. 

12.1.42 
REFERENCE DIAMETER Diameter of the reference circle. 

12.1.43 
REFERENCE CYLINDER Reference surface of a cylindrical gear, on which the nominal gear tooth dimensions are given. 

12.1.44 
ROOT CYLINDER Root surface of a cylindrical gear. 

12.1.45 
ROOT CIRCLE 1. For cylindrical gears the cross section of the root cylinder; 2. For bevel gears the line of intersection of the root cone and the reference back cone. 

12.1.46 
TIP CYLINDER Tip surface of a cylindrical gear. 

12.1.47 
TIP CIRCLE 1. For cylindrical gears the cross section of the tip cylinder; 2. For bevel gears the line of intersection the tip cone and the reference back cone. 

12.1.48 
BASE DIAMETER Diameter of the base circle. 

12.1.49 
PITCH DIAMETER Diameter of the pitch circle. 

12.1.50 
TOOTH FLANK {THREAD FLANK} Portion of the surface of a gear tooth {worm thread} lying between the tip surface and the root surface. 

12.1.51 
RIGHT FLANK {LEFT FLANK} Right {left} tooth flank when the observer sees, from a conventionally chosen reference side, the tooth upright. 

12.1.52 
ACTIVE FLANK Portion of a tooth flank that contacts with one or more tooth flanks of a mating gear. 

12.1.53 
USABLE FLANK Largest portion of the tooth flank or thread flank of an individual gear or worm which may be used as active flank. 

12.1.54 
NOMINAL FLANK Usable flank from which manufacturing errors are counted out. 

12.1.55 
CORRESPONDING FLANKS Flanks of a given gear that are either right flanks or left flanks. 

12.1.56 
OPPOSITE FLANKS Two flanks of a gear, of which one is a right flank and the other is a left flank. 

12.1.57 
FILLET [TOOTH FILLET] Portion of the tooth flank or thread flank between the usable flank and the root surface. 

12.1.58 
TRACE OF A TOOTH {THREAD}, THEORETICAL Line of intersection of a tooth flank {thread flank} with a similar type coaxial surface of a gear {worm}. 

12.1.59 
TOOTH, STRAIGHT Gear tooth of which any theoretical tooth trace is situated in an axial plane of the gear. 

12.1.60 
TOOTH, SPIRAL [CURVILINEAR] Gear tooth of which the theoretical tooth trace at the reference surface is a curved line. 

12.1.61 
TOOTH, HELICAL Gear tooth of which the theoretical tooth traces are all a helix. 

12.1.62 
TOOTH, CIRCULAR Gear tooth of a spiral cylindrical gear or a spiral bevel gear, of which the theoretical tooth trace at the reference surface is a circular arc. 

12.1.63 
TOOTH, SKEW Gear tooth of the skew bevel gear. 

12.1.64 
ANGULAR PITCH Quotient of one revolution of a gear, in angular units, and the number of teeth. 

12.1.65 
CIRCULAR PITCH [TRANSVERSE PITCH] Arc length of the reference circle between two consecutive corresponding flanks. 

12.1.66 
DIAMETRAL PITCH 1.Factor pi, divided by the circular pitch in inches. 2. Quotient of the number of teeth and the reference diameter in inches. 

12.1.67 
(NORMAL) BASE PITCH Arc length of the base circle between the origins of the involutes of two consecutive corresponding flanks. 

12.1.68 
MODULE 1.Circular pitch in mm divided by factor pi 2.Quotient of the reference diameter in mm and the number of gear teeth. 

12.1.69 
NORMAL MODULE Quotient of the normal base pitch in mm and factor pi. 

12.1.70 
TOOTH SPACE {THREAD SPACE} Space between two adjacent gear teeth {worm threads} limited by the tip surface and root surface. 

12.1.71 
LEAD ANGLE Acute angle between the tangent to a helix and a plane perpendicular to the axis of the cylinder on which it lies. 

12.1.72 
HELIX ANGLE Complement of the lead angle. 

12.1.73 
LEAD OF A HELIX Distance between two consecutive intersection points of a helix and a line parallel to its axis. 

12.1.74 
AXIAL PITCH Distance between the intersection points with two consecutive corresponding flanks of a helical gear by any line parallel to its axis. 

12.1.75 
AXIAL MODULE Quotient of the axial pitch expressed in mm and the factor pi. 

12.1.76 
NORMAL TOOTH PROFILE {NORMAL THREAD PROFILE} Intersection line of a tooth flank {thread flank} and a surface orthogonal to the theoretical tooth trace {thread trace}. 

12.1.77 
AXIAL TOOTH PROFILE {AXIAL THREAD PROFILE} Intersection line of a tooth flank {thread flank} and a plane containing the gear axis {worm axis}. 

12.1.78 
TOOTH PROFILE, (TRANSVERSE) {THREAD PROFILE} Intersection line of a tooth flank {thread flank} and any defined surface which is perpendicular to the straightlinear generatrix of the reference surface. 

12.1.79 
USABLE PROFILE Part of the tooth profile or thread profile that belongs to the usable flank. 

12.1.80 
TOOTHED RING [TOOTHING] Part of a gear containing all gear teeth connected with each other by the root surface of the gear body. 

12.1.81 
FACEWIDTH Width over the toothed ring of a gear, measured along a straightlinear generatrix of the reference surface. 

12.1.82 
OVERLAP LENGTH, Length equal to the product of the face width and the tangent of the base helix angle. 

12.1.83 
OVERLAP RATIO Quotient of the face width and the axial pitch of a gear. 

12.1.84 
TOOTHED LINK Link having gear teeth other than a gear or a rack. 

12.1.85 
MESHING, CYCLOIDAL Tooth meshing using tooth profiles in a transverse plane that are cyclical curves (cycloid, epicycloid or hypocycloid). 

12.1.86 
GEAR, EXTERNAL Gear of which the teeth are formed at the outside of the root surface. 

12.1.87 
GEAR, INTERNAL Gear of which the teeth are formed at the inside of the root surface. 

12.1.88 
LENGTH, BASE TANGENT Distance between two parallel planes tangent to the opposite tooth flanks of two or more consecutive gear teeth (for an external gear) or tooth spaces (for an internal gear). 

12.1.89 
GEAR, INVOLUTE CYLINDRICAL Cylindrical gear of which every transverse tooth profile is an arc of an involute to a circle. 

12.1.90 
GEAR, CYCLOIDAL Gear whose tooth profiles are cycloidal curves, exact or approximate. 

12.1.91 
GEAR, SPIRAL CYLINDRICAL Cylindrical gear of which the theoretical tooth traces at the reference surface are curved lines. 

12.1.92 
COGWHEEL [LANTERN GEAR] [CAGE GEAR] Gear of which the gear teeth are cogs with axes parallel to the gear axis. 

12.1.93 
COG [PIN] Gear tooth of a lantern gear, shaped as a cylindrical roller of definite diameter. 

12.1.94 
DISTANCE OVER PINS {BALLS} Distance between two cylindrical rolls {balls} measured along the common normal to their surfaces contacting the opposite flanks. 

12.2 
Gear pair basics 

12.2.1 
DISTANCE, CENTRE Shortest distance between the gear axes in a gear pair with parallel axes or in a crossed axes gear pair. 

12.2.2 
DISTANCE, REFERENCE CENTRE For an external gear pair the half sum of the reference diameters of the two gears; for an internal gear pair the half difference of the reference diameters . 

12.2.3 
GEAR PAIR, EXTERNAL Gear pair of which the axodes of the gears are arranged one outside another. 

12.2.4 
GEAR PAIR, INTERNAL Gear pair of which the axode of one gear is arranged inside the axode of the other one. 

12.2.5 
RACK AND PINION Gear pair of which one link is a rack. 

12.2.6 
GEAR, DRIVING Gear that transmits motion to its mating gear such that the contact force works opposite to the motion direction of the gear. 

12.2.7 
GEAR, DRIVEN Gear that receives motion from its mating gear such that the contact force works in the motion direction of the gear. 

12.2.8 
PRESSURE ANGLE OF A GEAR Acute angle between the tangent to the tooth profile and the normal to the reference circle at the intersection point of the reference circle and the tooth profile. 

12.2.9 
PRESSURE ANGLE OF A GEAR PAIR [WORKING PRESSURE ANGLE] Acute angle between the contact normal at the pitch point and the normal to the line of centres. 

12.2.10 
SHAFT ANGLE Supplement of the angle between the vectors of angular velocity of the gears in a gear pair. 

12.2.11 
POINT OF CONTACT [CONTACT POINT] Any point at which two tooth profiles touch each other. 

12.2.12 
PITCH POINT Contact point or one of the points of contact between the pitch surfaces of two mating gears. 

12.2.13 
LINE OF TEETH CONTACT, COMMON Imaginary line, which during the tooth meshing consecutively coincides with the contact line between the tooth flanks of interacting gear teeth. 

12.2.14 
LINE OF CONTACT [CONTACT LINE] Line on the tooth flank on which in a given moment interacting gear teeth are in contact 

12.2.15 
PITCH LINE Intersection line of a tooth flank or thread flank with the pitch surface. 

12.2.16 
CONTACT NORMAL Normal to the interacting tooth flanks of mating gears in the point of contact. 

12.2.17 
ADDENDUM, WORKING Radial distance between the pitch surface and the tip surface ( for a bevel gear measured along the back cone). 

12.2.18 
DEDENDUM, WORKING Radial distance between the pitch surface and the root surface (for a bevel gear measured along the back cone). 

12.2.19 
BOTTOM CLEARANCE 1. In a cylindrical gear pair the distance, on the line of centres, between the root surface of a gear and the tip surface of the mating gear. 2. In a bevel gear pair the shortest distance between the root circle of a bevel gear and the tip circle of the mating gear, measured along the common generatrix of the two back cones. 

12.2.20 
CIRCUMFERENTIAL BACKLASH Maximum arc length of the pitch circle through which a gear can be rotated when the mating gear is fixed to the common frame. 

12.2.21 
SURFACE OF ACTION {PLANE OF ACTION} Surface {plane}, described by the common line of teeth contact, when it moves relative to the frame of the gear pair. 

12.2.22 
PITCH SURFACE [WORKING SURFACE] Coaxial surface of a gear that rolls without slip on the corresponding coaxial surface of a mating gear. 

12.2.23 
CONJUGATE SURFACES Tooth flanks of mating gears which, when in permanent contact, perform the transfer of motion in accordance with the given law. 

12.2.24 
PITCH CIRCLE Circle of intersection of the pitch cylinder and a plane perpendicular to the gear axis. 

12.2.25 
PITCH CYLINDER Pitch surface of a cylindrical gear in a gear pair with parallel axes. 

12.2.26 
AXIAL PLANE Plane of a cylindrical gear pair or a bevel gear pair that contains both gear axes. 

12.2.27 
PITCH PLANE Plane of a gear pair which is tangent to the pitch surfaces in the pitch point. 

12.2.28 
TRANSVERSE PLANE Plane of a gear pair which is perpendicular to the axial plane and to the pitch plane. 

12.2.29 
PRINCIPAL PLANE Plane of a gear pair in which the tooth profiles of interacting teeth are interenveloped. 

12.2.30 
TANGENT PLANE Plane of a gear pair tangent to the tooth flank or thread flank at a point of contact. 

12.2.31 
ANGLE OF TRANSMISSION, TRANSVERSE Angle through which a gear rotates between the beginning and ending of the contact on the transverse tooth profile. 

12.2.32 
RATIO, TRANSVERSE CONTACT Quotient of the transverse angle of transmission by the angular pitch. 

12.2.33 
INSTANTANEOUS AXIS (OF A GEAR PAIR) 1. In a gear pair with parallel axes or in a gear pair with intersecting axes, the instantaneous line of rotation of a gear relative to its mating gear. 2. In a crossed axes gear pair the instantaneous screw axis of a gear relative to its mating gear. 

12.2.34 
AXIS OF А MESHING Contact line of the reference surfaces of the gear pair, that does not move relative to the gear axes and that intersects all contact normals of interacting conjugate surfaces. 

12.2.35 
GEAR AXIS Geometrical rotation axis of a gear acting in a gear pair. 

12.2.36 
WORM AXIS Geometrical rotation axis of a worm acting in a worm gear pair. 

12.2.37 
AXODE (OF A GEAR) [AXOIDAL SURFACE] Surface of a gear (cylindrical, conical or hyperboloidal), generated by the instantaneous axis of a gear pair during relative motion of the mating gear. 

12.2.38 
MESHING, CUTTER TOOL Imaginary tooth meshing of a generating gear with the gear being cut. 

12.2.39 
CONSTANT CHORD Measure for the tooth thickness of an involute cylindrical gear: the distance between two contact lines, at opposite flanks, while the tooth is symmetrically in contact with the basic rack. Note: the measure is constant for all gear teeth. 

12.2.40 
HEIGHT, CONSTANT CHORD Radial distance between the midpoint of the constant chord and the gear tooth tip of the involute cylindrical gear. 

12.3 
Gear pair with parallel axes 

12.3.1 
LINE OF CENTRES Straight line, perpendicular to both gear axes, between the centres of the pitch circle. 

12.3.2 
LINE OF ACTION (,TRANSVERSE) Common normal to two transverse tooth profiles of the mating gears at their point of contact. 

12.3.3 
LENGTH OF PATH OF CONTACT [LENGTH OF LINE OF ACTION] Distance along the line of action between the tip circle of the driven gear and tip circle of the driving gear. 

12.3.4 
ADDENDUM MODIFICATION Distance between the reference surface of a cylindrical gear and the datum plane of its basic rack. 

12.3.5 
MODIFICATION COEFFICIENT, ADDENDUM Quotient of the addendum modification, expressed in millimeters, and the normal module, or the product of the addendum modification expressed in inches, and the diametral pitch. 

12.3.6 
MODIFICATION COEFFICIENT, CENTRE DISTANCE 1. Quotient of the difference between the centre distance and the reference centre distance, expressed in millimeters, and the normal module, or 2. Product of this difference, expressed in inches, and the diametral pitch. 

12.3.7 
GEAR PAIR, INVOLUTE SPUR Cylindrical gear pair of which both gears are involute cylindrical gears. 

12.3.8 
XGEAR Involute cylindrical gear with nonzero addendum modification coefficient. 

12.3.9 
XGEAR PAIR, Gear pair containing at least one Xgear. 

12.3.10 
XZERO GEAR Involute cylindrical gear of which the addendum modification coefficient equals zero. 

12.3.11 
GEAR PAIR, XZERO Gear pair consisting of two Xzero gears. 

12.3.12 
GEAR PAIR, CYLINDRICAL Gear pair with parallel gear axes that contains mating gears of which the axodes and reference surfaces are cylindrical. 

12.3.13 
GEAR PAIR, PARALLEL HELICAL Cylindrical gear pair with helical gears. 

12.3.14 
GEAR PAIR, HERRINGBONE [DOUBLEHELICAL] Cylindrical gear pair with two herringbone gears. 

12.3.15 
GEAR PAIR, CYCLOIDAL Gear pair consisting of cycloidal gears. 

12.3.16 
GEAR PAIR, LANTERN Cycloidal gear pair in which one of the gears is a lantern gear. 

12.3.17 
GEAR PAIR, SPIRAL CYLINDRICAL Cylindrical gear pair consisting of mating spiral cylindrical gears. 

12.3.18 
GEAR PAIR, WILDHABERNOVIKOFF’S CYLINDRICAL [CIRCULARHELICAL GEAR PAIR] Parallel helical gear pair with gear teeth that have convex surfaces of the working addendum interacting with concave surfaces of the working dedendum, while the transverse contact ratio is equal or close to zero. 

12.3.19 
SPUR GEAR, EQUIVALENT Imaginary involute cylindrical gear of which the tooth dimensions in the transverse plane closely approximate those of a helical gear in the plane of the normal tooth profile. 

12.4 
Gear pair with intersecting axes 

12.4.1 
PITCH CONE Pitch surface of a bevel gear. 

12.4.2 
PITCH CONE ANGLE Angle between the gear axis of a bevel gear and the generatrix of its pitch cone. 

12.4.3 
REFERENCE CONE Reference surface of a bevel gear. 

12.4.4 
REFERENCE CONE ANGLE Angle between the gear axis of a bevel gear and the generatrix of its reference cone. 

12.4.5 
ROOT CONE Root surface of a bevel gear. 

12.4.6 
ROOT CONE ANGLE Angle between the gear axis of a bevel gear and the generatrix of its root cone. 

12.4.7 
TIP CONE Tip surface of a bevel gear. 

12.4.8 
TIP CONE ANGLE Angle between the gear axis of a bevel gear and the generatrix of its tip cone. 

12.4.9 
BACK CONE, REFERENCE Coaxial surface of a bevel gear that has a generatrix perpendicular to the generatrix of the reference cone. 

12.4.10 
APEX, REFERENCE CONE Apex of the reference cone. 

12.4.11 
CONE DISTANCE, REFERENCE Distance along the generatrix of the reference cone from the reference cone apex to the intersection with the generatrix of the reference back cone. 

12.4.12 
MESHING, SPHERICAL INVOLUTE Tooth meshing of bevel gears such that the theoretical tooth profiles at the principal plane are spherical involutes. 

12.4.13 
MESHING, OCTOID [QUASIINVOLUTE BEVEL MESHING] Tooth meshing of bevel gears such that the tooth flanks are formed by a flat or conical generating surface. 

12.4.14 
BEVEL GEAR, STRAIGHT Bevel gear of which the theoretical tooth traces are straight lines that intersect the gear axis in the reference cone apex. 

12.4.15 
BEVEL GEAR, SKEW Bevel gear of which the theoretical tooth traces at the reference cone are straight lines not passing through the reference cone apex. 

12.4.16 
BEVEL GEAR, SPIRAL Bevel gear of which theoretical tooth traces at the reference cone are curved lines. 

12.4.17 
SPIRAL ANGLE Acute angle between the theoretical tooth trace of a spiral bevel gear and the generatrix of the corresponding similar type coaxial surface, in a given point of the tooth trace. 

12.4.18 
BEVEL GEAR, ZEROL Bevel gear with circular teeth of which the spiral angle equals zero. 

12.4.19 
CROWN GEAR Bevel gear with a reference cone angle of 90 degrees. 

12.4.20 
CONTRATE GEAR [FACE GEAR] 1. Crown gear with a flat tip surface and a flatroot surface. 2. Bevel gear or hypoid gear with a tip cone angle and a root cone angle of 90 degrees. 

12.4.21 
OCTOID BEVEL GEAR [QUASYINVOLUTE BEVEL GEAR] Bevel gear defined from a crown gear with plane tooth flanks. 

12.4.22 
GEAR PAIR, BEVEL Gear pair of which the mating gears are bevel gears with intersecting axes. 

12.4.23 
GEAR PAIR, INVOLUTE BEVEL Bevel gear pair with spherical involute meshing. 

12.4.24 
GEAR PAIR, ANGULAR BEVEL Bevel gear pair with a shaft angle different from 90 degrees. 

12.4.25 
GEAR PAIR, STRAIGHT BEVEL Bevel gear pair consisting of two mating straight bevel gears with involute meshing. 

12.4.26 
GEAR PAIR, SKEW BEVEL Bevel gear pair consisting of two mating skew bevel gears with intersecting axes. 

12.4.27 
GEAR PAIR, SPIRAL BEVEL Bevel gear pair consisting of two mating spiral bevel gears. 

12.4.28 
GEAR PAIR, OCTOID [QUASYINVOLUTE BEVEL GEAR PAIR] Bevel gear pair with octoid meshing. 

12.4.29 
GEAR PAIR, CONTRATE [FACE GEAR PAIR] Gear pair consisting of a cylindrical gear and a contrate gear whose axodes are cones while the reference surfaces are cylindrical and flat respectively. 

12.4.30 
GEAR PAIR, FACE HYPOID Gear pair consisting of a cylindrical gear and a contrate gear whose axodes are singlespace rotation hyperboloids while the reference surfaces are cylindrical and flat respectively. 

12.4.31 
GEAR PAIR, EQUIVALENT [VIRTUAL] CYLINDRICAL (Imaginary) involute spur gear pair, of which the gear teeth in the principal plane are practically identical to the gear teeth of a bevel gear pair at the reference back cones. 

12.4.32 
GEAR PAIR, EQUIVALENT BEVEL [VIRTUAL BEVEL GEAR PAIR] Orthogonal bevel gear pair having an identical equivalent cylindrical gear pair with a given angular bevel gear pair. 

12.4.33 
CYLINDRICAL GEAR, EQUIVALENT [VIRTUAL CILINDRICAL GEAR] Each gear of an equivalent cylindrical gear pair. 

12.4.34 
BEVEL GEAR, EQUIVALENT [VIRTUAL BEVEL GEAR] Each gear of an equivalent bevel gear pair. 

12.4.35 
CYLINDRICAL GEAR, BIEQUIVALENT (Imaginary) Involute spur gear of which the dimensions in the principal plane are practically the same as those of a skew bevel gear or a spiral bevel gear in the section normal to the middle of the theoretical tooth trace. 

12.5 
Crossed axes gear pair 

12.5.1 
GEAR PAIR, HYPERBOLOID Crossed axes gear pair of which the axodes of both gears are singlespace rotation hyperboloids. 

12.5.2 
GEAR PAIR, FIRST TYPE HYPERBOLOID Hyperboloid gear pair of which the tooth flanks of both gears are formed in cutter tool meshing by the same generating surface, resulting in point contact between the mating gears. 

12.5.3 
GEAR PAIR, HYPOID First type hyperboloid gear pair of which the gears have a pitch surface and a reference surface that are conical. 

12.5.4 
GEAR PAIR, CROSSED HELICAL 1. Two mating helical gears with crossed axes. 2. First type hyperboloid gear pair in which the pitch surface and reference surface of both gears are cylindrical. 

12.5.5 
GEAR PAIR, SECOND TYPE HYPERBOLOID Hyperboloid gear pair of which the conjugate surfaces have line contact when the generating surface of one gear coincides with the usable flank of its mating gear. 

12.5.6 
GEAR PAIR, SPIROID Second type hyperboloid gear pair of which the pitch surfaces are conical, while the pinion has helical teeth. 

12.5.7 
WORM GEAR PAIR Second type hyperboloid gear pair of which the pitch surfaces and the reference surfaces are either cylindrical surfaces or singlespace rotation hyperboloids, while the pinion has helical teeth. 

12.5.8 
WORM GEAR PAIR, CYLINDRICAL [SINGLE ENVELOPING WORM GEAR PAIR] Worm gear pair containing a worm with a cylindrical reference surface and pitch surface. 

12.5.9 
WORM GEAR PAIR, FACE Worm gear pair of which the axodes of gears are singlespace rotation hyperboloids, such that the pitch surface and the reference surface of the face worm are flat and the pitch surface and reference surface of the mating worm wheel are cylindrical or conical. 

12.5.10 
RACKANDWORM GEAR PAIR Worm gear pair consisting of a cylindrical worm and a rack 

12.5.11 
AXIS, WORM Geometrical rotation axis of a worm in the frame of the worm gear pair. 

12.5.12 
CYLINDRICAL WORM [SINGLE ENVELOPING WORM] Worm of which the reference surface and the pitch surface are cylindrical. 

12.5.13 
CYLINDRICAL WORM, RULED Cylindrical worm whose usable flanks are generated by a straightlinear generatrix. 

12.5.14 
CYLINDRICAL WORM, NONRULED Cylindrical worm whose usable flanks are generated by a curved generatrix. 

12.5.15 
ENVELOPING WORM [HOURGLASS WORM] [GLOBOIDAL WORM] Worm with one or more helical threads, of which the tip surface and root surface are parts of toroids coaxial with the worm; the radii of their midcircles are equal to the centre distance of the crossed axis gear pair. 

12.5.16 
ENVELOPING WORM, RULED Enveloping worm of which the usable flanks are generated by a straightlinear generatrix. 

12.5.17 
ENVELOPING WORM, NONRULED Enveloping worm of which the usable flanks are generated by a curved generatrix. 

12.5.18 
WORM, INVOLUTE [WORM ZJ] Cylindrical ruled worm, whose transverse thread profile is an involute to a circle. 

12.5.19 
WORM, CONVOLUTE [WORM ZN] Cylindrical ruled worm whose transverse thread profile is a lengthened or shortened involute to a circle. 

12.5.20 
WORM, ARCHIMEDEAN [WORM ZA] Cylindrical ruled worm, whose transverse thread profile is an Archimedean spiral 

12.5.21 
FACE WORM Worm of a face worm gear pair. 

12.5.22 
SPIROID GEAR Gear of the spiroid gear pair. 

12.5.23 
SPIROID WORM Pinion of the spiroid gear pair. 

12.5.24 
CYLINDRICAL WORM, GROUND BY CONE WHEEL Cylindrical nonruled worm whose usable flank is an envelope of a generating cone that moves along the worm thread. 

12.5.25 
CYLINDRICAL WORM, GROUND BY TOROIDAL WHEEL Cylindrical nonruled worm whose usable flank is an envelope part of the outer or the inner surface of a generating torus that moves along the worm thread. 

12.5.26 
WORM GEAR, DOUBLEENVELOPING [GLOBOIDAL WORM GEAR] Worm wheel of which the usable flanks are capable of line contact with worm threads of an enveloping worm. 

12.5.27 
WORM GEAR PAIR, DOUBLEENVELOPING [GLOBOIDAL WORM GEAR PAIR] Worm gear pair consisting of an enveloping worm and a doubleenveloping worm gear. 

12.5.28 
OFFSET (OF TOOTH TRACE) 1. Shortest distance between the theoretical tooth traces produced and the reference cone apex of the crown gear from which the skew bevel gear is defined. 2. Shortest distance between the gear axes of a hypoid gear pair or a spiroid gear pair. 

12.6 
Geared mechanisms 

12.6.1 
GEAR MECHANISM (,SIMPLE) Mechanism consisting of one gear pair and a toothless link, which is the frame. 

12.6.2 
GEARED MECHANISM [TOOTHED MECHANISM] Mechanism having a gear pair of which at least one gear is neither the input link nor the output link. 

12.6.3 
GEAR AND CAM MECHANISM [GEARED CAM MECHANISM] Geared mechanism containing two parallel kinematic subchains, one with a gear pair and one with a cam and cam follower. 

12.6.4 
GEAR AND GENEVA CROSS MECHANISM [GEARED GENEVA MECHANISM] Geared mechanism containing two parallel kinematic subchains, one with a gear pair and one with a Geneva mechanism. 

12.6.5 
GEARED CRANKANDROCKER MECHANISM Geared mechanism containing two parallel subchains, one with a gear pair and one with a crankandrocker mechanism. 

12.6.6 
TRAIN, DIFFERENTIAL GEAR 1. Gear train with degree of freedom two that transforms motion of either two input links into motion of a single output link, or motion of a single input link into motion of two output links. 2. Planetary gear train with degree of freedom two. 

12.6.7 
RING GEAR Internal gear with immovable rotation axis, as applied in a planetary gear train. 

12.6.8 
SUN GEAR External gear with immovable axis of rotation , as applied in a planetary gear train. 

12.6.9 
PLANET CARRIER Link of a planetary gear train on which the axles of the planetary gears are arranged. 

12.6.10 
WAVE GEAR TRAIN [HARMONIC DRIVE] Specific kind of a planetary gear train with internal tooth meshing in which the gear body of the planetary gear is a flexible ring deformed in the process of transfer of motion. 