2661:) is a number used as an arithmetic convention established to simplify the determination of the proper test distance between a master and a work gear for a composite action test. It is used as a measure of the effective size of a gear. The test radius of the master, plus the test radius of the work gear is the set up center distance on a composite action test device. Test radius is not the same as the operating pitch radii of two tightly meshing gears unless both are perfect and to basic or standard tooth thickness.
24:
2005:
1620:
513:
298:
2747:
607:
238:
2755:
2062:
1651:
546:
349:
83:
627:
565:
1157:
826:
199:
1185:
910:
479:
447:
2670:
1477:
2050:
618:(double flank) is a method of inspection in which the work gear is rolled in tight double flank contact with a master gear or a specified gear, in order to determine (radial) composite variations (deviations). The composite action test must be made on a variable center distance composite action test device. and this is composite action test for double flank
1394:
1663:
246:
2092:
307:
2701:
1205:
419:
2739:
720:
2124:
1900:
1724:
1704:
1224:
987:
1518:
1341:
is the measure of gear tooth size which is normally used for metric system gears. It is similar to the
Diametral Pitch (DP), which is commonly used for UK system (inch measure) gears but they differ in the units used and in that they bear a reciprocal relationship. Module is the pitch circle diameter
789:
is the radius of the pitch circle in a cross section of gear teeth in any plane other than a plane of rotation. It is properly the radius of curvature of the pitch surface in the given cross section. Examples of such sections are the transverse section of bevel gear teeth and the normal section of
2230:
is the diameter of the standard pitch circle. In spur and helical gears, unless otherwise specified, the standard pitch diameter is related to the number of teeth and the standard transverse pitch. Standard reference pitch diameter can be estimated by taking average of gear teeth tips diameter and
1083:
Distinction is made as to the direction and algebraic sign of this reading. A condition wherein the actual tooth flank position was nearer to the datum tooth flank, in the specified measuring path direction (clockwise or counterclockwise), than the theoretical position would be considered a minus
953:
is an imaginary cone tangent to the inner ends of the teeth, with its elements perpendicular to those of the pitch cone. The surface of the gear blank at the inner ends of the teeth is customarily formed to such a front cone, but sometimes may be a plane on a pinion or a cylinder in a nearly flat
920:
is the diameter of a circle at which the trochoid (fillet curve) produced by the tooling intersects, or joins, the involute or specified profile. Although these terms are not preferred, it is also known as the true involute form diameter (TIF), start of involute diameter (SOI), or when undercut
1695:(operating) is the curve of intersection of a pitch surface of revolution and a plane of rotation. It is the imaginary circle that rolls without slipping with a pitch circle of a mating gear. These are the outlines of mating gears. Many important measurements are taken on and from this circle.
390:, backlash is the striking back of connected wheels in a piece of mechanism when pressure is applied. Another source defines it as the maximum distance through which one part of something can be moved without moving a connected part. It is also called lash or play. In the context of
666:
teeth. The normals to the profiles of these teeth, at all points of contact, must pass through a fixed point in the common centerline of the two shafts. Usually conjugate gear tooth is made to suit the profile of other gear which is not made based on standard practice.
588:
defines the width of one tooth and one gap measured on an arc on the pitch circle; in other words, this is the distance on the pitch circle from a point on one tooth to the corresponding point on the adjacent tooth. This is equal to π divided by the
Diametral Pitch.
1492:. In a helical rack, a normal plane is normal to all the teeth it intersects. In a helical gear, however, a plane can be normal to only one tooth at a point lying in the plane surface. At such a point, the normal plane contains the line normal to the tooth surface.
1936:
2234:
The pitch diameter is useful in determining the spacing between gear centers because proper spacing of gears implies tangent pitch circles. The pitch diameters of two gears may be used to calculate the gear ratio in the same way the number of teeth is used.
1580:
1123:
1103:
360:
of a bevel or hypoid gear is an imaginary cone tangent to the outer ends of the teeth, with its elements perpendicular to those of the pitch cone. The surface of the gear blank at the outer ends of the teeth is customarily formed to such a back cone.
890:
Total face width is the actual dimension of a gear blank including the portion that exceeds the effective face width, or as in double helical gears where the total face width includes any distance or gap separating right hand and left hand helices.
394:, backlash is clearance between mating components, or the amount of lost motion due to clearance or slackness when movement is reversed and contact is re-established. In a pair of gears, backlash is the amount of clearance between mated gear teeth.
556:(operating) is the shortest distance between non-intersecting axes. It is measured along the mutual perpendicular to the axes, called the line of centers. It applies to spur gears, parallel axis or crossed axis helical gears, and worm gearing.
1975:
1868:
1328:
connects the centers of the pitch circles of two engaging gears; it is also the common perpendicular of the axes in crossed helical gears and worm gears. When one of the gears is a rack, the line of centers is perpendicular to its pitch line.
2772:
For an observer looking at the reference face, so that the tooth is seen with its tip uppermost, the right flank is on the right and the left flank is on the left. Right and left flanks are denoted by the letters “R” and “L” respectively.
1794:
779:
686:. There is theoretically point contact between the teeth at any instant. They have teeth of the same or different helix angles, of the same or opposite hand. A combination of spur and helical or other types can operate on crossed axes.
1882:
2720:
876:
2638:
1373:
When converting between module and DP there is an inverse relationship and normally a conversion between the two units of measure (inches and millimeter). Taking both of these into consideration the formulae for conversion are:
1914:
The pitch plane of a rack or in a crown gear is the imaginary planar surface that rolls without slipping with a pitch cylinder or pitch cone of another gear. The pitch plane of a rack or crown gear is also the pitch surface.
698:
is the point of intersection of bevel gear axes; also the apparent point of intersection of the axes in hypoid gears, crossed helical gears, worm gears, and offset face gears, when projected to a plane parallel to both axes.
2300:
1084:(-) deviation. A condition wherein the actual tooth flank position was farther from the datum tooth flank, in the specified measuring path direction, than the theoretical position would be considered a plus (+) deviation.
397:
Backlash is unavoidable for nearly all reversing mechanical couplings, although its effects can be negated. Depending on the application it may or may not be desirable. Reasons for requiring backlash include allowing for
2465:
is the diameter of the standard pitch circle. In spur and helical gears, unless otherwise specified, the standard pitch diameter is related to the number of teeth and the standard transverse pitch. It is obtained as:
2361:
640:
Outer cone distance in bevel gears is the distance from the apex of the pitch cone to the outer ends of the teeth. When not otherwise specified, the short term cone distance is understood to be outer cone distance.
2545:
1357:
UK system (inch measure) gears are more commonly specified with the
Diametral Pitch (DP) which is the number of teeth per inch of diameter of the pitch circle. The units of DP are inverse inches (1/in).
2022:
Total radial composite deviation (double flank) is the total change in center distance while the gear being tested is rotated one complete revolution during a double flank composite action test.
1342:
divided by the number of teeth. Module may also be applied to UK system gears, using inch units, but this usage is not in common use. Module is commonly expressed in units of millimeters (mm).
1683:
in bevel gears is the angle between an element of a pitch cone and its axis. In external and internal bevel gears, the pitch angles are respectively less than and greater than 90 degrees.
576:
of a worm gear is perpendicular to the gear axis and contains the common perpendicular of the gear and worm axes. In the usual case with axes at right angles, it contains the worm axis.
1911:
of a pair of gears is the plane perpendicular to the axial plane and tangent to the pitch surfaces. A pitch plane in an individual gear may be any plane tangent to its pitch surface.
1466:
2016:(double flank) is the greatest change in center distance while the gear being tested is rotated through any angle of 360 degree/z during double flank composite action test.
1404:, for assembling bevel gears or hypoid gears, is the distance from the crossing point of the axes to a locating surface of a gear, which may be at either back or front.
34:
3030:
1878:
are the imaginary planes, cylinders, or cones that roll together without slipping. For a constant velocity ratio, the pitch cylinders and pitch cones are circular.
2451:
2431:
2769:
It is convenient to choose one face of the gear as the reference face and to mark it with the letter “I”. The other non-reference face might be termed face “II”.
894:
For a cylindrical gear, effective face width is the portion that contacts the mating teeth. One member of a pair of gears may engage only a portion of its mate.
2404:
2384:
1092:
324:, in a bevel gear or hypoid gear, is the distance in the direction of the axis from the apex of the pitch cone to a locating surface at the back of the blank.
847:. A face gear has a planar pitch surface and a planar root surface, both of which are perpendicular to the axis of rotation. It can also be referred to as a
2551:
1215:
of spur gears, helical gears, and worms are those in which the profile in a transverse plane (exclusive of the fillet curve) is the involute of a circle.
93:
2241:
2711:
is the radius of the circular arc used to join a side-cutting edge and an end-cutting edge in gear cutting tools. Edge radius is an alternate term.
1985:
is the radius of curvature of a tooth profile, usually at the pitch point or a point of contact. It varies continuously along the involute profile.
2971:
2306:
1237:
177:
3048:
Machinery's
Handbook Twenty-Fifth Edition, by Erik Oberg, Franklin D. Jones, Holbrook L. Horton, and Henry H Ryffle, 1996, Industrial Press Inc.
1556:
181:
1927:
is perpendicular to the axial plane and to the pitch plane. In gears with parallel axes, the transverse and the plane of rotation coincide.
2472:
1547:
at the right. For below center offset the pinion has a left hand spiral, and for above center offset the pinion has a right hand spiral.
637:
in a bevel gear is the general term for the distance along an element of the pitch cone from the apex to any given position in the teeth.
1196:
is the angle whose arc on the base circle of radius unity equals the tangent of the pressure angle at a selected point on the involute.
151:
978:
is difference between the highest and lowest gear ratios and may be expressed as a percentage (e.g., 500%) or as a ratio (e.g., 5:1).
123:
738:
The
Diametral Pitch (DP) is the number of teeth per inch of diameter of the pitch circle. The units of DP are inverse inches (1/in).
3071:
2979:
1066:
is a machining process for making gears, splines, and sprockets using a cylindrical tool with helical cutting teeth known as a hob.
64:
2218:
is the circle which intersects the involute at the point where the pressure angle is equal to the profile angle of the basic rack.
2183:
2019:
Tooth-to-tooth radial composite tolerance (double flank) is the permissible amount of tooth-to-tooth radial composite deviation.
1293:
is larger for smaller gear diameters. It is understood to be measured at the standard pitch diameter unless otherwise specified.
1038:
is greater for larger gear diameters. It is understood to be measured at the standard pitch diameter unless otherwise specified.
130:
3076:
2151:, the shaft angle is given when starting a design, and it does not have a fixed relation to the pitch angles and spiral angles.
1509:
In a spiral bevel gear, one of the positions of a normal plane is at a mean point and the plane is normal to the tooth trace.
1273:
is the axial travel (length along the axle) for one single complete helical revolution about the pitch diameter of the gear.
1087:
The direction of tolerancing for index deviation along the arc of the tolerance diameter circle within the transverse plane.
108:
46:
843:
set typically consists of a disk-shaped gear, grooved on at least one face, in combination with a spur, helical, or conical
137:
937:, denotes the angle between an element of the front cone and a plane of rotation, and usually equals the pitch angle.
119:
730:
have surfaces modified in the lengthwise direction to produce localized contact or to prevent contact at their ends.
210:
is the height by which a tooth of a gear projects beyond (outside for external, or inside for internal) the standard
2730:
is a modification of a tooth profile whereby a small amount of material is removed near the tip of the gear tooth.
651:
Inner cone distance in bevel gears is the distance from the apex of the pitch cone to the inner ends of the teeth.
1495:
Important positions of a normal plane in tooth measurement and tool design of helical teeth and worm threads are:
2139:, the shaft angle lies between the oppositely rotating portions of two shafts. This applies also in the case of
2681:
is the diameter of the addendum circle at the central plane of a worm gear or of a double-enveloping worm gear.
2025:
Total radial composite tolerance (double flank) is the permissible amount of total radial composite deviation.
407:
1421:
1839:
corresponds, in the cross section of a rack, to the pitch circle (operating) in the cross section of a gear.
3004:
2692:
is the radius of the throat of an enveloping worm gear or of a double-enveloping worm, in an axial plane.
387:
381:
176:
construction and function, together with definitions of the terms. The terminology was established by the
1785:
is the intersection of the tooth surface and the outside cylinder of a helical gear or cylindrical worm.
2103:
is the imaginary surface that coincides with the bottoms of the tooth spaces in a bevel or hypoid gear.
1091:
1735:
is the intersection of the tooth surface and the pitch cylinder of a helical gear or cylindrical worm.
1600:
644:
Mean cone distance in bevel gears is the distance from the apex of the pitch cone to the middle of the
144:
1715:
is the imaginary cone in a bevel gear that rolls without slipping on a pitch surface of another gear.
887:
of a gear is the length of teeth in an axial plane. For double helical, it does not include the gap.
2115:
is the imaginary surface that coincides with the bottoms of the tooth spaces in a cylindrical gear.
1080:
The displacement of any tooth flank from its theoretical position, relative to a datum tooth flank.
2206:
has a planar pitch surface and straight teeth that are at right angles to the direction of motion.
463:
372:
in a bevel gear is the distance along an element of the back cone from its apex to the pitch cone.
1314:
921:
exists, as the undercut diameter. This diameter cannot be less than the base circle diameter.
257:
coincides with the tops of the teeth of a gear and is concentric with the standard (reference)
3024:
2985:
2975:
2172:
1946:
are directions in the pitch plane, and correspond to the principal cross sections of a tooth.
817:
is the imaginary surface that coincides with the tops of the teeth of a bevel or hypoid gear.
403:
337:
282:
1815:
is the lead angle on the outside cylinder. It is the complement of the outside helix angle.
1028:
is the angle between the helical tooth face and an equivalent spur tooth face. For the same
1005:
of a tooth on a bevel gear or pinion is the portion of the tooth surface near its inner end.
998:
of a tooth on a bevel gear or pinion is the portion of the tooth surface near its outer end.
1053:
100:
2436:
2409:
2036:
in a bevel or hypoid gear, is the angle between an element of the root cone and its axis.
1994:
1571:
is the surface that coincides with the tops of the teeth of an external cylindrical gear.
1114:
is the surface that coincides with the tops of the teeth of an internal cylindrical gear.
801:
in a bevel or hypoid gear, is the angle between an element of the face cone and its axis.
1269:
is the axial advance of a helix gear tooth during one complete turn (360°), that is, the
1543:. In determining the direction of offset, it is customary to look at the gear with the
711:
in a bevel or hypoid gear is the circle of intersection of the back cone and face cone.
3066:
2389:
2369:
1769:
is the lead angle on the base cylinder. It is the complement of the base helix angle.
3060:
2633:{\displaystyle D={\frac {N}{P_{d}}}={\frac {Np}{\pi }}={\frac {N}{P_{nd}\cos \psi }}}
2135:
is the angle between the axes of two non-parallel gear shafts. In a pair of crossed
1964:
1604:
1146:
533:
that are in engagement in any machine. The smaller gear is usually referred to as a
491:
270:
266:
3044:
3042:
3040:
1935:
1555:
1236:"Bottom land" redirects here. For information on the similar term "bottomland", see
198:
2136:
2004:
1650:
258:
172:
This page lists the standard US nomenclature used in the description of mechanical
2754:
2746:
2669:
2061:
1579:
1133:
is the diameter of the addendum circle of an internal gear, this is also known as
1122:
1102:
1017:
has a planar pitch surface and teeth that are oblique to the direction of motion.
237:
2295:{\displaystyle d={\frac {N}{P_{d}}}={\frac {pN}{\pi }}\qquad {\text{spur gears}}}
406:, and to prevent jamming. Backlash may also result from manufacturing errors and
218:; also, the radial distance between the pitch diameter and the outside diameter.
2148:
1393:
1285:
between the helical tooth face and an equivalent spur tooth face. For the same
1042:
770:
in a bevel gear, is the angle between elements of the root cone and pitch cone.
512:
399:
297:
82:
2091:
606:
348:
2793:
2782:
2144:
1758:
is the helix angle on the base cylinder of involute helical teeth or threads.
1592:
950:
934:
898:
834:
545:
507:
2989:
2356:{\displaystyle d={\frac {N}{P_{nd}\cos \psi }}\qquad {\text{helical gears}}}
2140:
1974:
1867:
1204:
1156:
825:
530:
418:
2738:
1619:
1184:
909:
756:
The
Diametral Pitch (DP) is equal to π divided by the Circular Pitch (CP).
626:
564:
478:
446:
1793:
1476:
778:
719:
2798:
2194:
has a cylindrical pitch surface and teeth that are parallel to the axis.
1535:
In the adjacent diagram, (a) and (b) are referred to as having an offset
1247:
is the surface at the bottom of a gear tooth space adjoining the fillet.
262:
193:
2123:
2049:
1899:
1881:
1747:
of a helical, involute gear or involute worm lies on its base cylinder.
1723:
1703:
1505:
the plane normal to the pitch helix at center of space between two teeth
1488:
is normal to a tooth surface at a pitch point, and perpendicular to the
1415:
is the value of the module in a normal plane of a helical gear or worm.
245:
2719:
2700:
1662:
1637:
is a round gear and usually refers to the smaller of two meshed gears.
1070:
875:
336:
of a bevel gear is the angle between an element of the back cone and a
2182:
306:
2540:{\displaystyle d=km={\frac {zp}{\pi }}=z{\frac {m_{n}}{\cos \beta }}}
1628:
1544:
1529:
844:
662:
transmit uniform rotary motion from one shaft to another by means of
534:
3008:
1223:
986:
1952:
The transverse direction is a direction within a transverse plane.
1517:
2753:
2745:
2737:
2181:
2122:
2090:
2003:
1973:
1934:
1880:
1866:
1792:
1722:
1618:
1578:
1554:
1516:
1392:
1121:
1101:
985:
874:
824:
777:
718:
625:
605:
391:
197:
901:, different definitions for effective face width are applicable.
229:
in a bevel gear, is the angle between face cone and pitch cone.
663:
173:
679:
is a gear that operate on non-intersecting, non-parallel axes.
1603:
it is the maximum diameter of the blank. The term applies to
1591:
of a gear is the diameter of the addendum (tip) circle. In a
1172:, on an involute curve and a radial line to the intersection,
76:
17:
1827:
is a helix on the pitch cylinder, normal to the pitch helix.
33:
deal primarily with the United States and do not represent a
1258:
is the (sometimes flat) surface of the top of a gear tooth.
269:, the addendum circle lies on the outside cylinder while on
1955:
The normal direction is a direction within a normal plane.
2147:, the shaft angle is the sum of the two pitch angles. In
1949:
The axial direction is a direction parallel to an axis.
1502:
the plane normal to the pitch helix at center of tooth;
682:
The term crossed helical gears has superseded the term
104:
42:
2554:
2475:
2439:
2412:
2392:
2372:
2309:
2244:
1499:
the plane normal to the pitch helix at side of tooth;
1424:
2968:
273:the addendum circle lies on the internal cylinder.
2632:
2539:
2445:
2425:
2398:
2378:
2355:
2294:
1528:is the perpendicular distance between the axes of
1460:
261:and radially distant from it by the amount of the
1168:is the angle between a radius vector to a point,
2083:coincides with the bottoms of the tooth spaces.
2073:Root Circles for internal & external gears
8:
3029:: CS1 maint: multiple names: authors list (
1804:is the helix angle on the outside cylinder.
1539:, while those in (c) and (d) have an offset
109:introducing citations to additional sources
2758:Notation and numbering for an internal gear
2750:Notation and numbering for an external gear
340:, and usually is equal to the pitch angle.
1480:Planes at a pitch point on a helical tooth
3005:"Bull Gear, Inc. - What is a Bull Gear!?"
2609:
2599:
2581:
2570:
2561:
2553:
2518:
2512:
2491:
2474:
2438:
2417:
2411:
2391:
2371:
2348:
2326:
2316:
2308:
2287:
2271:
2260:
2251:
2243:
2160:
1457:
1442:
1429:
1423:
65:Learn how and when to remove this message
2766:(flank) forms the side of a gear tooth.
2718:
2699:
2668:
1898:
1702:
1475:
1461:{\displaystyle m_{n}=m_{t}\cos \beta \,}
1222:
1203:
1183:
1155:
908:
563:
544:
511:
477:
445:
417:
347:
244:
236:
99:Relevant discussion may be found on the
2972:American Gear Manufacturers Association
2962:
2960:
2958:
2956:
2954:
2952:
2950:
2948:
2946:
2944:
2942:
2940:
2938:
2936:
2934:
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2930:
2928:
2926:
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2916:
2914:
2912:
2910:
2908:
2906:
2904:
2902:
2900:
2898:
2896:
2894:
2892:
2890:
2888:
2886:
2884:
2882:
2880:
2878:
2876:
2874:
2872:
2870:
2868:
2866:
2864:
2862:
2860:
2858:
2856:
2854:
2852:
2850:
2848:
2846:
2844:
2842:
2840:
2838:
2836:
2834:
2810:
1238:Upland and lowland (freshwater ecology)
178:American Gear Manufacturers Association
3022:
3003:Tony Casey, President Bull Gear, Inc.
2832:
2830:
2828:
2826:
2824:
2822:
2820:
2818:
2816:
2814:
2453:is the helix angle for helical gears.
610:Schematic of the composite action test
529:is used to refer to the larger of two
31:The examples and perspective in this
1364:PD = Pitch Circle Diameter in inches
1176:, of the curve with the base circle.
744:PD = Pitch Circle Diameter in inches
182:American National Standards Institute
180:(AGMA), under accreditation from the
7:
966:is the center of the pitch circle.
467:
435:
431:
49:, or create a new, as appropriate.
14:
2463:standard reference pitch diameter
2457:Standard reference pitch diameter
2228:standard reference pitch diameter
1859:) and is on the line of centers.
1852:
1607:, this is can also be known from
1596:
1348:PD = Pitch Circle Diameter in mm
211:
2060:
2048:
1851:is the point of tangency of two
1661:
1649:
1489:
1090:
495:
459:
305:
296:
92:relies largely or entirely on a
81:
22:
2347:
2286:
2008:Total composite variation trace
1856:
645:
215:
2433:is the diametrical pitch, and
2386:is the total number of teeth,
747:CP = Circular Pitch in inches
592:CP = Circular Pitch in inches
1:
1983:Profile radius of curvature
1970:Profile radius of curvature
120:"List of gear nomenclature"
45:, discuss the issue on the
3093:
3077:Knowledge (XXG) glossaries
2780:
2231:gear teeth base diameter.
2170:
2014:radial composite deviation
2000:Radial composite deviation
1992:
1962:
1855:(or of a pitch circle and
1626:
1595:it is the diameter of the
1312:
1308:
1280:
1235:
1144:
1068:
1051:
1040:
832:
505:
379:
280:
191:
1030:
434:is the circle from which
3072:Technology-related lists
1296:A spur gear tooth has a
1106:Diameters, Internal Gear
470:surfaces are developed.
2406:is the circular pitch,
2222:Standard pitch diameter
1623:Pinion and annular gear
1126:Internal gear diameters
787:Equivalent pitch radius
774:Equivalent pitch radius
494:is the diameter of the
241:Internal gear diameters
194:Addendum in engineering
2759:
2751:
2743:
2742:Profile of a spur gear
2724:
2705:
2674:
2634:
2541:
2447:
2427:
2400:
2380:
2357:
2296:
2187:
2128:
2096:
2009:
1979:
1940:
1904:
1886:
1872:
1798:
1728:
1708:
1624:
1584:
1560:
1532:or offset face gears.
1522:
1481:
1462:
1398:
1228:
1209:
1189:
1161:
1127:
1107:
991:
914:
880:
830:
783:
724:
631:
611:
569:
550:
517:
483:
451:
438:profiles are derived.
423:
388:mechanical engineering
382:Backlash (engineering)
353:
250:
242:
203:
2992:. ANSI/AGMA 1012-G05.
2757:
2749:
2741:
2722:
2703:
2672:
2635:
2542:
2448:
2446:{\displaystyle \psi }
2428:
2426:{\displaystyle P_{d}}
2401:
2381:
2358:
2297:
2216:standard pitch circle
2210:Standard pitch circle
2185:
2126:
2094:
2007:
1977:
1938:
1902:
1884:
1870:
1796:
1726:
1706:
1622:
1582:
1558:
1520:
1479:
1463:
1396:
1361:DP = Diametral Pitch
1226:
1207:
1187:
1159:
1125:
1105:
989:
912:
878:
828:
781:
741:DP = Diametral Pitch
722:
629:
616:composite action test
609:
602:Composite action test
595:DP = Diametral Pitch
567:
548:
515:
481:
449:
421:
351:
315:Apex to back examples
248:
240:
201:
2974:. 2005. p. 72.
2552:
2473:
2437:
2410:
2390:
2370:
2307:
2242:
2161:Crossed helical gear
2095:Principal dimensions
1944:Principal directions
1939:Principal directions
1931:Principal directions
1674:Pitch Angle examples
1559:Cylindrical surfaces
1422:
1367:n = Number of Teeth
1351:n = Number of Teeth
1227:Top and bottom lands
1192:Expressed as ε, the
1166:involute polar angle
1164:Expressed as θ, the
1160:Involute polar angle
1152:Involute polar angle
813:, also known as the
782:Back cone equivalent
750:n = Number of Teeth
677:crossed helical gear
671:Crossed helical gear
352:Principal dimensions
202:Principal dimensions
105:improve this article
2673:Worm gear diameters
1802:Outside helix angle
1789:Outside helix angle
1656:Angle relationships
1345:MM = Metric Module
1194:involute roll angle
1188:Involute roll angle
1180:Involute roll angle
458:corresponds to the
2760:
2752:
2744:
2725:
2706:
2690:Throat form radius
2685:Throat form radius
2675:
2630:
2537:
2443:
2423:
2396:
2376:
2353:
2292:
2188:
2129:
2097:
2010:
1980:
1941:
1905:
1887:
1873:
1813:Outside lead angle
1808:Outside lead angle
1799:
1781:(tip or addendum)
1729:
1709:
1625:
1601:throated worm gear
1585:
1583:Wormgear diameters
1567:(tip or addendum)
1561:
1523:
1482:
1458:
1399:
1315:Lead (engineering)
1229:
1210:
1190:
1162:
1128:
1108:
992:
915:
881:
831:
784:
725:
632:
612:
570:
551:
518:
484:
452:
424:
370:Back cone distance
365:Back cone distance
354:
251:
243:
204:
3011:on 6 January 2012
2628:
2594:
2576:
2535:
2504:
2399:{\displaystyle p}
2379:{\displaystyle N}
2351:
2345:
2290:
2284:
2266:
2173:Spiral bevel gear
2167:Spiral bevel gear
1402:Mounting distance
1397:Mounting distance
1389:Mounting distance
759:DP = 3.1416 / CP
404:thermal expansion
338:plane of rotation
283:Angle of pressure
170:
169:
155:
75:
74:
67:
3084:
3049:
3046:
3035:
3034:
3028:
3020:
3018:
3016:
3007:. Archived from
3000:
2994:
2993:
2964:
2639:
2637:
2636:
2631:
2629:
2627:
2617:
2616:
2600:
2595:
2590:
2582:
2577:
2575:
2574:
2562:
2546:
2544:
2543:
2538:
2536:
2534:
2523:
2522:
2513:
2505:
2500:
2492:
2452:
2450:
2449:
2444:
2432:
2430:
2429:
2424:
2422:
2421:
2405:
2403:
2402:
2397:
2385:
2383:
2382:
2377:
2362:
2360:
2359:
2354:
2352:
2349:
2346:
2344:
2334:
2333:
2317:
2301:
2299:
2298:
2293:
2291:
2288:
2285:
2280:
2272:
2267:
2265:
2264:
2252:
2064:
2052:
1925:transverse plane
1919:Transverse plane
1756:Base helix angle
1751:Base helix angle
1665:
1653:
1589:outside diameter
1575:Outside diameter
1551:Outside cylinder
1467:
1465:
1464:
1459:
1447:
1446:
1434:
1433:
1094:
1054:Herringbone gear
1048:Herringbone gear
799:Face (tip) angle
794:Face (tip) angle
598:CP = 3.141 / DP
309:
300:
165:
162:
156:
154:
113:
85:
77:
70:
63:
59:
56:
50:
26:
25:
18:
3092:
3091:
3087:
3086:
3085:
3083:
3082:
3081:
3057:
3056:
3053:
3052:
3047:
3038:
3021:
3014:
3012:
3002:
3001:
2997:
2982:
2966:
2965:
2812:
2807:
2790:
2785:
2779:
2736:
2717:
2698:
2687:
2679:throat diameter
2667:
2665:Throat diameter
2659:
2646:
2605:
2604:
2583:
2566:
2550:
2549:
2524:
2514:
2493:
2471:
2470:
2459:
2435:
2434:
2413:
2408:
2407:
2388:
2387:
2368:
2367:
2322:
2321:
2305:
2304:
2273:
2256:
2240:
2239:
2224:
2212:
2200:
2180:
2175:
2169:
2157:
2121:
2109:
2089:
2077:
2076:
2075:
2074:
2070:
2069:
2068:
2065:
2057:
2056:
2053:
2042:
2031:
2012:Tooth-to-tooth
2002:
1997:
1995:Rack and pinion
1991:
1989:Rack and pinion
1972:
1967:
1961:
1933:
1921:
1897:
1892:
1865:
1845:
1833:
1821:
1810:
1791:
1775:
1767:Base lead angle
1764:
1762:Base lead angle
1753:
1741:
1721:
1701:
1689:
1678:
1677:
1676:
1675:
1671:
1670:
1669:
1666:
1658:
1657:
1654:
1643:
1631:
1617:
1577:
1553:
1515:
1474:
1438:
1425:
1420:
1419:
1410:
1391:
1383:DP = 25.4 / MM
1377:MM = 25.4 / DP
1335:
1326:line of centers
1322:
1320:Line of centers
1317:
1264:
1253:
1241:
1234:
1221:
1202:
1182:
1154:
1149:
1143:
1131:Inside diameter
1120:
1118:Inside diameter
1112:inside cylinder
1100:
1098:Inside cylinder
1078:
1076:Index deviation
1073:
1061:
1056:
1050:
1045:
1023:
1011:
984:
972:
960:
949:of a hypoid or
943:
927:
907:
873:
837:
823:
807:
796:
790:helical teeth.
776:
765:
736:
734:Diametral Pitch
717:
705:
692:
673:
660:Conjugate gears
657:
655:Conjugate gears
624:
604:
582:
562:
554:Center distance
549:Center distance
543:
541:Center distance
523:
510:
504:
476:
444:
416:
384:
378:
367:
346:
330:
319:
318:
317:
316:
312:
311:
310:
302:
301:
290:
285:
279:
255:addendum circle
235:
233:Addendum circle
224:
196:
190:
166:
160:
157:
114:
112:
98:
86:
71:
60:
54:
51:
40:
27:
23:
12:
11:
5:
3090:
3088:
3080:
3079:
3074:
3069:
3059:
3058:
3051:
3050:
3036:
2995:
2980:
2809:
2808:
2806:
2803:
2802:
2801:
2796:
2789:
2786:
2781:Main article:
2778:
2775:
2735:
2732:
2716:
2713:
2697:
2694:
2686:
2683:
2666:
2663:
2655:
2645:
2642:
2641:
2640:
2626:
2623:
2620:
2615:
2612:
2608:
2603:
2598:
2593:
2589:
2586:
2580:
2573:
2569:
2565:
2560:
2557:
2547:
2533:
2530:
2527:
2521:
2517:
2511:
2508:
2503:
2499:
2496:
2490:
2487:
2484:
2481:
2478:
2458:
2455:
2442:
2420:
2416:
2395:
2375:
2364:
2363:
2343:
2340:
2337:
2332:
2329:
2325:
2320:
2315:
2312:
2302:
2283:
2279:
2276:
2270:
2263:
2259:
2255:
2250:
2247:
2223:
2220:
2211:
2208:
2199:
2196:
2179:
2176:
2171:Main article:
2168:
2165:
2156:
2153:
2120:
2117:
2108:
2105:
2088:
2085:
2072:
2071:
2066:
2059:
2058:
2054:
2047:
2046:
2045:
2044:
2043:
2041:
2038:
2030:
2027:
2001:
1998:
1993:Main article:
1990:
1987:
1971:
1968:
1963:Main article:
1960:
1957:
1932:
1929:
1920:
1917:
1896:
1893:
1891:
1888:
1876:Pitch surfaces
1871:Pitch surfaces
1864:
1863:Pitch surfaces
1861:
1844:
1841:
1832:
1829:
1820:
1817:
1809:
1806:
1790:
1787:
1774:
1771:
1763:
1760:
1752:
1749:
1740:
1737:
1720:
1717:
1700:
1697:
1688:
1685:
1673:
1672:
1667:
1660:
1659:
1655:
1648:
1647:
1646:
1645:
1644:
1642:
1639:
1627:Main article:
1616:
1613:
1609:major diameter
1605:external gears
1576:
1573:
1552:
1549:
1514:
1511:
1507:
1506:
1503:
1500:
1473:
1470:
1469:
1468:
1456:
1453:
1450:
1445:
1441:
1437:
1432:
1428:
1409:
1406:
1390:
1387:
1334:
1331:
1321:
1318:
1313:Main article:
1300:of 90°, and a
1279:is 90° to the
1263:
1260:
1252:
1249:
1233:
1230:
1220:
1217:
1213:Involute teeth
1208:Involute teeth
1201:
1200:Involute teeth
1198:
1181:
1178:
1153:
1150:
1145:Main article:
1142:
1139:
1135:minor diameter
1119:
1116:
1099:
1096:
1077:
1074:
1069:Main article:
1060:
1057:
1052:Main article:
1049:
1046:
1041:Main article:
1022:
1019:
1010:
1007:
983:
980:
971:
968:
959:
956:
942:
939:
926:
923:
906:
903:
872:
869:
865:contrate wheel
833:Main article:
829:Face worm gear
822:
819:
806:
803:
795:
792:
775:
772:
768:Dedendum angle
764:
763:Dedendum angle
761:
735:
732:
716:
713:
704:
701:
696:crossing point
691:
690:Crossing point
688:
672:
669:
656:
653:
623:
620:
603:
600:
586:Circular Pitch
581:
580:Circular Pitch
578:
561:
558:
542:
539:
522:
519:
506:Main article:
503:
500:
475:
472:
468:involute tooth
443:
440:
436:involute tooth
422:Involute teeth
415:
412:
380:Main article:
377:
374:
366:
363:
345:
342:
329:
326:
314:
313:
304:
303:
295:
294:
293:
292:
291:
289:
286:
281:Main article:
278:
277:Pressure angle
275:
271:internal gears
267:external gears
234:
231:
227:Addendum angle
223:
222:Addendum angle
220:
189:
186:
168:
167:
103:. Please help
89:
87:
80:
73:
72:
37:of the subject
35:worldwide view
30:
28:
21:
13:
10:
9:
6:
4:
3:
2:
3089:
3078:
3075:
3073:
3070:
3068:
3065:
3064:
3062:
3055:
3045:
3043:
3041:
3037:
3032:
3026:
3010:
3006:
2999:
2996:
2991:
2987:
2983:
2981:1-55589-846-7
2977:
2973:
2969:
2963:
2961:
2959:
2957:
2955:
2953:
2951:
2949:
2947:
2945:
2943:
2941:
2939:
2937:
2935:
2933:
2931:
2929:
2927:
2925:
2923:
2921:
2919:
2917:
2915:
2913:
2911:
2909:
2907:
2905:
2903:
2901:
2899:
2897:
2895:
2893:
2891:
2889:
2887:
2885:
2883:
2881:
2879:
2877:
2875:
2873:
2871:
2869:
2867:
2865:
2863:
2861:
2859:
2857:
2855:
2853:
2851:
2849:
2847:
2845:
2843:
2841:
2839:
2837:
2835:
2833:
2831:
2829:
2827:
2825:
2823:
2821:
2819:
2817:
2815:
2811:
2804:
2800:
2797:
2795:
2792:
2791:
2787:
2784:
2776:
2774:
2770:
2767:
2765:
2764:tooth surface
2756:
2748:
2740:
2734:Tooth surface
2733:
2731:
2729:
2721:
2714:
2712:
2710:
2702:
2695:
2693:
2691:
2684:
2682:
2680:
2671:
2664:
2662:
2660:
2658:
2651:
2643:
2624:
2621:
2618:
2613:
2610:
2606:
2601:
2596:
2591:
2587:
2584:
2578:
2571:
2567:
2563:
2558:
2555:
2548:
2531:
2528:
2525:
2519:
2515:
2509:
2506:
2501:
2497:
2494:
2488:
2485:
2482:
2479:
2476:
2469:
2468:
2467:
2464:
2456:
2454:
2440:
2418:
2414:
2393:
2373:
2350:helical gears
2341:
2338:
2335:
2330:
2327:
2323:
2318:
2313:
2310:
2303:
2281:
2277:
2274:
2268:
2261:
2257:
2253:
2248:
2245:
2238:
2237:
2236:
2232:
2229:
2221:
2219:
2217:
2209:
2207:
2205:
2197:
2195:
2193:
2184:
2177:
2174:
2166:
2164:
2162:
2154:
2152:
2150:
2146:
2142:
2138:
2137:helical gears
2134:
2125:
2118:
2116:
2114:
2113:root cylinder
2107:Root cylinder
2106:
2104:
2102:
2093:
2086:
2084:
2082:
2067:Internal gear
2063:
2055:External gear
2051:
2039:
2037:
2035:
2028:
2026:
2023:
2020:
2017:
2015:
2006:
1999:
1996:
1988:
1986:
1984:
1978:Fillet radius
1976:
1969:
1966:
1965:Profile angle
1959:Profile angle
1958:
1956:
1953:
1950:
1947:
1945:
1937:
1930:
1928:
1926:
1918:
1916:
1912:
1910:
1901:
1894:
1889:
1883:
1879:
1877:
1869:
1862:
1860:
1858:
1854:
1853:pitch circles
1850:
1842:
1840:
1838:
1830:
1828:
1826:
1818:
1816:
1814:
1807:
1805:
1803:
1795:
1788:
1786:
1784:
1780:
1773:Outside helix
1772:
1770:
1768:
1761:
1759:
1757:
1750:
1748:
1746:
1738:
1736:
1734:
1725:
1718:
1716:
1714:
1705:
1698:
1696:
1694:
1686:
1684:
1682:
1664:
1652:
1640:
1638:
1636:
1630:
1621:
1614:
1612:
1610:
1606:
1602:
1598:
1594:
1590:
1581:
1574:
1572:
1570:
1566:
1557:
1550:
1548:
1546:
1542:
1538:
1533:
1531:
1527:
1519:
1512:
1510:
1504:
1501:
1498:
1497:
1496:
1493:
1491:
1487:
1478:
1471:
1454:
1451:
1448:
1443:
1439:
1435:
1430:
1426:
1418:
1417:
1416:
1414:
1413:Normal module
1408:Normal module
1407:
1405:
1403:
1395:
1388:
1386:
1384:
1381:
1378:
1375:
1371:
1368:
1365:
1362:
1359:
1355:
1352:
1349:
1346:
1343:
1340:
1332:
1330:
1327:
1319:
1316:
1311:
1310:
1305:
1303:
1299:
1294:
1292:
1288:
1284:
1283:
1278:
1274:
1272:
1268:
1261:
1259:
1257:
1250:
1248:
1246:
1239:
1231:
1225:
1218:
1216:
1214:
1206:
1199:
1197:
1195:
1186:
1179:
1177:
1175:
1171:
1167:
1158:
1151:
1148:
1147:Involute gear
1141:Involute gear
1140:
1138:
1136:
1132:
1124:
1117:
1115:
1113:
1104:
1097:
1095:
1093:
1088:
1085:
1081:
1075:
1072:
1067:
1065:
1058:
1055:
1047:
1044:
1039:
1037:
1033:
1032:
1027:
1020:
1018:
1016:
1008:
1006:
1004:
999:
997:
988:
981:
979:
977:
969:
967:
965:
957:
955:
952:
948:
940:
938:
936:
932:
924:
922:
919:
918:Form diameter
913:Form diameter
911:
905:Form diameter
904:
902:
900:
895:
892:
888:
886:
877:
870:
868:
866:
862:
861:contrate gear
858:
854:
850:
846:
842:
836:
827:
820:
818:
816:
812:
804:
802:
800:
793:
791:
788:
780:
773:
771:
769:
762:
760:
757:
754:
751:
748:
745:
742:
739:
733:
731:
729:
728:Crowned teeth
721:
715:Crowned teeth
714:
712:
710:
702:
700:
697:
689:
687:
685:
680:
678:
670:
668:
665:
661:
654:
652:
649:
647:
642:
638:
636:
635:Cone distance
630:Cone distance
628:
622:Cone distance
621:
619:
617:
608:
601:
599:
596:
593:
590:
587:
579:
577:
575:
574:central plane
568:Central plane
566:
560:Central plane
559:
557:
555:
547:
540:
538:
536:
532:
528:
520:
514:
509:
501:
499:
497:
493:
492:involute gear
489:
488:base diameter
482:Base diameter
480:
474:Base diameter
473:
471:
469:
465:
462:, and is the
461:
457:
456:base cylinder
450:Base cylinder
448:
442:Base cylinder
441:
439:
437:
433:
432:involute gear
429:
420:
413:
411:
409:
405:
401:
395:
393:
389:
383:
375:
373:
371:
364:
362:
359:
350:
343:
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335:
327:
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308:
299:
287:
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268:
264:
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179:
175:
164:
153:
150:
146:
143:
139:
136:
132:
129:
125:
122: –
121:
117:
116:Find sources:
110:
106:
102:
96:
95:
94:single source
88:
84:
79:
78:
69:
66:
58:
48:
44:
43:improve this
38:
36:
29:
20:
19:
16:
3054:
3013:. Retrieved
3009:the original
2998:
2967:
2771:
2768:
2763:
2761:
2727:
2726:
2708:
2707:
2689:
2688:
2678:
2676:
2656:
2653:
2649:
2647:
2462:
2460:
2365:
2233:
2227:
2225:
2215:
2213:
2203:
2201:
2191:
2189:
2158:
2149:hypoid gears
2141:worm gearing
2132:
2130:
2112:
2110:
2100:
2098:
2080:
2078:
2033:
2032:
2024:
2021:
2018:
2013:
2011:
1982:
1981:
1954:
1951:
1948:
1943:
1942:
1924:
1922:
1913:
1908:
1906:
1903:Pitch planes
1875:
1874:
1848:
1846:
1836:
1834:
1825:normal helix
1824:
1822:
1819:Normal helix
1812:
1811:
1801:
1800:
1797:Normal helix
1782:
1778:
1776:
1766:
1765:
1755:
1754:
1744:
1742:
1732:
1730:
1712:
1710:
1693:pitch circle
1692:
1690:
1687:Pitch circle
1680:
1679:
1634:
1632:
1608:
1597:crown circle
1588:
1586:
1568:
1564:
1562:
1541:above center
1540:
1537:below center
1536:
1534:
1530:hypoid gears
1525:
1524:
1508:
1494:
1486:normal plane
1485:
1483:
1472:Normal plane
1412:
1411:
1401:
1400:
1385:
1382:
1379:
1376:
1372:
1370:DP = n / PD
1369:
1366:
1363:
1360:
1356:
1354:MM = PD / n
1353:
1350:
1347:
1344:
1338:
1336:
1325:
1323:
1306:
1301:
1297:
1295:
1290:
1286:
1281:
1276:
1275:
1270:
1266:
1265:
1255:
1254:
1244:
1242:
1212:
1211:
1193:
1191:
1173:
1169:
1165:
1163:
1134:
1130:
1129:
1111:
1109:
1089:
1086:
1082:
1079:
1063:
1062:
1035:
1029:
1025:
1024:
1015:helical rack
1014:
1012:
1009:Helical rack
1002:
1000:
995:
993:
990:Heel and toe
975:
973:
963:
961:
946:
944:
930:
928:
917:
916:
896:
893:
889:
884:
882:
864:
860:
856:
852:
848:
840:
838:
814:
810:
808:
798:
797:
786:
785:
767:
766:
758:
755:
753:DP = n / PD
752:
749:
746:
743:
740:
737:
727:
726:
723:Crowned gear
709:crown circle
708:
706:
703:Crown circle
695:
693:
684:spiral gears
683:
681:
676:
674:
659:
658:
650:
643:
639:
634:
633:
615:
613:
597:
594:
591:
585:
583:
573:
571:
553:
552:
526:
524:
487:
485:
455:
453:
427:
425:
410:under load.
396:
385:
369:
368:
357:
355:
333:
331:
322:Apex to back
321:
320:
288:Apex to back
259:pitch circle
254:
252:
226:
225:
212:pitch circle
207:
205:
171:
161:October 2012
158:
148:
141:
134:
127:
115:
91:
61:
52:
32:
15:
2650:test radius
2644:Test radius
2155:Spiral gear
2145:bevel gears
2133:shaft angle
2127:Shaft angle
2119:Shaft angle
2081:root circle
2040:Root circle
1909:pitch plane
1895:Pitch plane
1885:Pitch cones
1849:pitch point
1843:Pitch point
1733:pitch helix
1727:Tooth helix
1719:Pitch helix
1707:Pitch cones
1681:Pitch angle
1641:Pitch angle
1490:pitch plane
1309:Helix angle
1302:helix angle
1282:helix angle
1245:bottom land
1232:Bottom land
1043:Helix angle
1036:helix angle
1026:Helix angle
1021:Helix angle
964:gear center
958:Gear center
931:front angle
925:Front angle
857:crown wheel
496:base circle
466:from which
460:base circle
428:base circle
414:Base circle
400:lubrication
249:Root circle
3061:Categories
2805:References
2794:Gear ratio
2783:Worm drive
2777:Worm drive
2728:Tip relief
2723:Tip relief
2715:Tip relief
2709:Tip radius
2704:Tip radius
2696:Tip radius
2289:spur gears
2034:Root angle
2029:Root angle
1857:pitch line
1837:pitch line
1831:Pitch line
1745:base helix
1739:Base helix
1713:pitch cone
1699:Pitch cone
1593:bevel gear
1298:lead angle
1291:lead angle
1277:Lead angle
976:gear range
970:Gear range
951:bevel gear
947:front cone
941:Front cone
935:bevel gear
899:bevel gear
885:face width
879:Face width
871:Face width
853:crown gear
849:face wheel
835:Crown gear
646:face width
531:spur gears
516:Bevel gear
508:Bevel gear
502:Bevel gear
408:deflection
334:back angle
328:Back angle
216:pitch line
192:See also:
131:newspapers
55:March 2023
3015:4 January
2625:ψ
2622:
2592:π
2532:β
2529:
2502:π
2441:ψ
2342:ψ
2339:
2282:π
2204:spur rack
2198:Spur rack
2192:spur gear
2186:Spur gear
2178:Spur gear
2101:root cone
2087:Root cone
1455:β
1452:
841:face gear
821:Face gear
811:face cone
805:Face cone
527:bull gear
525:The term
521:Bull gear
358:back cone
344:Back cone
101:talk page
47:talk page
3025:cite web
2990:65562739
2799:Sprocket
2788:See also
1599:. In a
1569:cylinder
1256:Top land
1251:Top land
815:tip cone
464:cylinder
376:Backlash
263:addendum
208:addendum
188:Addendum
184:(ANSI).
41:You may
1779:outside
1565:outside
1304:of 0°.
1071:Hobbing
1064:Hobbing
1059:Hobbing
933:, in a
265:. For
145:scholar
2988:
2978:
2366:Where
2143:. In
1890:Planes
1668:Angles
1635:pinion
1629:Pinion
1615:Pinion
1545:pinion
1526:Offset
1521:Offset
1513:Offset
1339:module
1333:Module
1289:, the
1034:, the
954:gear.
897:For a
845:pinion
535:pinion
490:of an
430:of an
147:
140:
133:
126:
118:
90:This
3067:Gears
2159:See:
1783:helix
1307:See:
1219:Lands
392:gears
152:JSTOR
138:books
3031:link
3017:2012
2986:OCLC
2976:ISBN
2762:The
2677:The
2648:The
2461:The
2226:The
2214:The
2111:The
2099:The
2079:The
1923:The
1907:The
1847:The
1835:The
1777:The
1743:The
1731:The
1587:The
1563:The
1380:and
1337:The
1324:The
1287:lead
1271:Lead
1267:Lead
1262:Lead
1243:The
1110:The
1031:lead
1001:The
996:heel
994:The
982:Heel
974:The
945:The
929:The
883:The
809:The
707:The
694:The
664:gear
614:The
584:The
572:The
486:The
454:The
426:The
402:and
356:The
332:The
253:The
206:The
174:gear
124:news
2619:cos
2526:cos
2336:cos
1449:cos
1003:toe
863:or
386:In
214:or
107:by
3063::
3039:^
3027:}}
3023:{{
2984:.
2970:.
2813:^
2202:A
2190:A
2163:.
2131:A
1823:A
1711:A
1691:A
1633:A
1611:.
1484:A
1137:.
1013:A
962:A
867:.
859:,
855:,
851:,
839:A
675:A
648:.
537:.
498:.
3033:)
3019:.
2657:r
2654:R
2652:(
2614:d
2611:n
2607:P
2602:N
2597:=
2588:p
2585:N
2579:=
2572:d
2568:P
2564:N
2559:=
2556:D
2520:n
2516:m
2510:z
2507:=
2498:p
2495:z
2489:=
2486:m
2483:k
2480:=
2477:d
2419:d
2415:P
2394:p
2374:N
2331:d
2328:n
2324:P
2319:N
2314:=
2311:d
2278:N
2275:p
2269:=
2262:d
2258:P
2254:N
2249:=
2246:d
1444:t
1440:m
1436:=
1431:n
1427:m
1240:.
1174:A
1170:P
163:)
159:(
149:·
142:·
135:·
128:·
111:.
97:.
68:)
62:(
57:)
53:(
39:.
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