IKROM RAHMONOV. O zbekiston Respublikasi Xalq ta limi vazirligi umumiy o rta ta lim maktablari uchun darslik sifatida tavsiya etgan

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1 IKM MNV ekiston espuliksi Xlq t limi virligi umumi o rt t lim mktlri uchun rslik sifti tvsi etgn To lirilgn v qt ishlngn 2-nshri QITUVI NSIYT-MT IJDIY UYI TSKENT 2014

2 U K (075) KK Òqrichilr :. SIYEV, T. IXSIYEV Niomi nomigi TDPU «him geometri, chimchilik v uni o qitish metoiksi» kfersi otsentlri; S. USMNV. vloni nomigi XTXQTMMI otsenti; N. Q QV Toshkent shhr 118-mktning oli toifli chimchilik fni o qituvchisi. Drslik folnilgn shrtli elgilr Mshqlr Svollr Testlr Topshiriqlr ro prllel chiiqlr (tekisliklr) ro perpenikulr chiiqlr (tekisliklr) espulik mqsli kito jmg rmsi mlg lri hisoin ijr uchun chop etili. ISN qituvchi NMIU, 2010 qituvchi NMIU,

3 S ZSI himchilik fni o quvchilrning tsvvur hm tfkkur qilish qoilitini o stiri. Tsvvur es shkli v fovi o lishi mumkin. quvchilrning fovi tsvvurlrini oshirish mqsi ulrg chimg oir n nvi svollr v mshqlr erili. Mshqlr o rtch () v shi () o lshtiruvchi hm iqtiorli () o quvchilrning ilimini hisog olgn hol tuilgn. oirgi mon mshin v jiholr ishl chiqrish tenologilrini chimlrni o qishni ilmsn turi egll o lmi. hunki hr ir mutssis v uqori mlkli ishchi tenik ormi turli uumlr v ulrning etllrini ssh hm nort qilish ishtirok eti. himchilikk oi ilimlrni to liq egllshning sosi shrtlrin iri grfik svoonlik (chimlr chiish v o qishni ilish)ir. himni o qish v chiishni ilishning sosi chimchilik hr ir nrsning shrtli rvish solshtiri tsvirlnishini mukmml egllshn iort. uning uchun chimchilik fnini egllshg hrkt qilish loim. r ir mvu so ngigi svollrg jvo eri, mshqlrni to liq jri orsngi, fnni to liq o lshtirishingi mumkin. rch muhnislr o g olri v fikrlrini ifolsh fqt chimlrn folnishi. Shu oisn un chimlr hujjt hisolni v jhon ishl chiqrilign rch snot mhsulotlri hm uro g or uumlri fqt chimlr sosi torlni. Umumn olgn, rch fnlr, sosn, chimlr ormi tushuntirili. hunki, chim hr qn nrsning qqol ko rinishini t minlign tsvir-hujjt hisolni. Nrsning niq shkli v o lchmlrini to liq ifolign v uumni nort qil olign tekislikgi tsvir chim eili. him es tenik tiliir. himlr chiish qoisini o rgtuvchi fn chim geometri hisolni. Shu oisn, chim geometri chimchilikning grmmtiksi eili. M lumki, geometri fni figurlrni nri jihtn ili olsilr. himchilik fni es ulrni tekislik chiish o li iln mli o rgnsilr. Demk, unn chim geometrining grmmtiksi geometri fni eknligi m lum o li. himchilik v geometri fnlri ir-iri iln chmrchs og liq o lgnligi ois, geometri fnini put o lshtiri olsngi, chimchilik fnini n shiroq ilishingig imkon tug ili. 3

4 urmtli o quvchi! Si, 1-sinfnoq o qish jroni rch fnlrn turli ko rinishgi chimlrn folni ilim olmoqsi. Eni chimlrni ilmi sos chiish v o qishni o rgnishg kirishmoqsi. uning uchun chimlrni chiish v o qituvchingi tgn nrslrni oi orishingi uchun quigilrg eg o lishingi loim: 1. himchilik ftri. u ftrni o ingi s olishingi mumkin. 12 vrqli ktk ftrning o rtsigi simlrini ehtiotlik iln chiqri oli, qisq tomong q qo ing. Shun ftringining vrqlri uun o li qoli. unn tshqri rmi ktkli mshqlr ftrin hm folnish mumkin. 2. himchilik lomi. himchilik lomi vrqlrig o qituvchingi ergn topshiriqlr chiili. Ulrning vrqlri qlinroq o li, usti hech qn chiiqlr o lmi. 3. himchilik solri. Ikkit uchurchkli chig ich (iri 30, 60, 90, ikkinchisi 45, 45, 90 ), gotovlni, o chirg ich v hr il qlmlr (qttiq hm umshoq). Drs vomi n rur o lign nrslrni o qituvchingi hm tishi mumkin. Xlqro tshkilot IS (Interntionl Stnrts rgnition)ning ko rstmsig inon rch sohlr shrtli elgilshlr lotin v unon lifosigi hrflr erilishi qul qilingn. Grfik tsvirlr hm nuqtlr, tekisliklr, testlr osh,,, D, E, F,...,,,... om α, β, γ, δ, ε,... hrflr elgilni. Drslikning ushu 2-nshri mliot o qituvchilrining tklif v istklrini hisog olgn hol i o grtirishlr, to lirishlr kiritili. Drslik hqigi fikr-mulohlringini quigi mnilg uorishingini so rmi. Toshkent 129, Nvoi ko chsi, 30. qituvchi NMIU. 4

5 1-. IZMILIK KUSIG KIIS r ir fnning po o lish trii uni qnchlik muhim hmitg eg eknligin, qimiligin, jmitning trqqiotig qo shotgn hisssin lolt eri. Itioi omlr o his-tug ulrini g orlrgi evorlrg, tog lrgi qolrg chiish ormi turli tsvirlr orqli muhrlshg hrkt qilishgn. u chigi-tsvirlr chimchilikning itioi oshlnishi hisolni, o sh vrgi omlr rtgn stlki chigilr ulrni fikr uritishg mjur qili, ongini rivojlntirishg turtki o lgnligi ehtimol. Demk, insonit trii ilk or rtilgn fn chimchilik (chimlr chiish) o lgnligig lolt er oli. Qim misrliklr turr jolrni, srolrni, iotonlrni qurish eng oi usul iln o ls-, u inshootlrning shkl v o lchmlrini tsvirl olgnlr. Qimgi mon ppiruslri, qolrg o i ishlngn rsmlr, evorlrgi nqqoshlik, ttotlik sn ti v shung o shsh tsvirlr o sh vr lqlrining chim sohsigi irinchi tushunchlrini ks ettiri. Shhrlrning sqlni qolgn plnlri, inolrning pln v fslri hm turli hujjtlr uning liliir. himchilikk oi stlki m lumotlr ermin 300 il muqm po o lgn. im me mori v muhnisi Mrk Vitruvi (milon vvlgi 1- srning ikkinchi rmi) tekislik inolrning tsvirlrini ssh o llrini ishl chiqqn. u iln u to g ri urchkli proeksilr ssh ishig sos solgn. ekiston Quimoor v qtom reologlr tomonin qish ishlri oli orilgn ermin olingi 2 1- mingilliklrg tlluqli omning oln v onin ko rinish tsviri topilgn. VI VII srg oi kumush iish inoning me mori fsi tsvirlngn. VII srn XV srgch rt sio fnning rch sohlri ktt ilmi utuqlrg erishilgn. Msln, mshhur olim Muhmm in Muso l-xormi ( ) unon olimi Ptoleme tomonin on qilingn i msllrni niq emsligini chimlr orqli isotl ergn. U o srlri turli mmlktlr, engi v tog lr, ktt ro v ko llrning ritlrini tsvirlgn. limning chign ritlrin to rttsi igch eti kelgn. u Nsr Foroi ( ) o ining geometrik sshlrg oir sri konstruktiv geometrik msllrni echishni on etgn. niqs, o grms prgàr ormi geometrik msllr echishni chimlr orqli tfsil on etgn. u hon eruni ( ) shr ichi esh il muntm ko poqliklr ssh mumkinligini chimlr orqli isotl ergn. ulr 5

6 1.1-chim. nori to rtoqlik (tetrer), ori oltioqlik (gekser), hvoi skkioqlik (okter), flki o nikkioqlik (oeker), moi igirmoqlik (ikoser) lrir (1.1-chim). rt sio chimchilikning muqrrrligini u hon erunining Jismlr ko lmi fo uch tomong: irinchisi uunlik, ikkinchisi kenglik, uchinchisi chuqurlik oki lnlik o l o nlgn o li. Jismning mvhum cho ilishi (proeksisi) ems, lki mvju cho ilishi (hqiqi kttligi) shu uch chiiq iln niqlni. u uch tomonning chiiqlri vositsi jism olti oqq eg o li, shunch oqlri iln u fo chegrlni. u olti oqlr mrki ir jonivor turgn o li (1.2- chim), uning ui shu oqlrn irig qrgn e ol qilins, u oqlr uning ol, orq, o ng, chp v ost tomonlri o li 1, egn fikrlrin ili olish mumkin. u es nn monvi to g ri urchkli (ortogonl) proeksilsh usulining o ginsiir. u li in Sino ( ) o ining qllr me ori sri o kuch srf qili, og ir uklrni uqorig ko trish, qttiq jismlrni o lklsh, jismlrni tekislsh v oshq mqslr uchun ishltilign menik solr esh il eknligini oi. ulr o q, richg, chig ir (lok), vint v pon hisolni. limning t riflgn menik solrin ilri 1.3-chim tsvirlngn. Miro Ulug ek ( ) ululr ritsini ju niqlik iln chign mshhur stronom olim eknligi utun unog m lum. uuk musvvir Kmoliin eho ( ) miniturlrin iri me mor qo li qurilish plni iln tsvirlngn. ssom o srlri qo llgn perspektiv qishiq urchkli ksonometri hisolni. rt sio olimlri o srlrini chiish chimlr chiish solri: jvr (chig ich), juptk (resfeer), mstur (leklo), prgàr oki suvu 1.2-chim. (sirkul) n folngnlr. 1 u hon eruni. Tnlngn srlr. Toshkent, Fn, II tom, 225-et. 6

7 1.3-chim. e himlrg hns (geometri), trh (pln), tr (fs), rej jvli (proeksi oki chim) egn nomlr erilgn. Demk, rt sio chimchilik o ig os hns fni iln irg rivojlngn. Qimgi chimlrning ju o qismigin igch sqlni qolgn. uning sosi si qurilgn sro, istehkom, msji v mrslr nn qt qurilmsligi uchun chimlr oqi tshlngn. Shun o ls, 1.4-chim Iroqi muqrns ko rinishigi kpitelli ustunning chimsi (Ust Shirin Muro chimsi) sqlni qolgn. u chim ustun fs tsvirlngn o li, uning shklini ko rstish uchun chiqrilgn kesim hm qo shi erilgn. Fn v tenik rivojlnishi iln chimlr hm tkomillshi ori. himlr o triig eg o lishi iln irg, lqlr mnitining trqqi etishig oi o lgn trini hm sql qoli. smlr, hkllr v chimlrg qr, qimgi lqlr to g risi ko p m lumotlr olish, shuningek, ktt hmitg eg o lgn ogorliklrni qt tiklsh mumkin o li. Frnsu olimi v vlt roi Gospr Monj ( ) o vrigch chimchilikk oi o lgn rch ilimlrni umumlshtiri, 1799-il him geometri kitoini osmn chiqri. Shunn eri chim geometri Monj metoi e hm uritili. Monj kitoi chimchilik grmmtiksi chim geometri troflich on qilingn. u vr chim geometrining mohiti ju ktt o li, Monjning o i Ñhim unogi tenik iln shug ullnign rch milltlr uchun tushunrli til, ni teniklr tiliir, egn ei. Demk, chimlrni to g ri chiish usullri, shuningek, chimchilik o jligining rch sohsini to g ri tshkil qilish hqigi fn chimchilik 1.4-chim. eili. 7

8 Xlq o jligining turli trmoqlri folnilign chimlr hr il nom iln uritili. Msln, vo, friklr turli stgohlr, mshinlr, vigtellr, o lchsh solri kilrni ssh uchun tuilgn chimlr mshinsolik chimlri, ino, ko prik, to g on, o l, knl, muof inshootlrini qurish ishltilign chimlr muhnislik-qurilish chimlri, er sthini tsvirlsh chimlri topogrfik chimlr eili. Topogrfik chimlrn ritlr tuish, muhnislik inshootlrini, GES, suv omori kilrni loihlsh v ulrni tegishli mon to g ri jolshtirish mqsi folnili. Semlr, grfiklr, plkt v igrmmlr illustrtsi chimchiligi sosini tshkil qili. himchilikning rch turlri sosi hisolngn geometrik chimchilik hm mvju. Geometrik chimchilik rch ssh usullrini o ichig olgn o li, nrs v hr il egri chiiqlr mjmusining chimsi itt proeksi jrili. Stnrtlshtirish tenik trqqiotini telshtirish muhim hmitg egir. Stnrtlr tenik hujjtlr o li, ulr uumlrning o lchm, shkl, og irlik, mteril v oshq siftlrini ko rsti. him stnrtlri qonun kuchig eg. himlrni stnrtlshtirish iln chimlrni chiish ilm-illikk rhm erili. Ntij chimlrni tt qilish ir illikk erishili, chimlr qer, qchon v kim tomonin chiilgnin qt i nr, to g ri tushunilishi t minlni. 1.5-chim o quv ustonlri rs pti slign kursining chimsi v ormchi tsvir sifti uning qqol tsviri hm erilgn. i nrsning konstruksisi so o ls, uning qqol tsvirini o lchmlri iln erish kifo (1.6-chim) qili chim chim

9 himchilik qurollri. himchilik uumlri v solrig gotovlni, chig ich, uchurchkliklr, leklolr, resshin, trnsportirlr kiri. himchilik jiholrig chimchilik stollri, chimchilik ttlri, chimchilik menimlri; chim sholrig es chim qog oi, qlm, o chirg ich, tush, qog oqgichlr kiri. Qlmlr v ulrni ishg torlsh. himchilik ishltilign qlmlr uch il umshoq, qttiq, o rtch qttiq qlmlrg o lini. Yumshoq qlmlr umshoqligig qr M, 2M, 3M; qttiq qlmlr qttiqligig qr T, 2T, 3T; o rtch qttiqlikgi qlmlr es T oki TM iln elgilni. oshq mmlktlr torlngn K-I-N rusumli qlmlrning umshoqlri, 2, 3; qttiqlri, 2, 3; o rtchsi iln elgilni. himlr T oki 2T qlm chiili. himning ustin ostiri chiish uchun TM oki M rusumli qlm ishltili. Qlmni ishg torlsh. Qlmning ochilgn og och qismining uunligi mm, grfitining uunligi 8 10 mm o lishi loim (1.7- chim, ). Qlm uchi grfitini m qum (jilvir) qog on (1.7- chim, ) folni, ung ishql o tkirlni. Sirkul ingichk chiiqlrni chiish uchun 1.7-chim, ko rstilgnek qlmning sterjenini ir tomonlm qumqog og ishql o tkirlni. hiilgn chimni ustin osi chiish qlm uchi kurk shkli torlni S e 1.7-chim. 1.8-chim. (1.7-chim, e). oirgi vqt chimlr chiish turli o g onlikgi grfit sterjenli qlmlrn folnilmoq. Ingichkroq sterjenlrn ingichk chiiqlrni, o g onroq sterjenlrn kontur chiiqlrni chiish folnish mumkin. chirg ich (reink). himchilik, sosn, umshoq o chirg ichlr ishltili (1.8-chim). rtiqch chiiqlrni o chirish pti chim chp qo l iln osi turili v o chirili. hig ich. him chiish chig ichning millimetrlngn qirrsin folnili. hig ichning ikkl chim chiilign qirrlri silliq v to g ri o lishi kerk. Uchurchkliklr. himchilik rslri uchun 45 ½45 ½90 v 30 ½60 ½90 urchkli ikkit uchurchklik o lishi tvsi etili. Uchurchklikning to g ri urchgi niq slgnligi quigich tekshirili. Uchurchklikning 9

10 1.9-chim. ir tomonini chig ichning to g ri qirrsig qo i (uchurchklikning 1-holti, 1.9-chim, ) vertikl kteti o ich chiiq chiili, so ngr chig ichning vitini o grtirmsn, ni chig ichni qo g tmsn uchurchklikni oshq tomoni iln qo ili (2-holt, 1.9-chim, ). Shun uchurchklikning kteti olingi chiilgn chiiqq ustm-ust tushs (1.9-chim, ), 90 li urchk niq slgn hisolni. gr uchurchklikning kteti olin chiilgn chiiq iln ustm-ust tushms (1.9-chim, ), 90 li urchk to hisolni. Uchurchklik noto g ri ishlngn o li, uning tomonini qumqog og ishql to g rilsh mumkin. himchilik, sosn, og ochn slgn uchurchkliklrn folnili. hunki qlm grfiti qog og v chig ich qirrsig ishqlni v m lum miqor uqlngn rrchlrni selluloi v plstmss chig ichlr mgnit ki o ig torti v utun chim o ich surkli. Ntij chim m lum miqor ifloslni. Gotovlni (chimchilik solri to plmi). lnlrni chiign, chiiqlrni o lchign, chimlrni tushlign v oshq ishlrni jrish uchun qo llnilign solr to plmi gotovlni eili (1.10-chim). himchilik sirkuli. hiign (1.11-chim, ) v o lchign (1.11- chim, ) sirkullr o li. hiign sirkul ln v ln olrini chiish ishltili. ln oki ulrning olrini chiishg kirishishn olin sirkulning grfit sterjenini v ignsining uchlrini rvr qili olish kerk (1.12-chim, ). Ulrning noto g ri jolshishi 1.12-chim, ko rstilgn. ejlsh sirkuli oki o lchgich. lchmlrni o lchsh chig ichin chimg v chimn o lchsh chig ichig ko chirish uchun rejlsh sirkulin, ni o lchgichn folnili chim, o lchgich sirkuli ko rstilgn. Sirkulg qlm o rnig ign o rntils, o lchch sirkuli hosil o li (1.11-chim, ). him qog oi. DS 597 g inon uqori siftli rusumli v oi rusumli chim qog olri ishl chiqrili. rusumli qog o uoq vqt sqlnign muhim chimlrni chiishg chim.

11 chim. To g ri Noto g ri 1.12-chim. mo ljllngn. rusumli qog o uoq vqt sqlnish tl qilmign chimlrni chiish ishltili. Ish o rnini tshkil qilish. Ish o rni vvlo shi oritilgn o lishi kerk. Ishning sifti v unumi, sosn, shung og liq. Yorug lik tiimi oki sun imi ish o rnig uqorin, chp tomonn iro olinroqn tushishi loim. n shun ko chrchmi, chig ich qirrsi, qlm v chimg qo lning sosi tushmi hm chiotgn chim usti ju tiniq ko rini. hiish vqti to g ri o tirish ktt hmitg eg. quvchi chim chiish vqti osh v elklrni to g ri tuti, oling iro engshi o tirishi kerk. Ko iln chim qog o orsigi msof mm o lishi loim. Ko krkni prtg oki chim stolig tir o tirish rmi. Ko krk iln prt orlig i kmi mm msof o lishi kerk. oqlrni iloji orich polg kfti iln tir o tirish loim. 1. him e nimg tili? 2. rt sio chimchilikning rivojlnish trii to g risi nimlrni ilsi? 3. Stnrt nim? 4. hiish solrig nimlr kiri? him uumlrig-chi? 5. Uchurchkliklrni to g ri oki noto g riligi qn tekshirili? 6. Qn qlmlr o li? Ulr qn elgilni? Musvvir Kmoliin eho o srlrini qn ksonometri jrgn?. Perspektiv.. Qishiq urchkli ksonometri.. Frontl imetri. D. Frontl iometri. 2-. IZMLNI TXT QILIS. STNDT. FMT. MSST himni tt qilish. Qlm iln chim chiish. him chiishning irinchi osqichi chiiqlrni qlm iln ingichk qili chii chiqishn iortir. Qlm iln chim chiish sosi qoilr. lchmlr chimg o lchsh chig ichi oki rejlsh sirkuli ormi o lch qo ili. gr chiilign shkl simmetrik o ls, u vqt vvl simmetri o qi chiili. erilgn o lchmning rmi simmetri o qining ikki tomonig o lch 11

12 qo ili. Yormchi chiiqlrni chiish qlm uchi 1.7-chim, ki oki grfit sterjeni ingichk o lgn sng qlmn folnili. him chiishning ikkinchi osqichi chiilgn chimning ustin ostiri chiili. himni ostiri chiish qlm qog oning siftig qr tnlni. Qog o sthi g ir-uur o ls, qttiqroq qlm, silliq o ls, umshoqroq qlm tnlni. himni eng vvl mrk, simmetri o q chiiqlri v ingichk chiiqlrni chiishn oshlsh kerk. So ngr lnlr, riusli olr, kein to g ri chiiqlr ustin ostiri chiish tvsi etili. sosi kontur, ni chimgi rch o g on chiiqlr ormchi ingichk chiiqlr ustin 2.1-chim ko rstilgnek, o rt qoliri chiili. Shuni unutmslik kerkki, o g on kontur, ni o g on chiiqlr ingichk chiiqlr ichin chiils, etl konturi kichiklshi, tshqrisin chiils, kttlshi keti. Sirkulg o rntish uchun to g ri chiiqlrning ustin ostiri chiilign qlmg nistn iro umshoqroq qlm olish loim. Shun chiiqlr niq chiili v qog ogi lnlr mrklri jolshgn nuqt hn ortiq kengi ketmi. 12 Mrklrni sql qolish uchun sirkul oog igi ignni chim tekisligig perpenikulr o lishig 2.1-chim. hm ignning to mtoq tomonigi chiqi turgn uchin folnishg ktt e tior erili. ln riusining kttligig qr ignni kerkli vitg o grtiri turish loim. itt mrkli konsentrik lnlrni chiish sentrik egn moslmn folnili. him tor o lgnn kein ortiqch chiiqlr o chirili, tolri o ls to g rilni. rtiqch oki to chiilgn chiiqlrni o chirish shlonlrn folnish tvsi etili. Stnrtlr, formt (ichim) lr v sosi ouv. Stnrt ekiston espuliksining konstruktorlik hujjtlri gon tiimi ( KYT) il qul qilingn v DSt 2.001:2003 e elgilni. KYT stnrtining elgilnishig misol: DSt :2003 Stnrt ro tg olingn il Guruhgi stnrtning trti rqmi Stnrt guruhining klssifiktsisi shifri KYT stnrtining klssi ekiston Dvlt stnrtining elgisi (ineksi) KYT stnrtlrining rchsi stnrtlshtirish trmoqlrro tiimining 2-klssig kiri.

13 Formt (ichim) lotinch so o li, shkllntirish egn m noni nglti. DSt 2.301:2003 ko rstmsig muvofiq, hmm chimlr m lum ichimgi stnrt jori etilgn o lchmgi qog og chiili. Stnrt sosi esht 4, 3, 2, 1 v 0 (2.2-chim, ) ichim tsiqlngn. rch ichimlr uchun o lchm irligi sifti o lchmlri mm o lgn 4 ichim qul qilingn. Qolgn ichimlr 4 ning ir tomonini ikkig, ikkl tomonini hm ikkig v hoko ko ptirishn hosil qilini. him ichimi hoshisi v sosi ouvi. DSt 2.401:2003 ko rstmsig muvofiq, mshinsolik ishl chiqrish chimlri sosi ouvlr chim qog o hoshisining pstki o ng tomoni urchgi jolshtirili. sosi ouvg chim tsvirlngn jismning nomi, chim kim tomonin v qchon chiilgnligi, kim tomonin tekshirilgni v qul qilingni, chiilgn jismning mterili, msshti kilr oili. himni lom oki kito qili tikish mqsi uning hoshisi chim qog olrning chp tomonin 20 mm, qolgn uchl tomonin 5 mm n jo qolirili chiili (2.2-chim, ). 2.3-chim, o quv chimsining sosi ouvining o lchmlri v shkli, 2.3-chim, es uning grflrini to lirish trtii ko rstilgn. Tikish uchun teshiklr sosi ouv o rni chim. 13

14 hii iov Q. 10 X 09 Tekshiri Ikromov. 10 X mkt 8- sinf QISTIM hrm 1:1 ¹ chim. him msshtlri. Tenik ju m sot etllri oki ju ktt, msln, pt terish komnining unkeri, ulr, ko prik kilrn folnili. Ulr ju ktt o lchmlrg eg. Lekin ulrni chim hqiqi kttligi chii o lmi. him qog oig sig irish mqsi ktt nrslrni kichrtiri, kichik nrslrni es kttlshtiri chiishg to g ri keli. uning uchun chim msshtlrin folnili. himning uunlik (kttlik) o lchmlri iln uumning mos uunlik o lchmlri o rtsigi nist chim msshti e tili. Ko pinch nrslrning chimlrini o ining hqiqi o lchmi, ni hqiqi ko rinishi 1:1 (irg ir) mssht chiishg hrkt qilini. Mssht oilgn sonlrg qr chim qn chiilgni ilini. Detl ikki mrt kichiklshtiri chiilgn o ls, 1:2 (irg ikki) e elgilni. Detl ikki mrt kttlshtirili chiilgn o ls, 2:1 (ikkig ir) e oili. Shun qili, mssht kichik son irinchi o li, msln: 1:2, 1:5, 1:10 ko rinishlr oils, kichrtirish msshti, ktt son irinchi o li, msln: 2:1, 5:1, 10:1 ko rinishlr oils, kttlshtirish msshti, 1:1 ko rinish oils, hqiqi kttlikgi mssht eili. DSt 2.302:2003 tomonin chimlr chiish quigi msshtlr elgilngn. 14

15 M2:1 M1:1 M1: chim. Kichrtirish msshtlri: 1:2, 1:2,5, 1:4, 1:5, 1:10, 1:15, 1:20, 1:25, 1:40, 1:50, 1:75, 1:100, 1:200, 1:400, 1:500, 1:800, 1:1000. qiqi kttlik msshti: 1:1. Kttlshtirish msshtlri: 2:1, 2,5:1, 4:1, 5:1, 10:1, 20:1, 40:1, 50:1, 100:1 v hoko. sosi ouv mssht uchun lohi jrtilgn grfg M elgi qo ilm 1:1 oki 1:2, oki 2:1 v hoko ko rinishi oili. oshq jolrg M hrfi qo shi oili. Msln, M1:1 oki M2:1, oki M1:2 v hoko ko rinishi oili. 2.4-chim qistirm hr il msshtlr chiilgn. rt hqiqi kttligi, ni M1:1, chp tomon ikki mrt kichik, ni M1:2, o ng tomon ikki mrt ktt, ni M2:1 msshtlr ko rstilgn. Qn mssht chiilishig qrm, chim uning hqiqi kttlikgi o lchmlri qo ilgn. 1. himgi ortiqch v to chiiqlr qn o chirili? 2. Mssht nim? Msshtlr chim qn ko rinish oili? 3. 4 ichim qn o lchmlrg eg? 4. oshi chiiqlri ichim chegrlrin qn msof chiili? 5. sosi ouv chimning qsi urchgig chiili? Ung nimlr oili? 1. Ikkit 4 ichim torlng v hoshisi hm sosi ouvini chiing. 2. Qistirm turli msshtlr tsvirlngn. Ulrn ittsi (2.5-chim, ) M1:1 erilgn o li,,, D lr qn mssht chiilgnliklrini niqlng. 15

16 2.5-chim. D Qn mssht erilgn: M2:1?. Kichrtirish.. Nturl (sli).. Kttlshtirish. D. Nist. 3-. IZIQ TULI. LM Q YIS QIDLI Nrslrni tekislik (qog o sthi) tsvirlsh folnilign chiiq v uning ilm-illigi ijokor hli tomonin rtilgn uuk grfikvi kshfiot hisolni. DSt 2.303:2003 tomonin chim chiiqlrining quigi turlri elgilngn: 1. sosi tutsh, o g on. 2. Ko rinms kontur, shtri. 3. Ingichk tutsh. 4. Mrki v o q shtri-punktir. 5. Tutsh to lqin. 6. Ikki nuqtli shtri-punktir chiiqlr (3.1-chim). himlr jismlrning ko g ko rini turgn shklini tsvirlsh qo llnilign sosi tutsh o g on chiiq ko rinign kontur chiiqlr eili. himlr jismlrning ko g ko rinmign qismini tsvirlovchi chiiq shtri chiiq e tli. Tsvirni ikkit simmetrik (ir il) qismlrg jrtuvchi shtri-punktir chiiq o q oki simmetri chiig i eili. lnlrning mrkin ir-irig perpenikulr o tuvchi shtri-punktir chiiqlr mrk chiiqlriir. q, simmetrik v mrk chiiqlri jism tsviri konturin 3 5 mm chiqi turs s. Unn ortiqchsi o chiri tshlni. sosi o g on tutsh chiiqning qlinligi lotinch s hrfi iln elgilni. oshq chiiqlrning o g onligi sosi o g on tutsh chiiqning tnl olingn qlinligig og liq o li. Ingichk tutsh chiiqlr o lchm chiiqlri, chetg chiqrish o lchm chiiqlri, chimlrni chiish folnili. Tutsh to lqin chiiqlrn etl to liq tsvirlnmgn, ui tsvirlngn 16

17 5 1 s=0,6...1, s/3...s/2 2 3 s/3...s/ s/3...s/2 5 s/3...s/2 6 s/3...s/ chim. jolr, ikki nuqtli shtri-punktir chiiqn etl oilmlri folnili. himgi tsvirning kttligi v murkkligig qr, sosi o g on tutsh chiiq orqli tsvirlnotgn kontur chiiqning o g onligi s=0,6 mm n to 1,4 mm gch olini. Qul qilingn kontur chiiqning o g onligi shu chimning rchsi ir il o lishi loim. Kontur chiiqlrning o g onligig qr, ko rinms kontur chiiq shtrilrining uunligi 2 mm n 6 mm gch o lishi kerk. Shtrilr orlig i 2 mm gch olini. Shuningek, shtrilr uunligi v ulr orsigi msof shu chimning rch joi ir il o lishi kerk. Shtri-punktir chiiqlr shtrilrning uunligi tminn 15 mm n 30 mm gch, shtrilr orsigi msof 3 mm n 5 mm gch o lishi loim. Shtrilr orsi nuqt iro cho ilgn nuqt ko rinishi tsvirlni. Shtri-punktir chiiqlr ln mrki nuqt iln ems, lki shtrilrning o ro kesishishi, oiri shtri iln tugllnishi loim. ln imetri 12 mm n kichikroq o ls, ulrgi mrk chiiqlri tutsh qili chiili. lchm qo ish qoilri. lchm qo ish qoilri DSt 2.307:2003 to liq on qilingn. himg qr etlning qn ktt-kichiklik chiilgnini niqlshg orm erign o lchmlr chim o lchmlri eili. 2 himchilik, 8-sinf 17

18 5 S5 3 tesh lchmlr o lchm chiiqlri v o lchm sonlri ormi ko rstili. Mshinsolik chimlri chiiqli o lchmlr hmm vqt millimetr hisoi qo ili. Lekin mm elgisi chim tushiri qolirili. urchk o lchmlri rj elgilri iln ko rstili. him qn mssht chiilishin qt i nr, ung hmm vqt o sh etlning hqiqi o lchmlri qimti qo ili. lchm chiiqlri etlning konturin ung prllel qili, 7 10 mm msof o tkili (3.2-chimgi 26, 76,... o lchmlr). lchm sonlri o lchm chiig ining ustin o rtrog i oki ung qinroq jo ko rstili. lchm chiiqlri oshq chiiqlr iln kesishmsligi loim. Shuning uchun eng vvl kichik, kein ktt o lchm qo ili (3.2-chimgi 10, 26, 76 o lchmlr). himgi vertikl o lchm chiiqlri ustig qo ilgn o lchm sonlrini o qish v ulrni oish qul o lishi uchun chimni sot strelksi o nlishi, chpn o ngg 90 g uri qrli v oili. him hr ir o lchm ir mrt ko rstili. Detlning eng ktt o lchmlrini, ni kengligi, lnligi, eni oki qlinligini ko rstuvchi o lchmlr grit o lchmlr eili (3.2-chimgi 5, 40, 76 o lchmlr). Grit o lchmlrni ko rstuvchi o lchm chiiqlri vertikl v goriontl chiiqlrg prllel olini. lchm chiiqlri chiqrish chiiqlrig strelk uchi iln tegi turishi kerk. Strelkning tuilishi 3.3-chim, ko rstilgn. Strelk kttligi kontur chiiqlrning o g onligig og liq o li, chimning hmm joi ir il kttlik o li. hiqrish chiiqlri oirgi strelkn 2 3 mm chiqi turs kifo, ortiqchsini o chiri tshlsh loim. urchk o lchmlrini qo ish qoilri 3.3-chim, erilgn. Shtril qo ilgn jogi urchk o lchmlri chiqri ko rstili. ln imetrlrining o lchmlrini ko rstish o lchm soni olig hmm vqt imetrni ifolovchi shrtli elgi qo ili (3.3-chim, f). iuslrning o lchmlrini ko rstuvchi o lchm soni olig hmm vqt rius elgisi oili (3.3-chim, ). 3.4-chimgi ln v rius o lchmlrig e tior ering chim.

19 S S S 60 f e 3.3-chim chim. him kvrt teshik oki kvrt chiqiq (o rtiq) o lchm soni olig kvrt elgisi qo ili (3.3-chim, e). Detl ir il element, ni lnli silinrik teshik ko p mrt tkrorlns v ulrning imetrlri o lchmlri ir il o ls, ir ilgi o lchm tkror qo ilmsn, hmmsi uchun itt teshikk uning nechtligi oi ko rstili (3.2-chimgi 3 tesh. 4 o lchmg qrng). ln chim to liq tsvirlnms, ni rmin ortiq chiils hm imetrning o lchm chiig i 3.4-chim, ko rstilgnek ui chiili. Lekin ln imetrining o lchm soni to liq ko rstili. gr o lchm sonini, ni ln imetrining qimtini oish uchun jo etrli o lms, u sonni 3.4-chim, ko rstilgnek chiqri oish mumkin. gr ln imetri 12 mm n kichik o ls, strelklrni ln tshqrisin qo ish tvsi etili (3.4-chim, gi 5). gr riuslrning o lchmlri 5 mm n kichik o ls, o lchm strelksini 19

20 chim. 3.4-chim, giek (5) o tshqrisin qo ish mumkin. hiqrish chiiqlri v ko rinr kontur chiiqlri orsigi jo o lchm sonini oish uchun etrli o lms, o lchm chiig ini v ulrgi strelklrni 3.5-chim, ko rstilgnek qo ish mumkin. lchm chiig igi strelklrni qo ish uchun jo etrli o lmgn hollr chiqrish chiig igi i strelklrni nuqt iln lmshtirish mumkin (3.5- chim, ). 1. him chiiqlrining nomlri v ulrning o g onliklri qn tnlni? 2. ln mrklrigi chiiqlr qn chiili? 3. Nim uchun chimlrg o lchm qo ili? 4. Qn holtlr o lchm sonlrining olig shrtli elgilr qo ili? u elgilr qn oili? 5. himlrgi o lchmlr qn irlik ifolni? 1. him chiiq turlrin tuilgn nmunlr 3.6-chim erilgn. Shulrn ittsini chiiqlr orliqlrini rejlsh sirkuli oki chig ich o lch, msshtg rio qilgn hol kttlshtiri chiing. 2. himchilik ftringig hr il kttlikgi 5 tn ln v ln riuslrini chiing hm o lchmlrini qo i chiqing. 3. himchilik ftringig, so ngr chim qog oig ir nechtn kontur, ni o g on chiiqlr chii chiqing. 4. Yssi etl chimlri erilgn (3.7-chim). Ulrn ittsini msshtg rio qilgn hol ko chiri chiing v o lchmlrini qo ing hm chimni tt qiling. sosi ouv v o lchm sonlrini omng. 20

21 3.6-chim. Detlning eng ktt (lnlik, uunlik, eni) o lchmlri qn tli?. Dimetr.. ius.. Grit. D. Kvrt. 1-grfik ish. hiiq turlri. Detlg o lchm qo ish qoilri. qituvchi topshirig i sosi jrili. S5 S S5 S chim. 400 D 21

22 4-. IZM SIFTLI V ULNING LMLI rf (shrift) lr insonit tomonin rtilgn t oishning eng qul mni shkli hisolni. himchilik shriftlri. Umumi tushunchlr. himlrgi hr qn ouvlr DSt 2304:2003 tlig muvofiq niq v qqol oilishi loim. Dvlt stnrti chiilign chimlrning hmmsi oilign ouvlrni ushu shriftlr oishni tl eti. him shrifti o ining oiligi, hrflr v rqmlrning ir il o g onlik o lishi v oim 75 qilik oilishi iln rkterlni. him shriftlri DSt 2304:2003 g muvofiq quigi o lchmlr tsiqlngn: 2,5; 3,5; 5; 7; 10; 14; 20; 28; Shriftlrning o lchmlri e, osh hrflrning lnligi h iln ifolnishig tili. Msln, osh hrfning lnligi 10 mm o ls, shriftning o lchmi hm 10 o li. Stnrtg muvofiq, shriftlr tik v qi vit oilishi mumkin. Ulrni oish qul o lishi uchun ormchi ktk to rlr chii olish kerk o li. To rlr ktklri kengligi shu to rg oilign hrflr chiig ining o g onligig teng o li (4.1-chim). rflrning lnligi h, oilishi o g onligi iln elgilns, eni v hrflr orsigi msof g qnch to g ri kelishi iln niqlni (4.1-, 4.2-, 4.3-chimlrg qrng). Shriftlrni oish ostki qismi tor o lgn hrf ustki qismi tor o lgn hrf iln onm-on jolshgn hollr ulr orsigi msof kmtirili (4.3-chim). Ko pchilik osh hrflrning eni trti o ich olingi shriftning o lchmig to g ri keli. Msln, 10 shriftning kengligi, ni eni 7 mm o li. osh hrflr chiiqlrining o g onligi 1/10 h olini. Msln, 10 o lchmli shrift chiiqlrining o g onligi 1 mm g to g ri keli h 1 h 1 h h chim.

23 5 2 e , h 1 h h ,5 7 2 h h chim. osh v om hrflrning konstruksilri v ulrning oilishi ko rstilgn o li, om hrflr lnligi, sosn, osh hrflr lnligi (h) ning 5/7 qismini tshkil eti. Msln, 10 o lchmli shrift omsining lnligi 7 mm o li. Yom hrflrning chiiqlri o g onligi 1/10 h olini. 10 o lchmli shriftgi om hrf chiig ining o g onligi 0,7 mm g teng o li. Yom hrflr iln oilgn osh hrflr hm om hrflr chiiqlri o g onligi oili. 1. Shriftlr qsi stnrt o ich oili? 2. Shriftlr qn stnrt o lchmlr oili? 3. osh shriftlrning lnligi qn hrf iln elgilni? Eni-chi? Yoilish o g onligi-chi? 4. Yom hrflr lnligi osh hrflr lnligi h ning qnch qismini tshkil eti? 23

24 ,5 1,5 2 h 7 1,5 1,5 0,5 0,5 3, ,5 4.3-chim. 1. rf chiiqlrining o g onligi uning lnligi h g qn nist oili?. 1/6.. 1/8.. 1/10. D. 2/5. 2. rflr orsigi msof qnch qili olini? ,5.. 2,5. D. 2. Yuqori q etilgn svollrg om jvo torlng S V YZM FL MD QMLNING YZILISI Kunlik hotimi v turli ior hm tshkilotlr rsmi lifo hrflri ouvlr oli orili. himlr fqt stnrt shriftlrn folnili. 5.1-chim lotin shriftig soslngn chim ouvlri, r v rim rqmlrining tuilishi v oilishi ko rstilgn. qmlrning lnligi v eni (1 n oshqlri) osh hrflrning lnligi v enig teng o li. 1 rqmining chiig i uning oilish chiig ig, eni 3 g teng qili oili.

25 5.1-chim. him ouvlrini jrish uchun mli ko rstmlr. him shriftlrini oish ormchi to rlr chiishn oshlni. Shrift qiligini chiish uchun trnsportir oki 30 v 45 urchkli ikkit uchurchklik ormi str sosig 75 urchklr o tkili. 25

26 5.2-chim. Lotin v kirill lfviti shriftlrining to rlrn folni oilishi 5.1- v 5.2-chimlr ko rstilgn. Shriftlrni oish ulrning ir-irig o shshligin folnish tvsi etili. i hrflrni oish ormchi to rlrning o rtsin o tuvchi, ni 1/2 h chiiqni elgil olishg to g ri keli. rflrning o rtsigi to g ri oki qrilish chiiqlrining o g onligi o rt chiiqning usti oki tgi jolshgn o li. So lr orsigi msof e=6, ouvgi qtorlr orsigi msof =17, hrflr orsigi msof 2 qili olini. Ktk ftr shriftlr oish. him shriftlrni ktk ftr oish nch qul. Dftr 75 qilik chiiq o tkish uchun to rtt 26

27 ktk v itt ktk igonli o l chiiq o tkili (5.3-chim). 4 t ktk lnligi 20 mm, 3 t ktk lnligi 15 mm, 2 t ktk es 10 mm ni tshkil qili. Eng vvl 3 t ktk lnligi shriftlrni oi mshq qilish tvsi etili. un shriftlr enini 2 t ktk kengligi olini. Keinchlik 2 t ktk lnligigi 10 o lchmli shriftni, so ngr itt ktk 5 o lchmli shriftni oi mshq qilini osh hrflr o lchmi iln om hrflr o lchmi 5.3-chim. ir-irin qn frq qili? 2. Shriftlr o ro qn o shshliklr mvju? 3. Qn hollr shriftlrni ormchi ktklrn folnmsn oish mumkin? itt 12 vrqli ktk ftrg 14 (15), 10, 7, 5 o lchmli osh v om shriftlr hm rqmlrni oing. Ktk ftr shriftlr qiligi qn ktklr nisti (igonli) ormi niqlni?. 4 v v v 2. D. 5 v grfik ish. him shriftlrini oish. qituvchi topshirig i sosi jrili. 6-. GEMETIK YSSL. TULI XIL IZIQL IZIS r qn chimni chiish o ro prllel v perpenikulr chiiqlrni chiishg to g ri keli. itt chiiq mrklri ir-irin o ro teng msof jolshgn ir necht teshiklri or etllr hm uchri. Goriontl chiiqlr o tkish. Goriontl to g ri chiiqlr hmm vqt goriont (ufq) chiig ig prllel olini. Shuning uchun hm goriontl chiiq chim chim qog oining otiq tomonig prllel o tkili. Goriontl chiiqlr chpn o ngg qr chiili. ro prllel goriontl chiiqlr chiishning eng qul usuli ikkit uchurchklik oki chig ich v uchurchklik ormi chiishir (6.1-chim). Ikkit uchurchklik ormi prllel chiiqlr chiilgn ulrning ittsi o nltiruvchi qili olini, u qo g li ketmsligi uchun uni chp qo l iln osi turili. Ikkinchisi o nltiruvchi uchurchklik qirrsig suri chiili. Vertikl chiiqlr chiish. Vertikl chiiqlr goriont (ufq) chiig ig perpenikulr o tkili. Yer tik turgn nrslr, ot, vertikl turgn nrslr eili. Shung ko r, un chiiqlr vertikl chiiqlr e tli. him vertikl chiiqlr chim qog oining tik on tomonlrig prllel oki goriontl chiiqlrg perpenikulr qili o tkili. 27

28 Vertikl chiiqlr pstn uqorig qr chiili. Vertikl prllel chiiqlr chiishning eng qul usuli chig ich v uchurchklikn oki ikkit uchurchklikn folni chiishir (6.2- chim,, ). Qi chiiqlr chiish. Qi holtgi chiiqlr goriontl v vertikl chiiqlrg 6.1-chim. nistn itiori urchk jolshi. Vertikl oki goriontl chiiqlr o vitini o grtirs, qi chiiqlrg o ti qoli. Goriontl v vertikl holtn oshq holtni egllgn chiiqlr qi chiiqlr eili. Qi chiiqlr, chimgi holtig ko r, uqorin pstg oki pstn 6.2-chim. uqorig qr chiili (6.3-chim). ro prllel chiiqlrni sirkul ormi oki o lch qo ish o li iln hm chiish mumkin. Msln, to g ri chiiq kesmsig 30 mm msof ung prllel to g ri chiiq o tkish uchun sirkul 30 mm o lch v nuqtlrn olr chiili v ulrg urinm 6.3-chim. o tkili (6.4-chim, ). Yoki v nuqtlrn to g ri chiiq kesmsig 90 urchk ingichk chiiq chiili v ulrg 30 mm o lchm qo ili. So ngr hosil o lgn 1- v 2- nuqtlr o ro tutshtirili (6.4-chim, ). ro perpenikulr chiiqlr 6.4-chim. chiish. Ikkit chiiq ir-irig nistn 90 urchk hosil qili jolshs, ulrni o ro perpenikulr chiiqlr eili. un chiiqlrni niq chiish uchun olin goriontl oki vertikl, oki itiori vitgi qi chiiq chii olini. Goriontl chiiqq nuqtsi orqli ung perpenikulr chiiq o tkish uchun uchurchklikning 90 li urchgi to g ri chiiqq nuqtn 6.5-chim, ko rstilgnek chiili. hig ich oki uchurchklik ormi goriontl chiiqn prllel surili, ikkinchi uchurchklikning on qirrsi nuqtg 6.5-chim, giek qo i chiili. Yoki sirkul ormi nuqtn ikkl tomong ir il rius olr chiili, to g ri chiiq iln kesishgn nuqtlr 1 v 2 n 1 oki 2 n kttroq ir il olr chiili. Yolrning o ro kesishotgn

29 chim. v 4- nuqtlri o ro tutshtirils, erilgn chiiqq perpenikulr chiiq hosil o li (6.5-chim, ). Vertikl v qi chiiqlrg hm perpenikulr chiiq ui goriontl chiiqq o tkilgn perpenikulr chiiq ki o tkili. To g ri chiiq kesmsini o ro teng o lklrg o lish. Tenik etllrning chimlri chiilotgn i, orliqlri o ro teng o lgn lnli (silinrik) teshiklrning itt o q jolshgnligini uchrtmi. unn tshqri, ko p geometrik sshlr to g ri chiiqlrni m lum miqor o ro teng o lklrg o lish tl qilini. Msln, kesmsini o ro teng 5 o lkk o lish uchun, to g ri chiiq kesmsining nuqtsin itiori urchk ormchi to g ri chiiq o tkili (6.6-chim, ). Shu o tkilgn ormchi chiiqq nuqtn oshl itiori uunlikgi ir il 5 t kesm o lch qo ili (6.6-chim, ). Eng oirgi 5-nuqtni nuqt iln tutshtiri, 4-, 3-, 2- v 1- nuqtlrn 5 chiiqq prllel chiiqlr o tkili (6.6-chim, ). Shun kesm o ro teng 5 o lkk o lini. u ormchi uchurchk usuli eili. 1. Qn chiiqlr goriontl chiiqlr eili? Qn chiiqlr vertikl chiiqlr eili? Qi chiiqlr-chi? 2. ro prllel chiiqlr qn o tkili? ro perpenikulr chiiqlrchi? 6.6-chim. 29

30 1. himchilik ftringig, so ngr chim qog oig turli ko rinishgi o ro prllel v perpenikulr chiiqlr o tking (3.6-chim). 2. Itiori uunlik kesm tnl oling, so ngr uni olin 3 g, kein 5 g teng o ling. D V tekisligig prllel tekisliklrgi kvrtning qsi chiig i vertikl hisolni?., D.., D.. D,. D. D. 7-. UK YSS V ULNI TENG LKLG LIS. QIYLIK V KNUSLIKL Tenik etllr, moslmlr v oshq solr turli urchklr uchri. Ulrni chim tsvirlsh m lum qoi v sshlrn folnili. urchklr ssh. himchilik hr il uumlrning chimlrini chiish, ulr uchrign turli ko rinishgi urchklrni sshg to g ri keli. r qn urchkni trnsportir v sirkul oki uchurchkliklr ormi ssh mumkin (7.1-chim). urchklrni sirkul ormi o lish. To g ri urchk ni teng ikkig o lish nuqtn itiori kttlikgi rius iln o chiili v uning urchk tomonlri iln kesishtirili (7.2-chim, ). 1- v 2- nuqtlrn o ro kesishign ir ilgi olr chiils, ulr kesishi E nuqtni hosil qili. E nuqt iln tutshtirils, urchk teng ikkig o lini (7.2-chim, ). E chiiq urchkni teng ikkig o luvchi issektris chiig i eili. Itiori o tkir urchkni teng ikkig o lish 7.3-chim ko rstilgn. To g ri urchkni teng uchg o lish uchun nuqtn itiori kttlikgi ormchi ln oi sirkul chiili. Shu oning kttligini o grtirmsn 1- v 2-nuqtlrn sirkul n olr chiils, 3- v 4- nuqtlr hosil o li. 3- v 4-nuqtlr iln tutshtirili, shun to g ri urchk teng uchg o lini (7.4-chim). To g ri urchkni teng to rt o lkk o lish uchun, vvl u urchk teng ikkig o li olini ( chim. 30

31 1 1 E chim chim chim. 7.5-chim. chim, ), so ngr hr qsi o lkni n ikkig o li chiqili. Shun to g ri urchk teng to rtg o lini (7.5-chim). Qilik v konuslik. ot v mshin etllri qilik v konusliklr ko pl uchri. Msln, imortlrning tomlri, temiro l relslrigi qilik, chelk, g jo mrgi tiqin, fsklr konuslik qo llnili (7.6- chim). Qilik. To g ri urchkli uchurchkning giðotenusi iln goriontl kteti orsi hosil o lgn o tkir urchk qilik eili. himlr qilik ikki sonning ir-irig nisti ko rinishi oili. Qilikni niqlovchi sonlr olig Qilik so i oki F shrtli elgi qo ili. Qilik urchgi α to g ri urchkli uchurchk ktetlri v ning nistig teng (7.7-chim), ni / oki α = /. 7.6-chim. :l 1:5 10% α chim

32 D D D h 7.8-chim. 20% h 7.9-chim. h D h 7.10-chim. Misol. 1:5 nistgi qilik slsin. uning uchun ktetlrining nistlri 1:5 o lgn to g ri urchkli uchurchk sli. u er vertikl kteti ir o lkk, ni 10 mm g, goriontl kteti esh o lkk, ni 50 mm qili olini (7.7-chim, ). 7.7-chim, 10% (foili) qilikk misol keltirilgn. Konuslik. G jo mrgi tiqinining konusliligi ikkl sos imetrlri irmsining ulr orsigi msofg o lgn nistig teng, ni k = = 2i D h (7.8-chim). u er qilik konuslikning rmig teng o li. himlr konuslik qimtini elgilovchi sonlr olig Konuslik so i oki elgisi qo ili. Konuslik elgisining o tkir urchgi (uchi) konus uchi tomong qrti chiili. Dimetri D v uunligi l iln elgilngn konusning konusliligi tenglm o ich niqlni (7.9-chim, ). Kesik konusning ko- nusliligi k = D iln niqlni (7.9-chim, ). h Misol. him ko rstilgn etl konussimon qismining konusliligini D niqlng. uning uchun k = = = oki 20% o li (7.10- h chim). 1. To g ri urchkni qn ssh mumkin? 30 li urchkni-chi? 120 li urchkni-chi? 2. urchkni teng ikkig o luvchi chiiq qn tli? 1. Uchurchkliklr ormi 30, 60, 90 v 120 li urchklrni sng. 2. To g ri urchkni sirkul ormi olin teng ikkig, so ngr teng uchg o ling. Qilikni hosil qiluvchi sirt niqlnsin?. Qvriq.. Tekis (og m).. Konussimon. D. Shrsimon. 32

33 8-. MUNTZM K PUKL YSS Muntm ko purchklr uch il usul sli. 1-usul. lnlrni o ro teng o lklrg o lish v muntm ko purchklr ssh. r qn ln imetri uni teng ikkig o li (8.1-chim, ). ro perpenikulr ikkit ln imetri uni teng to rt qismg o li (8.1-chim, ). r qsi qismni ikkig o lish orqli lnni teng skki o lkk o lish mumkin (8.1-chim, ). lnni o lish hosil o lgn nuqtlr o ro ketm-ket tutshtirils, muntm ko purchklr hosil o li (8.1-chim, e, f). lnni teng uch o lkk o lish. lnni sirkul ormi o ro teng uch, olti, o n ikki qismlrg o lish to g ri urchkni teng uch o lkk o lishgi usuln folnili. lnni teng uch o lkk o lish uning mrki orqli vertikl mrk chiig i o tkili. u chiiqning ln iln kesishotgn nuqtsi orqli sirkul ln riusig teng o iln ln ikki nuqt kesishtirili (8.2-chim, ). Shun ln teng uch o lkk o lini. Vertikl mrk chiig igi 1- v niqlngn 2-, 3- nuqtlr o ro tutshtirils, muntm uchurchk sli (8.2-chim, ). lnni teng olti o lkk o lish. lnni teng uchg o lishning vomi hisolni. Eng olin ln teng uchg o li olini (8.2-chim, ). So ngr riusni o grtirmsn 1- nuqtn o chiili. Shun ln teng olti o lkk o lini (8.3-chim, ). Topilgn rch nuqtlr ketm-ket o ro tutshtirils, muntm oltiurchk hosil o li (8.3- chim, ). e f 8.1-chim chim chim himchilik, 8-sinf 33

34 lnni teng o n ikki o lkk o lish. uning uchun ln stl teng olti o lkk o li olini (8.3-chim, ). So ngr goriontl mrk chiig i v uning ln iln kesishotgn 4- hm 10- nuqtlrin sirkul ln riusig teng olr chiils, ln o ro teng 12 o lkk o lini (8.4-chim, ). rch nuqtlr ketm-ket o ro tutshtirils, muntm o n ikki urchk sli (8.4-chim, ). lnni teng esh o lkk o lish. ln riusi teng ikkig o li olini. uning uchun nuqtn sirkul ln riusig teng o iln ln kesishtirili. osil o lgn v nuqtlr tutshtirili, shun rius E nuqt niqlni. E nuqt riusni teng ikkig o li (8.5- chim, ). E nuqtn E1 rius o chiils, goriontl mrk chiiq K nuqt hosil o li. 1 v K nuqtlr tutshtirils, lnni teng esh o lkk o luvchi kesm, ni lnning eshn ir o lgi (vtri) hosil o li (8.5-chim, ). 1K kesm iln ln chiig i eshg o li chiqili (8.5-chim, ). rch nuqtlr ketm-ket tutshtirils, eshurchk sli (8.5-chim, e). lnni trnsportir ormi hm teng esh o lkk o li chiqish mumkin. M lumki, ln 360 g teng. lnni eshg o lmoqchi o lsk 360:5=72 li mrki urchk hosil o li. ln mrki n oshlnuvchi u mrki urchklrni trnsportir ormi ssh mumkin. lnni teng etti o lkk o lish. u er lnni teng uchg o - lishgi usul qo llnili. Muntm uchurchk ir tomonining teng rmi muntm ettiurchkning ir tomonig to g ri keli (8.6-chim, ). Yoki lnni teng eshg o lishgi usuln hm folnish mumkin. Ungi E kesm muntm ettiurchklikning ir tomonig to g ri keli chim. E E K K 1K 1K e 8.5-chim. 4 34

35 1 8.6-chim. E F E 7 6 F chim (8.6-chim, ). Yoki lnni o ro teng oltig o lishgi usuln folnili. uning uchun lnning goriontl v vertikl mrk chiiqlri chii olini hm ungi v nuqtlrn ln riusig teng olr chiili. u olrning ln iln kesishgn v E nuqtlri o ro tutshtirili (8.7-chim, ). 1- nuqtn ln chiig ig F kesm sirkul 7 mrt o lch qo ils, ln teng etti qismg o lini (8.7-chim, ). osil qilingn hmm nuqtlr o ro ketm-ket tutshtirils, muntm ettiurchk sli (8.7-chim, ). 2-usul. Muntm ko purchklrni fqt sirkul ssh hm mumkin. Msln, kesmning v nuqtlrin g teng rius olr chiils, ulr o ro kesishi. v nuqtlr iln tutshtirils, muntm uchurchk sli (8.8-chim, ). Muntm oltiurchk ssh uchun v nuqtlrn 60 urchk chiiqlr chiili v ulrg g teng kesmlr o lch qo ili, v D iln elgilni. Uning uqori qismi hm shu trti jrilishi mumkin (8.8- chim, ). Kvrtni chiish uchun geometrin hmmg shi m lum o lgn to g ri urchkni ssh usulin folnili. Msln, chiiqq uning uchin perpenikulr to g ri chiiq o tkish uchun chiiqn tshqri itiori nuqt tnl olini v unn rius ln chiili. ln iln chiiq kesishotgn 1- nuqtn ln imetri o tkili, ni 1- nuqtni iln tutshtiri, ln 2- nuqt topili. iln 2- nuqt tutshtirils, to g ri urchk sli (8.8-chim, ). Eni, to g ri urchk tomonlrig o ro teng v kesmlr o lch qo ili, v nuqtlrn v chiiqlrg prllel chii, D nuqt niqlni. Yoki sirkul 35

36 60 E 60 1 e F D 2 D 8.8-chim. F D D D e 8.9-chim. v nuqtn oki riuslr olr chiili, ulr o ro kesishtirili. Shun D nuqt topili (8.8-chim, e). 3-usul. hig ich v uchurchkliklr ormi hm muntm ko purchklrni ssh mumkin. Ulrning ir tomonini ssh chim ko rstilgn (8.9-chim,,,, e). Shu trti qolgn tomonlrini hm ssh mumkin. 1. lnning qsi elementi uning oltin ir qismig teng? 2. lnni uning qn elementi teng ikkig o li? lnning o ro perpenikulr ikkit imetri uni necht teng o lkk o li?. Ikkit.. To rtt.. ltit. D. esht. 1. Sirkul v trnsportir ormi lnni teng esh o lkk o ling. 2. Turli kttlikgi lnlrni 3, 6, 12 o lklrg o ling. 3. r il usullr lnlrni teng etti o lkk o ling. 4. Turli ko rinishgi muntm ko purchkliklr chiing. 9-. TUTSML. T G I, TMS V TKI UK TMNLINI TUTSTIIS Turmush (tenik) qo llnilign hr ir uum uni ishltilish shroitig mos, ichm, qul hm chiroli o lishi kerk. un uumlr tutshmlr ko p uchri. Mshin etllrini chiish ko pinch ir chiiqni ikkinchi chiiq oki ln iln, lnni olr iln rvon tutshtirishg to g ri keli. un tutshtirish tutshm eili. Msln, 9.1-chim shmt onlrin iri tsvirlngn o li, to g ri chiiq hm ln oi, shuningek, ln 36

37 olri o ro rvon tutshgn. To g - ri chiiqni ln oi iln, lnlrning rvon o tign joi v 90 nuqtlr tutshtirish nuqtsi eili. To g ri chiiqni ln oi iln, À lnni ln oi iln tutshtiruvchi mrki nuqt tutshtirish 90 mrki eili. nuqtn chiilgn o tutshtirish riusi eili. Tutshmlr to g ri chiiqni lng 9.1-chim. 9.2-chim. o tishini v lnlrning o ro urinish nuqtlrini niqlshg soslngn. Tutshmlr turlrini o rgnishn sosi mqs etl ko rinishlrini chiish umloqlsh mrki v o tish nuqtsini te v niq topish tjrisig eg o lishir. Tutshmlr sirkul ormi chiili. Shu sli u chiiqlr sirkul egri chiiqlri hm eili. lng urinm to g ri chiiq o tkish. lng urini o tuvchi to g ri chiiqning urinish nuqtsi ni ln mrki iln tutshtirili v urinm to g ri chiiq g perpenikulr qili o tkili (9.2-chim). Yoki to g ri chiiqq lnni urinm qili o tkish uchun to g ri chiiqgi nuqtn ung perpenikulr chiiq o tkili v urintirilign ln riusi n oshl o lch qo ili, nuqt niqlni. Kein nuqtn to g ri chiiqq urinm ln o tkili (9.2-chim). Ikkit to g ri chiiqq urinm ln oini o tkish. To g ri chiiqlr o ro prllel, perpenikulr, o tms v o tkir urchklr jolshishi mumkin. ro prllel to g ri chiiqlrni riusli o iln umloqlsh uchun ikkl to g ri chiiqq perpenikulr ormchi to g ri chiiq o tkili. osil o lgn v nuqtlr orlig i teng ikkig o lini v nuqt topili. nuqt orqli riusli o iln o ro prllel to g ri chiiqlr tutshtirili (9.3-chim). To g ri, o tkir v o tms urchk tomonlrini tutshtirish. Tenik etllrning niq ishlngnligini tekshirish mqsi turli klirlrn folnili. Shulrn iri thlil qilins, uning to g ri, o tkir v o tms urchklri umloqlngn o li (9.4-chim). To g ri urchklrni umloqlsh uchun ulrning kesishgn joi nuqtn tutshtirish riusi g teng rius o chiili. Shun to g ri urchk tomonlri v nuqtlr hosil o li (9.5-chim, ). v nuqtlrn urchk tomonlrig perpenikulr ormchi chiiqlr o tkils, ulr o ro kesishi tutshtirish mrki hosil o li (9.5- chim, ). Yoki v nuqtlrn sirkul tutshtirish riusi g teng olr chiils, ulr o ro kesishi tutshtirish mrki niqlni (9.5- chim, ). Shunn kein nuqtn urchk v nuqtlr orqli umloqlni (9.5-chim, e). 37

38 chim chim. Î tms v o tkir urchklrni umloqlsh hm to g ri urchkni umloqlsh ki mlg oshirili. Tutshtirish riusi msof urchkning tomonlrig prllel ormchi to g ri chiiqlr o tkili. u ormchi chiiqlr o ro kesishi, tutshtirish mrki ni hosil qili (9.6-chim, ). nuqtn urchk tomonlrig ormchi perpenikulr chiiqlr o tkils, urchk tomonlri v o tish nuqtlri niqlni (9.6-chim, ). nuqt orqli urchk umloqlni. 1. Tutshm e nimg tili? Misol keltiring. 2. Tutshtirish mrki e nimg tili v u qn niqlni? 3. Tutshtirish nuqtsini qn niqlsh mumkin? 4. urchklrni tutshtirish mrki qn niqlni? e 9.5-chim. 9.6-chim. 38

39 1. Itiori kttlik ln chii, ung urinm to g ri chiiq o tking. 2. To g ri chiiqn 30 mm msofgi nuqtn urinm ln chiing. 3. rlig i 40 mm li o ro prllel ikkit to g ri chiiqq urinm ln oi o tking mm g teng rius to g ri urchkni umloqlng. lng urinm to g ri chiiq uning riusig nistn qn vit o li?. Prllel.. g m.. Itiori. D. Perpenikulr YLN V T G I IZIQNI TUTSTIIS Tenik folnilign gk klitining qo l ushlnign sopi v kllgi o ro olr iln silliq tutshtirilgn o li. Ikkit lnni to g ri chiiq iln tutshtirish. ir o l ikkit lng urini o tign itt to g ri chiiq ikkit lnni itt to g ri chiiq iln tutshtirish eili. lnlr imetrlri o ro teng o ls, 10.1-chimgiek tsvirlni. u er urinish nuqtlri 1 v 2 orqli o tuvchi ln riuslri 1 v 1 2 lr t to g ri chiiqq perpenikulr o li. lnlr imetrlri hr il o ls (10.2-chim), to g ri chiiqning lnlr iln urinish nuqtlri 1 v 2 ni niqlsh uchun lnlr mrklri o rtsi 2 nuqtn v 1 nuqtlrn o tuvchi ormchi ln chiili v mrkn l rius chiilgn kichik lnni nuqt kesi. iln nuqt tutshtirili vom ettirili. Shun mrkli ln 1-nuqt hosil o li. l n 1 g prllel chii l mrkli ln ikkinchi tutshtiruvchi nuqt 2 niqlni. 1- v 2- nuqtlr o ro tutshtirili vom ettirils, ikkl lng urinuvchi to g ri chiiq t hosil o li. ln v to g ri chiiqni ln oi iln tutshtirish. uning uchun erilgn tutshtirish riusi msof to g ri chiiqq prllel ormchi chiiq o tkili. ln riusi l g tutshtirish riusi ni qo shi, l + rius ln mrki l n ormchi o chiili, ormchi chim. t t 10.2-chim. 39

40 chim tesh chim. to g ri chiiq kesishtirili. Ntij tutshtirish mrki hosil o li (10.3- chim, ). n to g ri chiiqq perpenikulr o tkils, to g ri chiiqgi o tish nuqtsi topili. iln 1 tutshtirils, lngi o tish nuqtsi niqlni. orqli tutshm sli (10.3-chim, ) chim chelk qulog i tutshmg misol qili erili. lng lnni urintirish. lng lnni urintirish ikki il ko rinish o li. irinchisi tshqi urinish l +, ikkinchisi ichki urinish l (10.5-chim,, ). lng lnni tshqi urintirish. 1 riusli lng riusli lnni urintiri chiish uchun l mrkn l + rius o chiils, mrk topili. un lnlrning mrklri orsigi msof ulrning riuslri ig inisig teng. mrkn l mrkli lng nuqt urinign riusli ln chiili (10.5-chim, ). lng lnni ichki urintirish. 1 riusli lng uning ichki to chim. 40

41 monin urintiri chiish uchun l n rius irili. un lnlrning mrklri orsigi msof ulrning riuslri irmsig teng. 1 n l rius o chiils, mrk niqlni. n rius 1 mrkli lng nuqt orqli urinign ln chiili (10.5- chim, ). 1, 2 mrklrn lnning v nuqtlrig hm o ro mrk urinign 1, 2 olr chiils, ulr tshqi urinm, riusli ln iln v nuqtlr orqli ichki tutshm hosil qilmoq (10.5-chim, ). 1. Tutshtirish mrki qn niqlni? 2. Tutshtirish nuqtlri qn niqlni? 40 mm li ln iln to g ri chiiqni 30 mm li o ormi tutshtiring. To g ri chiiqni ln mrkin 45 mm msof itiori o nlish oling. lnning ichki urinmsini niqlng D IKKIT YLNNI UINI YLN YYI YDMID Z TUTSTIIS r qn chiroli uumg nr tshlns, uning sirti turli ko rinishgi olr, to g ri chiiq oki qvriq (otiq) olr iln tutshtirilgn jolrni ko rish mumkin. Ikkit lnni uchinchi ln oi iln tshqi tutshtirish. Ikkit 1 v 2 mrkli lnlrni erilgn tutshtirish riusi iln tutshtirish uchun olin 1 + rius 1 n kein, 2 + rius 2 n ormchi olr chii, ulr kesishtirili. Shun tutshtirish mrki niqlni (11.1-chim, ). iln 1, iln 2 mrklr tutshtirils, lnlr o tish nuqtlri v lr topili. orqli v nuqtlr tutshtirili (11.1-chim, ) chim u tutshm turig misol keltirilgn chim. 41

42 Ikkit lnni uchinchi ln oi iln ichki tutshtirish. Misol. iuslri 1 30 mm, 2 15 mm li lnlrni 50 mm li rius iln ichki tutshtirilsin (11.3-chim, ). uning uchun ikkit 1 v 2 mrkli lnlrni erilgn tutshtirish riusi iln ichki tutshtirish uchun olin 1 rius 1 mrkn, kein chim. rius 2 mrkn ormchi olr chiili, ulr o ro kesishtirili. Shun tutshtirish mrki hosil o li (11.3-chim, ). iln 1 tutshtirili, uning vomi ln, iln 2 tutshtirili, uning vomi ikkinchi ln o tish nuqtlri niqlni (11.3-chim, ). orqli v nuqtlr sirkul tutshtirils, ichki tutshm sli chim mkur tutshmg misol keltirilgn chim tutshmli etlni osqichlr chiilishi ko rstilgn chim chim. 1. Tutshmlr e nimg tili? Misol keltiring. Tutshtirish nuqtsi e nimg tili? Tutshtirish mrki e-chi? 2. Tutshmlr turlrini ilsimi? 3. trofingig nr tshl tutshmlrg misollr ko rst olsimi? 11.6-chim erilgn tutshmlri mvju etllrn ittsini chimchilik ftringig ko chiri chiing. 42

43 chim. 7 e f chim

44 1 v 2 riusli lnlrni riusli ln oi iln tshqi tutshtirish niqlnsin , 2 +. D. + 1, 2. 3-grfik ish. Qilik v konuslik. Mssht tutshmlr figursi ko chiri chiili v o lchmlri qo ili. qituvchi topshirig i sosi jrili SIKUL V LEKL EGI IZIQLI Tenik qisilgn oki cho ilgn ln olrin tuilgn opiq qvriq sirtlr ko p uchri. un sirtlrning konturi ovl eili, uni chiish usullri ko p. vl ko pinch uning erilgn ikkit o qi o ich chiili. vl chiish. vlning ktt o qi = 120 mm, kichik o qi D = 90 mm erilgn o ls, ikkl o qi o ro perpenikulr qili o tki olini. Ktt v kichik o qlrg v D o lchmlr qo i chiqili. ni iln tutshtirili v ung n v ning irmsi E msof n o lch qo ili. E kesm teng ikkig o lini, uning o rtsin perpenikulr ormchi chiiq o tkili. u chiiq o qni 1 nuqt, D o qni 2 nuqt kesi. u nuqtlrni n o ng tomong v uqorig oli o ti, ulrni 3 v 4 e elgilni hm ulr o ro tutshtiri chiqili v vom ettirili (12.1-chim, ). vl chiig ini chiish 1 nuqtn oshlni. Sirkul 1 rius 1- v 2- nuqtlr orlig i, 2 rius 2- v 3- nuqtlr orlig i, 3 rius 3- v 4- nuqtlr orlig i v nihot 4 D rius 4- v 1- nuqtlr orlig i irlshtiri chiqili. Shun ovlning chimsi sli (12.1-chim, ). E E E E D 1 D chim. 44

45 S Prol Ellips ln Giperol D III 1 II IV I 1 1 V 5 1 VI 12 XI VII X 7 VIII D IX chim. Egri chiiq nuqtlrini sirkul ormi tutshtirishning imkoni o lms, ulrni rvon tutshtirish uchun leklolrn folnili. Shuning uchun un egri chiiqlr leklo egri chiiqlri eili. Leklo egri chiiqlri tenik turli mshin v pprtlr, loktorlr, projektorlr, ntennlr, tishli g ilirklrning tish profillri keng ko lm qo llnili. Qui shun egri chiiqlr, ni Ipti ( ) konus kesimlrin (12.2- chim, ) iri elliðsning chiilishi iln tnishmi. Elliðsni chiish. Elliðsning ktt o qi = 120 mm, kichik o qi D =90 mm erilgn o lsin. Uni chiish uchun mrki nuqtn imetrlri 90 v 120 mm li ormchi lnlr chii olini. lnlr o ro teng 12 qismg o li chiqili hm mrki orqli o tuvchi ormchi imetrlri o tkili (12.2-chim, ). Ktt lngi nuqtlrn vertikl, kichik lngi nuqtlrn goriontl ormchi chiiqlr o tkili, ulr kesishtirili. Shun elliðsning qo shimch nuqtlri I, II, IV, V, VII, VIII, X, XI topili v ulr erilgn,,, D nuqtlr orqli o tign qili leklo tutshtiri chiqili (12.2-chim, ). 1. vl iln elliðsning frqi v umumi tomonlri nim? 2. Nim uchun leklo egri chiig i eili? 3. trofingin ovl v elliðsg misollr ko rst olsimi? Ktt o qi =140 mm, kichik o qi D=100 mm li ovl v elliðs chiing. Ellips hosil qilish uchun kesuvchi tekislik konus o qig nistn qn vitni egllshi loim?. Perpenikulr.. Prllel.. g m. D. qi orqli o tign. 4-grfik ish. vl v elliðs chiish. qituvchi topshirig i sosi jrili. 45

46 13-. PYEKSIYLS USULLI. MKZIY V PLLEL PYEKSIYLS r qn oi oki murkk uum chimsi o ich torlni. himlr geometrik sshlrning niqligi iln jrli turi. uumning shkli, o lchmlri hqi to liq m lumot eruvchi vosit chim hisolni. him tsvirlsh usullri orqli hosil o li. Tsvir sshning sosi proeksilsh usuli hisolni. Nrslrni chimlr tsvirlsh usullri. Nrslrning tekislikgi tsviri proeksi eili. Proeksi lotinch so o li, oling, ilgrig tshlmoq egn m noni iliri. Proeksilsh usuli ikki il: mrki proeksilsh v prllel proeksilsh ko rinishi o li. Mrki proeksilsh. iror nrsning tekislikgi proeksisini hosil qilish uchun o sh nrsning o i, tsvir (proeksi) tushirish uchun tekislik v oritgich mni o lishi kerk chim, n shulr mvju o li, tsvir hosil qilish uchun stolgi qutining urchklri orqli chiroq nuri o tkili. hiroq nurlri stol tekisligi iln kesishi, qutin tushotgn soning konturini hosil qili. u er: nrs quti, tekislik stol sthi, oritgich mni chiroq, qutin tushotgn so tsvir (proeksi) hisolni. Eni qutini uchurchklik shkli iln, stol sthini tekisligi iln, chiroqni S nuqt iln lmshtiri, S nuqt orqli uchurchkning nuqtlri orqli o tuvchi ormchi chiiqlr o tkils, tekislik iln kesishi, ning proeksisini hosil qili (13.1-chim, ). u er S proeksilsh mrki, nrs, proeksi, proeksi tekisligi, S, S, S proeksilsh nurlri eili. Proeksilshning u ko rinishi mrki proeksilsh eili. himchilik nrsning nuqtlrini lotin lfvitining osh hrfi, uning proeksisini o sh hrfg shtri elgisi qo i oili. Prllel proeksilsh. Yoritgich mni sifti Quosh oki olins, prllel proeksilsh hosil qilish mumkin. hunki oritgich mrki u er cheksilik o li, Quosh v n kelotgn oritish nurlri o ro prllel e qul qilini. S S S chim.

47 s α s chim. Prllel proeksilsh, o nvti, ikki il ko rinish: qishiq urchkli v to g ri urchkli o li. Proeksilsh nuri s proeksilr tekisligi g nistn o tkir urchk osti erilgn o ls, ung prllel qili shklning nuqtlrin ormchi proeksilovchi nurlr o tkili. Ntij u nurlr iln kesishi, ning proeksisi qishiq urchkli proeksisini hosil qili (13.2-chim, ). gr proeksilsh nuri s proeksilr tekisligi g nistn perpenikulr, ni to g ri urchk erilgn o ls, to g ri urchkli proeksilsh hosil o li (13.2-chim, ). u er nrs, s proeksilsh o nlishi, proeksilr tekisligi, nrsning gi proeksisi,,, proeksilsh nurlri eili. To g ri urchkli prllel proeksilshni ortogonl (unonch orto to g ri, gonl urchk, ni to g ri urchkli) proeksilsh hm eili. Eni mrki v prllel (qishiq v to g ri urchkli) proeksilrni o ro tqqosl ko rmi. Mrki proeksi nrsning proeksisi o in ktt. Demk, u proeksi etlning chimsi orqli uning hqiqi kttligi to g risi fikr uritish qiin. Qishiq urchkli prllel proeksi olins, u er nrsning urchklri uili proeksilni. un proeksilsh hm etlning hqiqi ko rinishi chim to g ri tsvirlnmi. To g ri urchkli prllel proeksi nrs v uning proeksisi iririg teng. Demk, un proeksilsh turi jrilgn etl chimsig qr uning konstruksisi, ni tuilishi to g risi to liq m lumot olish mumkin. un chim to g risigi m lumot 13.3-chim keltirilgn. unn kein proeksilshning u turig, ni to g ri urchkli prllel proeksilshg soslni chimlr chimi. hunki hr qn chimlr to g ri urchkli prllel proeksig soslni chiili. To g ri urchkli prllel proeksilsh o rnig qisqch proeksilsh eili. Shun to g ri urchkli prllel proeksilsh tushunili. 47

48 1. Qn proeksilsh turlri mvju? 2. Mrki proeksi v prllel proeksi e nimg tili? 3. Proeksining o i nim? himchilik ftringig proeksilsh turlrini chii, ilimingini musthkmlng. Proeksilovchi nurlr itt mrkn chiqs, qn proeksilsh usuli eili?. Prllel.. Mrki.. ksonometrik. D. Qishiq chim KTNT V EPYU QID UMUMIY TUSUN Jismning fogi holtini niq ilish uchun foni o ro perpenikulr, V v W proeksilr tekisliklri ishtiroki skkit qismg jrtili. osil qilingn pprt oktnt (ot unonch skki, lotinch skkilik) e tli. ktnt v epur. Goriontl tekislik ning (14.1-chim, ) o rtsin uni kesi o tign frontl tekislik V o tkili (14.1-chim, ). Ikkl v V tekisliklrg perpenikulr o lgn uchinchi profil tekislik W ulrning o rtsin o tkils (14.1-chim, ), foni shrtli rvish skki qismg o luvchi oktnt hosil o li. v V tekisliklrning o ro kesishgn chiig i iln, v W lrning o ro kesishish chiig i iln, V v W lrning o ro kesishish chiig i iln elgilni.,, lrning oshi, ni ulrning o ro kesishish nuqtsi iln elgilni.,, lr koorint o qlri, koorint oshi eili. irinchi oktnt misoli epur hosil qilmi. V V W 14.1-chim. 48

49 V tekislikni o o rni qoliri, ni o qi trofi pstg, ni V ning ostig, W ni o qi trofi, ni V ning o ng onig V iln itt tekislik hosil qilgunch lntirili (14.2-chim, ). Shun uchl, V, W tekisliklr itt tekislik ko rinishig o ti v u epur e tli. Epur frnsuch so o li, tekis chim egn m noni nglti. Tekisliklrni chegrlovchi chiiqlrsi tsvirlsh qul qilingn (14.2-chim, ). Nuqtni itt, ikkit v ucht tekislikk proeksilsh. Fogi nuqt orqli g perpenikulr nur (ormchi chiiq) o tkils, nuqtning gi proeksisi hosil o li (14.3-chim, ). g perpenikulr qili V tekisligi o tkili, ung hm n perpenikulr nur o tkils, u iln kesishi, nuqtning V gi proeksisi ni hosil qili (14.3-chim, ), v V lrg perpenikulr qili W tekislik o tkils, irinchi oktnt hosil o li. u er hm n W g perpenikulr nur o tkils, ning W gi proeksisi niqlni (14.3-chim, ). goriontl proeksilr tekisligi; V frontl proeksilr tekisligi; W profil proeksilr tekisligi; nuqtning goriontl proeksisi; nuqtning frontl proeksisi; nuqtning profil proeksisi v,, lr proeksilovchi nurlr eili. Epur,, lr proeksilrni og lovchi chiiqlr eili (14.3-chim, e). unn kein epur o rnig chim e uritmi. V W V W W 14.2-chim. V V W 14.3-chim. e 4 himchilik, 8-sinf 49

50 1. ktnt nim? 2. ktnt qn hosil o li? 3. Epur nim v u qn hosil o li? 4. v V tekisliklr o ro kesishishin hosil o lgn chiiq qn elgilni? v W lrning kesishishin hosil o lgn chiiq-chi? V v W lrning kesishishin hosil o lgn chiiq-chi? Tomonlri 200½200 mm li ucht kvrt qlinroq qog on irinchi oktntproeksilsh pprtini sng.,, v koorint o qlrini elgilng. Epur nim?. tekislik.. V tekislik.. W tekislik. D. Tekis chim T G I IZIQNING PYEKSIYLI r qn uum geometrik shkllrn tuilgnligi m lum. nvti, geometrik shkllr to g ri oki egri chiiqlrn tshkil topgn o li, to g ri chiiq ikkit nuqt orqli o tkili. To g ri chiiq nuqtlr iln chegrlngn o ls, u to g ri chiiq kesmsi hm eili. To g ri chiiq proeksilr tekisliklrig nistn prllel, perpenikulr, og m o lishi mumkin. To g ri chiiq fqt itt proeksilr tekisligig perpenikulr o ls, msln, goriontl proeksilovchi (15.1-chim, ), V frontl proeksilovchi (15.1-chim, ), W profil proeksilovchi chiiq eili (15.1-chim, ). To g ri chiiq qsi proeksilr tekisligig perpenikulr o ls, o sh tekislikk nuqt ko rinishi, qolgnlrig o ining hqiqi kttligi proeksilni (15.1- chim,,, ) chim, e proeksilovchi to g ri chiiqlrning chimlri erilgn. To g ri chiiq fqt itt proeksilr tekisligig prllel o ls, o sh tekislikk hqiqi kttligi proeksilni, qolgnlrig es, qi o lgnligi uchun qisqri proeksilni (15.2-chim,,, ). To g ri chiiq qsi tekislikk prllel o ls, o sh tekislik nomi iln tli, ni goriontl (15.2-chim, ), V frontl (15.2-chim, ), W profil (15.2-chim, ) chiiqlr eili. D shkl g perpenikulr (15.3-chim) tsvirlngn o li, u uqori on qilingn to g ri chiiqlrn tshkil topgn. Ushu D shkl goriontl proeksilovchi v D, profil proeksilovchi v D chiiqlrn tuilgn. gr to g ri chiiq proeksilr tekisliklrig og m vitni egllgn o ls, un to g ri chiiq umumi vitgi to g ri chiiq eili chim,,, umumi vitgi to g ri chiiq kesmsining, V v W proeksilnishi ko rstilgn o li, uning proeksilri hqiqi uunligig nistn o gri (qisqri) tsvirlngn. Esl qoling! To g ri chiiq proeksilr tekisliklrig perpenikulr

51 V V D E F W W E D F X D X E F D D V W E F D E F E F V V W E 15.1-chim. e W V E F W 15.2-chim. 51

52 V D D 15.3-chim. W o ls, nuqt ko rinishi, prllel o ls, o ining hqiqi uunligig teng, umumi vit o ls, qisqri proeksilni. 1. To g ri chiiq nuqtlr iln chegrlngn o ls, u qn nomlni? 2. To g ri chiiq qn chiili? 3. g perpenikulr chiiq nim e tli? V v W lrg perpenikulrlri-chi? g prllellrichi? V v W lrg prllellri-chi? 4. g perpenikulr chiiq ung qn ko rinish proeksilni? V v W g perpenikulrlri-chi? chim, tsvirlngn umumi vitgi kesmning chimsi (epuri) ni o qituvchi ormi jring chimgi D to rturchkli shkl qn chiiqlrn tshkil topgnligini thlil qiling. g perpenikulr to g ri chiiq qn nomlni?. Goriontl.. Frontl.. Goriontl proeksilovchi. D. Profil. V V 15.4-chim. W 15.5-chim. 52

53 D D 16-. YSSI SKLLNING PYEKSIYLI 15.3-chim D to g ri to rturchkli ssi shklning g qn proeksilnishi ko rstilgn chim D to g ri to rturchkli shklning, V v W g proeksilnishi tsvirlngnligi erilgn. D tekis shklni olin g, kein v V g, so ngr, V v W g proeksilsh usullri iln tnishi chiqmi. 1. D tekis shklni g proeksilsh. Ushu D tekis shkl g prllel vit 16.1-chim, gi ki fo jolshgn o ls, u o ining hqiqi kttligi proeksilni. hunki D. uning uchun,, v D nuqtlrn g perpenikulr chiiqlr o tkili, chegrlni.,, v D lr o ro tutshtirili. 2.,, v D nuqtlrn V g perpenikulr chiiqlr o tkili, V chegrlni. uning uchun,, v D lrn tekisligi o ich g perpenikulr chiiqlr chiili, iln kesishtirili. osil o lgn, v D lrn V tekisligi o ich vertikl chiiqlr chiili, D nuqtlrn V g perpenikulr chiiqlr iln kesishtirili. Shun D ning V gi frontl proeksisi, D sli (16.1-chim, ). 3. D shkl W g nn V g proeksilngnek mlg oshirili (16.1-chim, ). 4. D tekis shklning, V, W gi chimsi (epuri) 16.2-chimgiek o li. V D D D D V D D D 16.1-chim. D D D W D 16.2-chim. 53

54 D D D D 16.3-chim. 80 D V Â D D 16.4-chim. Ñ 12 S 2 V D D Ñ 16.5-chim. Ñ 32 W S chim. e

55 gr tekis shkl, V v W g nistn umumi vit o ls, ni, V, W g prllel hm, perpenikulr hm o lmgn, tekis shkl fo proeksilr tekisliklrig nistn umumi vit jolshgn hisolni. un tekis shkllrning, V, W tsvirlnishi m lumot sifti 16.3-chim,,, erilgn. Uning, V, W gi chimsi 16.4-chim tsvirlngn. Tekis shklning erilgn proeksisi (16.5-chim) o ich uni osqichlr ko chiri chiish 16.6-chim,,,, e ko rstilgn. 1. g prllel o lmgn to g ri chiiq qn nomlni? u to g ri chiiq g qn proeksilni? V g-chi? W g-chi? 2. Umumi vitgi tekis shkl g qn proeksilni? V g-chi? W g-chi? Dftr, turli chig ichlr ki tekis shkllrn irini ish ftringig, V, W gi proeksilrini chiing. g prllel ssi shkl (tekislik) nim eili?. Profil.. Goriontl.. Frontl. D. g m ITT V Z PEPENDIKUL IKKIT PYEKSIYL TEKISLIGIG MDELNI PYEKSIYLS V TEKIS IZM (EPYU) SIL QILIS Konstruksisi so etllrni itt tekislik tsvirlsh mumkin. Msln, qistirm e tluvchi etlni tekisligig proeksilsh jroni 17.1-chim ko rstilgn. Qistirm g prllel o lgni uchun uning qlinligi ko rinmi. rtsigi silinrik teshik v qistirm konturining tsviri o ig teng tsvirlngn. him tekisligini frontl vitg keltirils, 17.1-chim, giek ko rinishg o ti. u er qistirmning qlinligi ko rstils, u to g risi to liq m lumotg eg o lish mumkin chim. S5 55

56 V V chim. V e 17.3-chim. 40 e S5 ro perpenikulr ikkit proeksilr tekisligi tsvirlr ssh. i etllr o ining konstruksisi so o lishig qrm ikkit proeksi tsvirlnishi tl qilini. Msln, 17.2-chim,, tekisligig proeksilnotgn prllelepiðe, uchurchkli prim v silinrlrg nr tshlsk, ulrning hmmsi ir il to g ri to rturchk shkli proeksilni. Ulrning ir-irin frqini V gi proeksilri orqli niqls o li. Lekin prllelepiðeni itt proeksi tsvirl, uning qlinligini ko rstish kifo (17.2-chim, ). Silinrni hm itt proeksi tsvirlsh uning imetrini ifolovchi shrtli elgin folnishning o i etrli (17.2-chim, ). mmo uchurchkli primning urchklri o ro qn jolshgnligini fqt ikkinchi tekislik kiritish orqli niqlsh mumkin (17.2-chim, e). Moel goriontl proeksilr tekisligi g konturi to g ri to rturchk (17.3-chim, ) V g o ining frontl konturi o ich proeksilnmoq. Moelni oli qo i, tekisligini pstg o q trofi frontl holtg kelgunch lntirils, tekis chim, ni epur hosil o li (17.3-chim, ). Proeksilrni og lovchi ormchi chiiqlr v tekisliklrni chegrlovchi chiiqlr hm stnrtg muvofiq tsvirlnmsligi mumkin (17.3-chim, ). unn kein nrslrning chi- 56

57 msi chiilgn, ulrning proeksilrini og lovchi chiiqlr tushiri qolirili. Proeksilr chiilotgn ulrni og lovchi chiiqlr or, e fr qilini. Lekin proeksilrni hr il jo tsvirlshg o l qo ilmi (17.3-chim, e) chimgi etlning proeksilrig e tior erils, goriontl proeksisi etlning o rtsigi silinrik teshik ln, V tekislik ko rinmotgnligi uchun u ko rinms kontur-shtri chiiq chiilgn. unn kein chim etlning ko rinmign elementlri shtri chiiq tsvirlni. Tenik shun etllr mvjuki, ulrni ucht v unn ortiq proeksilr tsvirlshg to g ri keli. i etlning ikkit proeksisi orqli uni to liq tsvvur qilish qiin. Msln, 17.4-chim, qqol tsvir erilgn etl olins, uning V W V W 1 W 17.4-chim. V W chim. 57

58 17.6-chim e f 17.7-chim. tuilishi nch murkk, ikki onigi evorlrin iri qi qili kesilgn. u evorning shkli fqt profil proeksilr tekisligi niq ko rini. hunki u o sh tekislikk prllel o li, ung o ining hqiqi kttligi proeksilni. unn tshqri, etlning shklini uning on v ostki soslrining o ro jolshishi to g ri urchkli eknligi W tekisligi niq ko rini. lingi v V tekisliklrig uchinchi proeksi tekisligi ulrg perpenikulr qili kiritili (17.4-chim, ). W tekislik profil proeksilr tekisligi eili. Profil so i frnsuch o li, on tomoni egn m nog to g ri keli. Detlni uchl proeksilr tekisliklri fosig qo i,,v,w proeksilr tekisliklrig proeksilri tushirili (17.5-chim, ). tekisligini o q trofi pstg, W tekisligini o qi trofi o ngg lntiri V iln itt tekislik hosil qilini (17.5-chim, ). Detlning profil proeksisi iln 58

59 frontl proeksisi goriontl chiiq ir-iri iln og lngnligig e tior ering. Stnrt tlig inon, etlning chimsi proeksilrni og lovchi chiiqlr tushiri tsvirlni (17.5-chim, ). un tsvirlshg kompleks chim hm eili. 1. him etl qlinligi qn ko rstili? chimgi etl tsviri nim uchun 30 soni olig, 40 soni olig elgilri qo ilgn? 3. Detlning chim ko rinmign qismlri qn chiiq chiili? 4. W proeksilr tekisligi qn nomlni? 5. Nim sn W tekisligi kiritili? 17.6-chim erilgn etllrn irining proeksilrini chiing chim etllrning ko rinishi 1, 2, 3, 4, 5 rqmlr, ulrning qqol tsvirlri,,, e, f hrflr iln elgilngn. ir-irig mos kelign etllrning qqol tsvirini proeksilrni solishtirish o li iln niqlng GEMETIK JISML V ULNING PYEKSIYLI r qn etl m lum trti jolshgn geometrik jismlrn tuilgn o li. Msln, resi o ilmgn oltni ollik. oltning kllgi oltiurchkli prim, sterjeni silinr, silinr uchigi fsksi kesik konuslrn tuilgn. Fikrn hr ir geometrik jismni ir-irin jrti, ni hr irini lohi tsvvur qili ko rmi (18.1-chim). Shun olt prim, silinr v konusn tuilgnligi m lum o li. Geometrik jism o ining sof ko rinishi hm uchri. Msln, g isht prllelepiðe (prim), qlm prim oki silinr, quvur silinr, koptok shr v hoko. Shulrn ko rini turuiki, turmushimi trofimini o r turgn nrslr turli geometrik jismlr ko - rinishi, m lum trti ulrning ig inisin tuilgn. i geometrik jismlrg quigilr kiri: prim (ku, prllelepiðe), silinr, konus, pirmi, shr. Ko poqliklr. ir il oki turli ko rinishgi ko purchkliklrn tuilgn geometrik jism ko poqlik eili. Ulrn fqt ku, prllelepiðe, prim, pirmilr o rgnili. Ko poqliklrn pirmi (tetrer) v uning elementlri 18.2-chim ko rstilgn. S,,, uchlri, sos, S, S, S oqlri, S, S, S,,, qirrlri hisolni. Demk, oqlrining o ro kesishotgn chiiqlri qirrlr, qirrlrning o ro kesishotgn nuqtlri uchlr, qirrlri orqli chegrlnotgn tekis shkllr oqlr eili. 59

60 Konus Silinr Prim 18.1-chim. Ku. Ku ko poqlik turkumig kiri v u oltit ir il kttlikgi kvrtlrn tshkil topi chim, kuni, V, W tekisliklrig proeksilsh ko rstilgn. Uning uchl (lnligi, kengligi v uunligi) o lchmlri () ir il. Shuning uchun uning chimsi o ro teng o lgn ucht kvrt orqli tsvirlnpti (18.3-chim, ). Ku o n ikkit qirrn tshkil topi v hr to rtt o ro prllel qirrlri, V, W g perpenikulr o lgni uchun nuqt ko rinishi, qolgnlri prllel vit o lgnligi uchun o ining hqiqi kttligi proeksilni. Prllelepiðe. Prllelepiðe ko poqliklrning ir ko rinishi hisolni, proeksilr tekisliklrig to g ri to rturchk shkli proeksilni (18.4-chim). Lekin uning uchl o lchmlri hr il: lnligi h, kengligi, qlinligi o li. Prim. Ko poqliklrn iri hisolngn prim turli ko rinish o li. Primning muntm oltiurchkligi tenik etllr ko p uchri. Msln, olt, gk kilr. S V W 18.2-chim chim. 60

61 Muntm oltiurchkli prim tekisligig muntm oltiurchk, V tekisligig ikki on og i iln prllel jolshgnligi uchun o sh oqlri hqiqi kttligi, qolgnlri qisqri proeksilni (18.5-chim). un primni chim eng olin ustn ko rinishi, ni gi goriontl proeksisini chiishn oshlsh loim. Shun uning V v W gi oqlrini tsvirlsh tolikk o l qo ilmi. un prim, sosn, ikkit D imetr, ni hmm qirrlri uchlrig urinm ln v lnligi h o lchmg eg o li. u prim simmetrik jism o lgni uchun V olingi oqlri orqsigi oqlrini to si proeksilni. W ikkit on og i ung perpenikulr V W h 18.4-chim. V W h t 18.5-chim. D 61

62 o lgni uchun to g ri chiiq, olingi ikkit og i orqsigi ikkit og ini to si proeksilni (18.5-chim,, ). 1. Qn geometrik jism ko poqlik eili? 2. Ku qn geometrik jism turig kiri? Uning qn elementlri mvju? 3. Kuning necht uchi or? 4. Ku n qn nomlr iln tli? 1. 50½50½50 o lchmgi kuning olin gi, kein v V gi, so ngr, V v W gi proeksilrini ish ftrig chiing. 2., V v W g nistn turli vitlrni egllgn prllelepiðe hm primni ish ftrig chiing. ltit ir il kvrtlrn tuilgn geometrik jism nim eili?. Prim.. Tetrer.. Ku. D. Prllelepiðe SILIND, KNUS, S V PIMIDNING PYEKSIYLI Tenik rch lnm hrktlr lnish silinri ormi jrili. lnish sirtlri, silinr, konus, shr (sfer) to g ri v egri chiiqning qo g lms o qi i trofi lnishin hosil o lishi 19.1-chim tsvirlngn. To g ri chiiqlr silinr v konus sovchilri eili, sfergi egri (ln oki rimln) chiiq meriinlrni hosil qili. Silinr. Tenik ilm-il ko rinish uchrign silinr tenik etllrning sosini tshkil qili. r qn lnm hrkt silinr orqli mlg oshirili. i i i S 19.1-chim. 62

63 V W h t V 19.2-chim. W h 19.3-chim. Silinr 19.2-chim, giek proeksilr tekisliklri tiimig jolshtirilgn o ls, uning gi proeksisi ln, V v W gi proeksilri ir il to g ri to rturchk ko rinishi tsvirlni. Silinr 19.3-chim, giek jolshgn o ls, uning V gi proeksisi ln, v W gi proeksilri to g ri to rturchk ko rinishi chiili. gr silinrni W g perpenikulr jolshtirils, uning W gi proeksisi ln, v V gi proeksilri to g ri to rturchk ko rinishi tsvirlni. Silinr hmm holt hm fqt ikkit imetr v h lnlikk eg o li. Konus. Konus hm silinr ki tenik etllr ju ko p ttiq etili. Konusning uchi kesilgn o ls, kesik konus eili. Konus 19.4-chim, giek proeksilr tekisliklri tiimi jolshgn o ls, tekisligi 63

64 t S S V S W h S S S S ln, V v W tekisliklri uchurchk ko rinishi chiili. Konus hm ikkit o lchmg imetr v h lnlikk eg. Shr (sfer). U tenik umlsh poshiðniklri qo llnili. Sfer um-umloq sirt o lgni uchun hmm tekisliklr o ig teng ln ko rinishi proeksilni (19.5-chim, ). Shrning itt o lchmi o li, lekin o lchm soni olig Sfer so i oili. Msln, chim, giek Sfer 40. Kesik konus. Kesik konus ucht o lchmg eg: D ktt imetri, kichik imetri v h lnligi. Konus o qi qsi proeksilr tekisligig perpenikulr o ls, o sh tekislikk ikkit ktt v kichik lnlr, qolgnlri trpetsi shkli proeksilni (19.6-chim, ). Lekin trpetsi ko rinishigi tomonlri vom ettirils, konus o qining vomi itt nuqt o ro kesishi (19.6-chim, ). himchilik qul qilingn shrtli elgilrni qo ll, silinr v konuslrni itt proeksi tsvirls hm o li (19.7-chim). Pirmi. Misr ehromlri shkln sosi to g ri urchkli (kvrt) pirmilr uno etilgn. Pirmi hr il: uchurchkli, to rturchkli, eshurchkli, oltiurchkli sosg eg o lgn muntm ko poqliklrg kiri. sosi kvrt pirmi 19.8-chimgiek proeksilr tiimig jolshtirils, tekisligig kvrt, oshq tekisliklrg uchurchk ko rinishi proeksilni. gi kvrtning urchklri orqli o tgn igonllri pirmi uchi iln tutshgn qirrlrining goriontl proeksilri hisolni chim.

65 S chim. h D 19.5-chim chim V S S S W S S h 1 S t S chim. Pirmining oqlri o ro kesishgn hosil o lgn jolri (chiiqlr) qirrlri, qirrlri orsigi tekis jolr (uchurchk v sosining shklig qr ko purchk) oqlr, qirrlri o ro kesishgn jo (nuqt) uchlri eili. 5 himchilik, 8-sinf 65

66 1. Silinr qn hosil o li? Konus v shr-chi? 2. Silinrning qn elementlri mvju? Konusning-chi? Shrning-chi? 3. Kesik konus necht o lchmg eg? 4. Pirmi qn ko rinishlr o li? 5. Pirmining qn elementlri mvju? Geometrik jismlrning hr irini chimchilik ftringig chii mshq qiling. itt mrk ikkit ktt v kichik ln, V v W trpetsi shkli tsvirlnign geometrik jism nim eili?. Silinr.. Kesik konus.. Pirmi. D. Sfer. 5-grfik ish. Geometrik jismlr proeksilrini chiish. qituvchi topshirig i sosi jrili K INISL. S V SSIY K INISL DSt 2.305:2003 g muvofiq etlning proeksilri ko rinish e uritili. himchilik etlning shklini to liq ifolsh mqsi turli tsvirlr (ko rinish, qirqim, kesim)n folnili. Kutuvchig nistn etlning ko rini turgn tomoni (sirti)ning tekislikgi tsviri ko rinish eili. ltit sosi ko rinishlrni hosil qilish mqsi 20.1-chim, gi etlni ichi o sh kuning o rtsig jolshtirili. Kuning oltit oqlrig to g ri urchk osti etl proeksilni. Shun etlning ku oqlrigi ko rinishlri (proeksilri) hosil o li (20.1-chim, ). osh v sosi ko rinishlr. Kuning oilmsi jrili (20.1-chim, ). Shun etlning sosi ko rinishlri o ro qn jolshgnligi qqol ko rini: V gi oln (osh), gi ustn, W gi chpn, 1 gi ostn, V 1 gi orqn, W 1 gi o ngn ko rinishlr eili. Stnrt tlig muvofiq ku oilmsi chegr chiiqlri oli tshlni tsvirlni (20.1-chim, e). him frontl proeksilr tekisligigi sosi tsvir, ni osh ko rinish sifti olini. Shun etlni u tekislikk nistn shun jolshtirish kerkki, etlning shkli v o lchmlri to g risi niqroq tsvvur qilishg imkon rtilsin. Shuning uchun hm etlning un tsviri osh ko rinish hm eili. Demk, etl to g risi eng ko p m lumot erign tsvir osh ko rinish hisolni. Detl chimsi chiilotgn ko rinishlr sonini eng km o lishig, mmo un etl to g risi to liq m lumot erign o lishig hrkt qilini. un stnrtlr elgilngn shrtli elgilr v ouvlrn smrli folnish tl qilini. 66

67 1 V W W 1 V 1 1 W 1 V W V 1 e 20.1-chim. 1. Ko rinishlr qn hosil qilini? 2. sosi ko rinishlr necht? 3. osh ko rinish qn ko rinish hisolni? 4. osh v oshq ko rinishlrg t rif ering. 1. sosi ko rinishlr necht?. itt.. Ikkit.. To rtt. D. ltit. 2. Qsi proeksilr tekisligigi ko rinish osh ko rinish e qul qilingn?. gi.. V gi.. W gi. D. P gi chim etlning qqol tsviri v ko rinishlri tsvirlngn.,, ko rinishlrning qsi iri 1 o nlishg mos kelishini niqlng. Shuningek, 2 v 3 o nlishlrg mos kelign ko rinishlrni hm toping chim. 67

68 21-. MLLIY V Q SIM K INISL uum sirtining iror qismi jolshgn elementini chegrl oli tsvirlshg to g ri kels, mhlli ko rinish, sosi ko rinishlrn iri ui tsvirlnign o ls, qo shimch ko rinishni ttiq etishg to g ri keli. Mhlli ko rinish. him ko rinishlr sonini kmtirish mqsi etlning ir qismini lohi ko rstish uchun mhlli ko rinish ttiq qilini. Mhlli ko rinish ingichk to lqinsimon chiiq iln chegrl qo ili chim, etlning chpn ko rinishini to liq chiish o rnig uning kerkli elementi tsvirlngn. n etl elementining shkli konturini tsvirlsh iln hm kifolnili (21.1-chim, gi ) chim, vl qismining shponk o rntilgn riqch (p) qismi tsvirlnishi iln etlning ustn ko rinishini tsvirlshg hojt qolmi. un qismn tsvirlshlr mhlli ko rinish eili. Qo shimch ko rinish. r oim hm uum sirtining iror qismigi elementini sosi oltit ko rinishning irortsig to g ri (uilmgn hol) tsvirlshning iloji o lms, u hol, uumning o sh ko rinishi sosi ko rinishlrg prllel o lmgn ngi qo shimch tekislik jrili v u qo shimch ko rinish eili (21.2-chim, ). Qo shimch ko rinish qul holtg uri tsvirlnishi mumkin. mmo uumning osh ko rinishigi qul qilingn vit o grmsligi kerk v urilgnligini ko rstuvchi elgi iln t minlnishi loim (21.2-chim, ). i hollr qo shimch ko rinish ouvsi v o nlishsi hm tsvirlnishi mumkin (21.2-chim, ) chim chim.

69 chim. De Ef 1. Mhlli ko rinish egn qn ko rinishni tushunsi? 2. Qo shimch ko rinish qn holtlr qo llnili? 21.3-chim etllr 1, 2, 3, 4, 5 rqmlr iln, mhlli ko rinishlr,,, D, E hrflr iln elgilngn. mmsig tegishli o nlishg mos ko rinishni toping MDELNING SLIG Q UNING K INISLINI IZIS Moelning o ig, ni slig qr uning ko rinishlrini chiishn olin 18- v 19- erilgn geometrik jismlrning proeksilri qn tsvirlnishi ko olig keltirili. Misol chim, qqol tsvir erilgn moelning ikkit ko rinishini chiing. Moel thlil qilins, u ikkit geometrik jismn tuilgn. Vertikl jolshgn prllelepiðe 22.1-chim. v uning olig ku qo ilgn. lin prllelepiðening osh v ustn ko rinishi chii olini (22.1-chim, ). Kein kuning oln v ustn ko rinishlri qo shi chiili (22.1-chim, ). Shu trti hr qn moel (etl) ning ko rinishlrini chiish mumkin. 1. Moel (etl) shkli nim uchun thlil qilini? 2. Moelning o ig qr uning ko rinishlri qn trti chiili? 1. himchilik onsigi moellrn folni ulrning ko rinishlrini chiing chimgi qqol tsvir erilgn etllrn ittsini thlil qiling v ko rinishlrini chiing. 69

70 22.2-chim. Moelning gi proeksisi qn ko rinish eili?. osh.. hpn.. Ustn. D. stn MDELNING ZIG Q UNING UT K INISINI IZIS Moelning o ig qr ko rinishlrini chiish uning shklini thlil qilishn oshlni. Misol. Moelning o ig qr ucht ko rinishini chiing. u er moelning qqol tsviri thlil qilins, uning sosi prllelepiðe usti rimsilinrik o iqli primn iort o li, ucht geometrik jismn, ni uch elementli moeln tshkil topgn (23.1-chim, ). Moelni quigi osqichlr chiili. 1. Moelning sosi ucht ko rinish chii olini (23.1-chim, ). 2. sosi ustig prim ucht ko rinish chiili (23.1-chim, ). 3. Primgi rimsilinrik o iq ucht ko rinish chii chiqili (23.1-chim, e). rtiqch chiiqlr o chirili, chim tt qilini. 1. Tenik etl shkli nim uchun thlil qilini? 2. Tenik etlning o ig qr uning kerkli ko rinishlrini chiing chim. 70 e 1. himchilik onsigi tenik etllrn folni ulrning kerkli ko rinishlrini chiing chimgi qqol tsvir erilgn etllrn ittsini thlil qiling v ko rinishlrini chiing. Doirvi kesik konusni necht ko rinish chiish tvsi etili?. Ucht.. Ikkit.. itt. D. To rtt.

71 23.2-chim DDIY MDEL IZMLINI TLIL QILIS, GEMETIK JISMLG JTIS r qn uum (etl) turli geometrik jismlrni o i mujssmlgn o li. Shu ois, etlni o qish ulrni fikrn geometrik jismlrg jrt ilish o t muhim hisolni. u jron etlni thlil qilish eili chim,, chonk qopqog i qqol tsvir v ikkit ko - rinish chiilgn. Shu etl necht v qn geometrik sirt ig inisin tshkil topgn? u svolg jvo erish mqsi hr ir geometrik sirt lohi jrti chiili. Detl oltit geometrik sirt ig inisin hosil o lgn (sli unn hm ko p, lekin u chim solshtiri olingn) o li, fqt uch il geometrik jism turi ko rstilgn. Detlgi hmm jismlr ko g niq ko rinmoq, lekin n hm niq chim. 1. Sfer 2. Silinr 3. Konus 71

72 24.2-chim chim. v qqolroq o lishini nr tuti, ulrni itt o q ir-irin jrti chiilgn (24.1-chim, ). r ir etl shkli uning jrign ishig qr niqlni. Msln, g ilirk lnm hrkt qilgnligi uchun u ln, hr qn suuqlik oki g ln teshik shi oqqnligi uchun hm quvurlr umloq silinrik qili ishlni. Detllrgi oltiurchkli primlr ulrni ur kiritish v chiqrish uchun imt qili v hoko. Eni, tenik etllr shkli v uning o lklri nim uchun kerkligi hqi qisqch fikr uritlik chim tsvirlngn etl silinrik teshikli primning ikki on tomoni uchurchk shkli jolshgn evorlri or. u evorlr primni prllelepiðe usti musthkm iriki turishi uchun imt qili. Detllr un evorlr musthkmlsh qovurg si oki qisqch qovurg eili. Ushu etlgi qovurg lr lnm hrkt qiluvchi silinrik teshik evorlrini musthkmlsh mqsi qo llnili. Tenik moellrni ssh geometrik jismlr moellrin folnish tvsi etili. Msln, kuning ustig silinr qo ils (24.3-chim, ), prllelepiðe ustig ku v uning ustig konus jolshtirils (24.3-chim, ), tenik moellr slgn o li. Shu trti hr il tenik moellrni jrish mumkin. 1. Tenik moellr qn sli? 2. Tenik moel (etl) lr qn thlil qilini? 3. Moelning o ig qr qsi ko rinishin oshl chiili? himchilik onsigi moellrn folni ko rinishlrini chiing. Detl qn trtigi geometrik jismlrn tuilgn.. Silinr, konus, shr, pirmi.. Shr, konus, prim, pirmi.. Prim, silinr, konus, shr. D. Pirmi, silinr, konus, shr. Sfer 72

73 25-. IZMLNI QIS TTII V QIDLI iror uumning chimsini o qish uchun olin uum chimsini lohi etllrg jrtili. So ngr hr ir etl sinchikl o rgni chiqili. himlrni o qish, ko pinch, etlning erilgn ko rinishlri o ich uning etishmign ko rinishini niqlsh, uning qqol tsvirini jrish orqli mlg oshirili. un jron grfikvi usul ormi o qish hm eili. Detlning erilgn ikkit ko rinishig soslni uchinchi ko rinishini niqlsh chim etlning osh v ustn ko rinishlri erilgn. Uning chpn ko rinishini niqlsh joi o ls, rhol etl qn geometrik jismlrn tuilgnligi thlil qilini. Detl sosi silinr, uning usti prim, primning ustki sosin pstg qrti, rimsilinr o ilgn. Umumi torgrlikn kein etlning uchinchi, ni chpn ko rinishini niqlshg o tili. him u jron osqichlr to liq ko rstilgn o li, hr qsi osqich o g on chiiqlr chiilgn. Detl elementlrining lnligi V n, eni n o lch olini chim chim. 73

74 25.3-chim Sfer chim osqich. Detlning ostki sosi o lchm chiili (25.1-chim, ). 2-osqich. o lchmgi prim chiili (25.1-chim, ). 3-osqich. o lchmgi prim ustki sosgi rimsilinr shtri chiiq chiili (25.1-chim, ). gr shu etlning olin qqol tsvirini chii olgnimi, uning uchinchi ko rinishini niql chiish n hm osonlshr ei chim, ko rinishlri erilgn etlning qqol tsvirini chiish (25.2-chim, ) orqli uning uchinchi ko rinishini o nlish o ich emlol chiish mumkin (25.2-chim, ). Detlning ikkit ko rinishi erilgn o ls (25.3-chim), uning uchinchi ko rinishini grfik usuli hm niqlsh mumkin. uning uchun 25.3-chim, ko rstilgnek ormchi oimi chiiq 45 urchk osti o tkili. Detl sosining chpn ko rinishi osh ko rinish iln itt goriontl chiiq otgnligi uchun ormchi chiiq chiili. Detlning ustn 74

75 ko rinishi orqli ormchi chiiqlr o tkili, 45 urchk o tkilgn oimi chiiq iln kesishtirili v vertikl chiiqlr chii, elementlrining lnligini niqlsh osh ko rinishn chiilgn goriontl ormchi chiiqlr iln kesishtirili. Ntij etl sosining chpn ko rinishi konturi hosil o li. Detlning ustki sosin chiilgn ormchi chiiq orqli uning uchinchi ko rinishi niqlni. Detlning o rtsin o tgn silinrik teshik uning chpn ko rinishi mrki o qi orqli osh ko rinishgi ki shtri chiiq chii qo ili (25.3-chim,,, ). 1. Tenik etllrgi oltiurchkli prim nim uchun kerk? 2. Detl chimsini o qish nimn oshlni? 3. Detlning erilgn ikkit ko rinishi o ich uchinchi ko rinishini niqlsh qn usullrn folnili? 25.4-chim erilgn etllrn ittsining ko rinishini erilgn o lchmlr, msshtg rio qilgn hol ko chiri chiing v uchinchi ko rinishini toping. Konusni qiil, silinrni ko k, primni shil, shrni sriq rngg o ng chim etlning uchinchi ko rinishi qn usul niqlngn?. osqichlr.. Yqqol tsvir.. Grfik. D. Thlil qilish MDELNING EILGN IKKI PYEKSIYSI YI UINI K INISINI YSS himni o qish jroni chimchilikni shi o rgnishg orm eri. Fovi tsvvurni shi o stirishg v chimlrgi rch shrtliliklrni to lroq o lshtirishg imkonit rti v o quvchi tomonin chimni te o qi olish qoilitini o stiri. Umumn, chimlrni o qish chim tsvirlngn etlning shklini to l tsvvur etishg v uning konstruktiv ususitlrini niqlshg, chimg qo ilgn hmm o lchmlrni o qishg, ulr etlning qsi qismig oiligini niqlshg o rgnishir. ulrn tshqri, chimni o qish ntijsi etlning nomi, u qn mteriln torlngnligini v chimning msshtini niql olishg orm eri. himni o qish eng qiin tomoni tsvirlngn etlning umumi shklini tsvvur qilishir. uning uchun mumkin qr ko proq chimlrni thlil qilishg o rgnishir. Ko pinch etllr ikkit ko rinish chiili. un chimni o qish uchun un tsvirlngn etlning qqol tsvirini chiish oki uning uchinchi ko rinishini ssh o li iln mlg oshirili (25.2-chim). u rs ( ) ni o tish jroni olingi rslr olingn ilimlrni tkomillshtirish mqsi hr ir o quvchig ikkit ko rinish tsvirlngn moelning krtochklri trqti chiqili. Fqt uchinchi ko rinish istlgn usul niqlnishi tushuntirili. 1. himlr qn o qili? 2. Nim sn moelning erilgn ikkit proeksisi o ich uchinchi ko rinishi niqlni? 3. Uchinchi ko rinish shroitg qr qn ko rinish hisolni? 75

76 ed Ef 26.1-chim. e f 26.2-chim chim etllrning ikkitn ko rinishlri 1, 2, 3, 4 rqmlri iln elgilngn. Shu etllrning on ko rinishlri,,, D, E hrflri iln elgilngn, etllrning ko rinishlrig mos kelign chpn ko rinishlrini niqlng chim keltirilgn etllr ko rinishigi etishmign chiiqlrni toping. 6-grfik ish. Detlning ikkit ko rinishigi etishmign chiiqlrini niqlng v uchinchi ko rinishini chiing. lchmlrini qo ing. qituvchi topshirig i sosi jrili. 76

77 27-. KSNMETIK PYEKSIYL QID UMUMIY TUSUN. QLNING JYLSISI Qimgi minitur srlrigi perspektiv sshlr monvi ksonometri qonun-qoilrig to g ri keli. ung uno mniti trii o ig os i qolirgn Kmoliin eho ( )ning miniturlri misol o l oli. Umumi tushunch. Mshin etllrini ssh, sosn, ulrning ish chimlrin folnili. Lekin u tsvirlrning sosi kmchiligi shunki, etl ko rinishi turli tekislik jrili. un hol chimning o qilishini qiinlshtiri. Shuning uchun, ml etlning ish chimsi iln irglik uning qqol tsviri hm qo shi erili. Detlning qqol tsviri, ni ksonometrik proeksisi qo shi erilgn ish chimlrini te v oson o qish mumkin o li. ksonometri unonch so o li, kson o q v metreo o lchsh egn m nog to g ri keli, o qlr o ich o lchsh egniir. ksonometrik proeksilr uch o lchmli qqol tsvir hisolni. Ulr,, koorint o qlri tiimi hosil o lishig qr to g ri v qishiq urchkli turlrg jrli. gr koorint o qlri orsigi urchklr o ro teng o ls, ni jism o lchmlri ushu,, o qlrg o grmsn ir il tsvirlns, to g ri urchkli ksonometri eili. Moo,, o qlri orsigi urchklrn ittsi qolgn ikkitsig nistn o gri tsvirlngn o ls, ni jism o lchmlri,, lrn ittsig o gri (kichiklshi) proeksilns, qishiq urchkli ksonometri eili. ksonometri koorint o qlri,, lrg ir il (kttlik) tsvirlnign jism sifti ku olini, uni qishiq, so ngr to g ri urchk osti ksonometrik proeksilr tekisligi P g proeksilsh jronini ko ri chiqmi. Qishiq urchkli frontl imetri. Kuning ir tomonini frontl P proeksilr tekisligi V g prllel jolshtiri, ksonometrik proeksi tekisligi P g proeksilmi (proeksilsh jroni 27.1-chim, ko rstilgn). u er, proeksilsh nurlrini o q uchun P V tekisligig perpenikulr olins, o q P g nuqt ko rinishi proeksilni. Shung ko r, proeksi- W lsh nurlrini uchun P g ikki mrt qisqrtiri proeksilnign 45 urchk osti qishiq olini. Shuning uchun hm u proeksi 27.1-chim. qishiq urchkli frontl imetrik 77

78 proeksi eili. u proeksini qishiq urchkli imetri oki frontl imetri eish hm mumkin. Dimetri unonch, ikki mrt km o lchsh egn m noni eri. Jism ir tomoni iln V g prllel jolshgni uchun hm frontl imetri eili. Frontl imetri kuning ir tomoni ksonometri tekisligi P g prllel jolshtirilgn, kuning V tekisligig prllel og i o ining hqiqi kttligi tsvirlni. u er kuning on tomon qirrlri v lrg hqiqi o lchmi qo ili. o qq es uning teng rmisi o lch qo ili. Shun ku ikki og i iln kvrt, oshq oqlri prllelogrmm shkli tsvirlni (27.1-chim, ). Frontl imetri o qlrning jolshishi. un v o qlr o ro 90 urchk, o q es u urchkni teng ikkig o li o ti (27.2-chim, ). u o qlrni 27.2-chim, giek ning vomig 45 urchk oki uchurchkliklr ormi 27.2-chim, giek chiish mumkin. v o qlr to g ri urchkni tshkil qilmgnligi uchun v W g jismning prllel tomonlri ikki mrt qisqrtiri tsvirlni. Demk, v o qlrg jism olchmi 100 foi o lch qo ils, o qq uning 50 foii o lch qo ilr ekn. To g ri urchkli iometrik proeksi. Kuni 27.3-chim, giek ksonometrik proeksilr tekisligi P g nistn ir il qilik jolshtiri, ung ku uchlri orqli proeksilsh nurlrini perpenikulr qili o tkils, kuning to g ri urchkli iometrik proeksisi hosil o li. To g ri urchkli iometrik proeksi qisqch iometri hm eili. Iometri unonch so o li, isos ir il (teng) egn m noni nglti. Iometri,, o qlr orsigi urchklr o ro teng o li, ulr 120 ni tshkil qili (27.3-chim, ). hunki ulr P tekisligig nistn ir il qilik proeksilni. Shun, msln, ku o ining hqiqi kttligig nistn m lum miqor o gri, ni qisqri, proeksilni. u o grish iometri uchl o qlr o ich ir il o li, 0,82 g teng. Lekin etl o lchmlrini iometrik o qlrg 0,82 mrt ko ptiri o lch qo ish nch noqul. DSt 2.305:2003 ning tvsisig inon, rch o qlrg etln o lch qo ilign qimtni 0, chim. 78

79 V W chim. e mrt kichik olmsn, uning hqiqi kttligigi o lchmlri qo ili. 1 Shun etlning iometrisi =1,22 0,82 mrt ktt tsvirlni. Iometrik o qlrni uchurchkliklr ormi 27.3-chim, giek chiish mumkin. Ulrni chimchilik ftri ktklr ormi hm chiish mumkin. nuqtn goriontl chiiqq 5 ktk, so ngr pstg 3 ktk olini nuqt iln tutshtirili (27.3-chim, e). 1. ksonometri e nimg tili? Frontl imetri v iometri e-chi? 2. Frontl imetri v o qlrg nistn o qq qnch o lch qo ili? 3. Iometri o qlr orsigi urchklr qnchg teng? ksonometri frontl imetri v iometri koorint o qlrini ish ftringig chiing. ksonometri so ining m nosi nim?. qlr o ich tekshirish.. qlr o ich o lchsh.. qlrni chiish. D. qlrni jrtish TEKIS SKLLNING KSNMETIYSINI YSS Ko poqlik sirtlrining oqlri, lnish sirtlrining soslri tekis shkllrn iort o li. Tekis shkllr ko purchklik, lnlr frontl imetri V tekisligi o ining hqiqi kttlikgi ko rinishi, ni o grmsn tsvirlns, qolgn v W tekisliklr o q o ich ikki mrt qisqrtiri tsvirlni. 79

80 1 X 2 Z 1 1/ chim 2 Z /2 1 X Z D D/2 D 28.2-chim. Tekis shkllr iometri, V v W tekisliklr ir il ko rinish v kttlik chiili, fqt ulrning frqi o ro turlich jolshgnligi o li. Tekis shkllrni frontl imetri chiish. Tekis shkllr, V, W tekisliklr qn ko rinish tsvirlnishini tqqoslsh mqsi, ulrni olin V, kein v W tekislik chiilishi iln tnishi chiqmi. Misol. Teng oqli uchurchklikning frontl imetrisini V, v W tekislik tsvirlng. 1. Uchurchklik V tekisligi uilmsn o ining hqiqi kttlikgi ko rinishi tsvirlni (28.1-chim, ). 2. Uchurchklikni tekisligi o lchmini g lmshtiri chiili. Shun o lchmi o ining hqiqi kttligi, o lchmi ikki mrt qisqrtiri qo ili (28.1-chim, ). 3. Uchurchklik W tekisligi 1 o lchmi o ining hqiqi kttligi, es o qq ikki mrt qisqrtiri o lch qo ili (28.1-chim, ). Xui shu trti kvrt hm V, v W tekisliklr chiili. Uchurchklik ki kvrt hm V o ining hqiqi kttligi tsvirlni (28.2-chim, ). Kvrtni tsvirlsh 28.2-chim, ko rstilgn. W kvrtni v V tekisliklrgi tsvirlri iln irglik qo shi chiilgn (28.2- chim, ). Muntm oltiurchklik hm V o ining hqiqi ko rinishi uilm tsvirlni (28.3-chim, ). v W tekisliklri o qq ikki mrt qisqrtiri o lch qo ili. ni o qq lmshtiri chiili. lin o qq 1T msof ikki mrt qisq o lch qo ili v o qq prllel chiili, T=TF orliq o lch qo ili. Z-nuqtn o qq prllel chiili, T1=T2 msof o lchni v g prllel 80

81 F E 2 T 1 X D F E F 1 T chim. D D 1 2 T F E chiili. 1- v 2-nuqtlrn 1D=1E, 2=2 kesmlr o lch qo ili, hosil qilingn nuqtlr o ro tutshtiri chiqili (28.3-chim, ). W tekisligi hm T msof o qq ikki mrt qisqrtiri o lch qo ili hm T nuqtn g prllel chiili, T1=T2 qisqrtirilm o lch qo ili. T v 2-nuqtlrn o qq prllel chiiqlr o tkili 2=2, T=TF, 1D=1E orliqlr shrtg muvofiq o lch qo ili. osil o lgn nuqtlr o ro tutshtirili (28.3-chim, ). Tekis shkllrni frontl imetri tsvirlnishi iln tnishi chiqqn eik. Eni ulrni iometri chiilishini o rgnmi. M lumki, iometri, V, W tekisliklr shkl o lchmlri o grishsi, ni o ining hqiqi kttligi chiili. Shun,V,W lr hr qn tekis shkl, turli jism v uumlr ir il ko rinish v kttlik tsvirlni. Misol. Muntm uchurchklikni V, v W lr jring (28.4-chim, ). 1. V o qq uchurchklikning (28.4-chim, ) v ungi 1-nuqt g 2- nuqt g o lch qo ili. 1-nuqtn g, 2-nuqtn g prllel ñhiiq chii nuqt hosil qilini (28.4-chim, ). osil o lgn nuqt v iln tutshtirili. 2. Uchurchklikni chiish uchun v ungi 1-nuqt o qq o lch qo ili. 1-nuqtn o qq prllel chiili, ung 1 orliq oli o tili. ni v iln tutshtirils, uchurchklik sli (28.4-chim, ) chim. 2 1 e 6 himchilik, 8-sinf 81

82 F D E 2 T 1 D D F D 2 E T 1 D Y D e D 2 E T F 28.6-chim. 1 Y 28.5-chim. E 2 D F T 1 e 3. Mkur uchurchklikni W chiish v ungi 1-nuqtni o qq oli o tili hm 1-nuqtn o qq prllel chiiq o tkili. 1 lnlik o lch qo ili, hosil o lgn nuqt v iln tutshtirili (28.4-chim, e ). Misol. Kvrtning iometrisini V, v W tekisliklr chiing (28.5- chim, ). 1. Kvrt (28.5-chim, ) ning tomoni V gi o qq o lch qo ili. v nuqtlrn o qq prllel chiiqlr o tkili, ulrg g teng kesmlr o lch qo ili hm hosil o lgn v D nuqtlr tutshtirili (28.5-chim, ). 2. Kvrtni chiish uchun tomoni g o lch qo ili v, n o qq prllel chiili. v nuqtlrn g teng kesmlr o lch qo ili, v D nuqtlr hosil qilini hm ulr o ro tutshtirili (28.5-chim, ). 3. W tekislik kvrt V v lrgi ki chiili. kesmni o qq o lch qo i, v nuqtlrn g prllel chiiqlr o tkili hm ulrg kesm o lch qo ish orqli v D nuqtlr niqlni (28.5- chim, e). Misol. Muntm oltiurchklikni V, v W tekisliklr chiing. 1. Muntm oltiurchkni V tekislik chiish uchun mrk T nuqt tnl olini v unn v o qlri o tkili (28.6-chim ). T nuqtn o qq T=TF, o qq 1- v 2-nuqtlr oli o tili v o qq prllel chiiqlr o tkili. 1- v 2- nuqtn 2D=2E (1=1) orliqlr o lch qo ili v hosil qilingn nuqtlr o ro tutshtirili (28.6-chim, ). 82

83 2. Ushu oltiurchkni chiish mrk T tnl olini v u orqli hm o qlr o tkili. T n g T=TF, o qq 1- v 2-nuqtlr oli o tili v ulrn hm o qq prllel chiiqlr chiili hm 1=1, 2D =2E kesmlr o lch qo ili. osil qilingn nuqtlr o ro tutshtirili (28.6-chim, ). 3. Mkur oltiurchk W 28.6-chim, gi ki ko rinish chiili. uning uchun tnl olingn T nuqtn v o qlri chiili, g T1=T2, g T=TF ko rinish o lch qo ili. 1- v 2- nuqtlrn o qq prllel chiiqlr chiili hm ulrg 1=1 (2E=2D) o lch qo ili, hosil qilingn nuqtlr o ro tutshtirili (28.6-chim, e). Frontl imetri ln V proeksilr tekisligig prllel jolshgni uchun ung o ining hqiqi ko rinishi lnligich tsvirlni. v W lrg o q o ich ikki mrt qisqri tsvirlngnligi uchun u ensi elliðs shkli tsvirlni. un tsvirlnign lnning ksonometrisi chiilign o ls, lnni V g prllel qili jolshtirish tvsi etili. M lumki, muntm oltiurchk lnni teng olti o lkk o lish orqli sli (28.7-chim). Iometri chiilgn oltiurchkning nuqtlrini ketm-ket egri chiiq silliq qili tutshtirils, lnning iometrisi elliðs hosil o li. Demk, ln iometri elliðs ko rinishi tsvirlnr ekn. Lekin lnni un chiish nch qiin. Stnrt tvsisig ko r elliðsni to rt mrkli ovlg lmshtiri chiili. u ovlni unn kein, shrtli rvish, elliðs e uritmi. lnlr iometri, V, W tekisliklr ir il ko rinishgi elliðslr tsvirlni (28.8-chim). u er elliðsning ktt o qi =1,22 g teng tsvirlni. Eng olin elliðsni tekisligi chiilishi iln tnishtirili. uning uchun: 1. Tsvirlnign ln chiili, uning mrki orqli,, o qlri hm g perpenikulr goriontl ormchi chiiq o tkili (28.9- chim, ). u goriontl chiiq elliðsning ktt o qi hisolni. ln iln kesishotgn chiiqlr elgil olini. V W 28.7-chim. D D =1, chim. D D=0,7 83

84 2 3 Z chim Y chim. 2. o qigi 1- v 2- nuqtlrni mrk qili 3, 4- v 5, 6- nuqtlr sirkul tutshtirili (28.9-chim, ) v 4- oki 5- v 6- nuqtlrni 1- oki 2- nuqt iln tutshtirils, goriontl chiiq 7- v 8- nuqtlr hosil o li. 7- v 8- nuqtlr orqli 3- v 6- hm 4- v 5- nuqtlrni sirkul tutshtirili (28.9-chim, ). u er tekisligigi elliðsning ktt o qi o li, kichik D o qi o q iln qo shili qoli. V tekisligi hm elliðs ui tekisligigi ki jrili. u er elliðsning ktt o qi o li, kichik D o qi o q iln qo shili qoli. V tekisligi elliðsni ssh chim, erilgn. Lekin u er 1- v 2- nuqtlrni o qining ln iln kesishotgn jolri elgilni. Elliðsning ktt o qini o qq perpenikulr qili o tkish 1- v 2- nuqtlrn chiilgn olrning o ro kesishotgn nuqtlrin folnili. W tekisligigi lnning iometrisi chim, erilgn. u elliðsni ssh ktt o qi, kichik D o qi o q iln qo shili qoli. un elliðsni ssh 1- v 2- nuqtlrni lnning o q iln kesishotgn jolri elgilni. Ktt o q 1- v 2- nuqtlrn chiilgn olrning o ro kesishishin folni o tkili. 1. Muntm ko purchk frontl imetri V g qn ko rinish tsvirlni? g-chi? W g-chi? 2. Nim uchun qishiq urchkli imetri frontl imetri hm eili? 3. Yssi shkllrning iometrisini W chiish o qi qtnshimi? 84

85 4. Yssi shkllrni frontl imetri jrish o qi uchun qn qimt olini? Ish ftrig turli ko rinishgi ssi shkllrning frontl imetrisini chiing. 1. Ish ftrig muntm ko purchklrning iometrisini, V, W lr chiing chim,, lrn folni itiori kttlikgi lnlrning iometrisini V v W chiing. lnni iometri chiish elliðs nimg lmshtirili chiili?. lng.. vlg.. voig. D. rmg DETLNING FNTL DIMETIK PYEKSIYSI Detl (moel) ning ksonometrisini sshn olin u qn geometrik jismlrn, jismlr es qn tekis (egri) shkllrn tshkil topgnligi o rgni chiqili. Shun tekis (egri) shkllrning ksonometrilri qn jrilgnligi hisog olini. Ko pinch, etlning ksonometrik proeksisi uning erilgn ko rinishlrin folni jrili. Misol. Sur e nomlnuvchi etlning frontl imetrisini uning erilgn osh v ustn ko rinishlrig inon jring (29.1-chim, ) chim. e 1. Frontl imetrik o qlr o tkili v etlning frontl, ni osh ko rinishi ko chiri chiili (29.1-chim, ). u etlning ol tomoni o li. 2. Detlning orq tomonini ssh uchun ol tomonigi urchk nuqtlri v ln mrkin o qq prllel ormchi chiiqlr chiili v ulrg etlning qlinligini ikki mrt qisqrtiri, ni o lch qo ili (29.1-chim, ) v chim tt qilini (29.1-chim, e). ln V n oshq tekisliklrg prllel to g ri keli qols, ulr elliðs shkli tsvirlni. Shuning uchun soslri tekisligigi konus v silinrning frontl imetrisini chiish ulrning 29.2-chim. 85

86 soslrini V g prllel vitg lmshtiri tsvirlsh tvsi etili (29.2- chim, ), ks hol, 29.2-chim, giek chiishg to g ri keli. Detlni frontl imetri ktk ftrg osqich iln chiish chim ko rstilgn. 1. Nim sn frontl imetri oki W g prllel lnlr V g lmshtiri chiili? 2. Nim uchun lnlr oki W elliðs ko rinishi tsvirlni? e 29.3-chim chim simn slgn ko rinishlrg mos frontl imetrisini niqlng chim chim erilgn etllrn irining frontl imetrisini chiing chim. 86

87 30-. DETLNING IZMETIK PYEKSIYSI Detlni iometri chiishn olin i geometrik jismlrning iometrisini jrish loim. Geometrik jismlrn simmetri o qi tekislikk perpenikulr jolshgn muntm oltioqli primning iometrisini chiish v o qlr chiili (30.1-chim, ). v 1 mrklr muntm oltioqli ko purchklik 28.6-chimgiek chiili (30.1-chim, ). So ngr 30.1-chim, gi ki tt qilini. S S 1 1 Y h 30.1-chim chim. Geometrik sirtlrn o qi tekislikk tik jolshgn konusning ko rinishi erilgn (30.2-chim, ), uning iometrisini chiish uchun sosi lnsini 28.9-chimg o shti chii olini. sosin lnligi h o lch qo ili v hosil o lgn nuqt S n konus sosi elliðsg urinm o tkili (30.2-chim, ). Misol ko ri chiqmi chim etlning ko rinishlri erilgn, uning iometrisini chiing. 1. Iometri o qlri v etlning sosi kvrt prim chiili (30.4-chim, ) hm sosi ustig eni 15 mm, lnligi 30 mm li prim qo - shi chiili chim chim. 87

88 2. Ustki prim ln mrklri niqlni (30.4-chim, ). ln mrklrin ksonometri o qlri v qo shimch o tkili. u mrklrn 20 mm li elliðslr 28.9,10-chimlrgiek chiili. Primning qlinligi hisoig teshikning orq tomoni ko rinmi. stki sosgi 15 mm li rimln olri 28.9-chim, giek chiili. 3. rtiqch chiiqlr o chirili, chim tt qilini (30.4-chim, ). 1. Nim sn iometri,v oki W tekislikk prllel lnlr ovlg lmshtiri chiili? 2. Iometri lnlr qn ko rinish chiili? V v W -chi? chim erilgn etllrn irini iometri chiing. 2. Kuning iometrisini itiori kttlik chiing v uning oqlrig lnning iometrisini mustqil chii, mshq qiling chim. 40 chiilgn elliðs (ovl) ning ktt o qi qsi koorint o qq perpenikulr o li?. g.. g.. g. D. t g. 7-grfik ish. Detlning erilgn ikkit ko rinishig inon uning frontl imetrisi oki iometrik proeksisini jrish. qituvchi topshirig i sosi jrili KSNMETIK PYEKSIYL YI MLIY MSG ULT mli mshg ulot rsi etlning ikkit ko rinishi sosi uning frontl imetrisi oki iometrisi chiili. Detlning ikkit ko rinishi tsvirlngn krtochklr hr ir o quvchig iniviul trqti chiqili v o qituvchi

89 krtochkgi etlning ko rinishlrini ko chiri chimsn, fqt uning frontl imetrisi oki iometrisi chiilishini tushuntiri. qituvchi o quvchilrning jrotgn ksonometrik proeksilrini kuti ori v qinlotgn o quvchilrg orm eri. Krtochklrgi etl ko rinishlri unch murkk o lmsligi v o quvchilr uni ir rs vomi jrishg ulgurishlri loim. qituvchi rs jroni o quvchilr o l qo otgn kmchiliklr hqi sinf ttsig chii tushuntiri. 1. Nim sn etlning ksonometrisini frontl imetri oki iometri jringi? Moel qn ksonometrik proeksi tsvirlngn (31.1-chim)?. Iometri,. Frontl imetri,. Trimetri, D. Perspektiv chim ESKIZL QID TUSUN V UNI IZIS SQILI Umumi tushunch. Ishl chiqrish ir mrt qo llnilign chimlr eskilr eili. Detlning hmm nistlrini sqlgn hol, chim solrini ishltm qo l, ko chml v msshtg rio qilm chiilgn chim eski eili. Eski, ot, uumning chimsini chiish uchun sos o li. Detllrni n eskiig qr hm ssh mumkin. Eski, sosn, mvju etlg qr chiili v u sosi eski eili. Konstruktorlik urosi ngi mshin, menim v oshqlrni loihlotgn etllrning konstruksisi eski ormi ishl chiqili. un eskilr loih eskilri eili. Eski chiish trtii. Eskilr chiilotgn etl elementlrining nistlrini, shklini sqlgn hol chiili. Detl nch ktt o ls, kichiklshtirili, nch kichik o ls, tmini kttlshtirili chiili. Ikkl hol hm mssht qo llnilmi v ung rio qilinmi. Lekin etl kttlshtirili oki kichiklshtirili chiilishin qt i nr un chimlrg etlning hqiqi o lchmlri qo ili. Ishni teltish mqsi eski chiish ln v uning oini hm lnni teng o lklrg o lishni sirkul jrish mumkin. Lekin keinchlik ln v uning oi ustin qo l chii chiqili. Detl hqigi rch m lumotlr eskig oili. Mukmml o lmgn, o lchmlri tushi qolgn, chl jrilgn eski etl ssh v ish chimsini tuish uchun roqsi hisolni. Eski olin qttiqroq qlm, kein ustin umshoq qlm chii chiqili chim eskii chiilign etlning sli qqol tsvir erilgn. Uning eskiini chiish uchun: 89

90 1. Detlning slig qr u hr tomonlm o rgnili; ichki v tshqi tuilishi iqqt iln ko n kechirili. 2. Detlning osh ko rinishi v n qnch 15 ko rinish chiilishi elgilni. Detlning osh ko rinishini shun tnlsh joiki, u etlning shkli hqi to liq tsvvur ersin Ktk qog og 4 ichim hoshisi, sosi ouv chiili v hr ir ko rinishning o rni 32.1-chim. ormchi chiiqlr elgilni, mrk v o q chiiqlri chii chiqili (32.2-chim, ). 4. Detlning ko rinign konturi chii chiqili v ko rinmign qismlri shtri chiiqlr chiili (32.2-chim, ). 5. Detlg o lchm chiiqlr chii chiqili (32.2-chim, ). 6. Detelg slin o lch olingn o lchmlri qo ili. rtiqch chiiqlr o chirili, eski tt qilini v sosi ouv oili (32.2-chim, e). Detlni o lchsh trtii. himlrg o lchmlr qo ish etllrning o ini o lchshg to g ri keli. Detllrni o lchsh msus o lchov solrin folnili. Ulrn qn folnish v ulrning nomlri 31.3-chim ko rstilgn. Po lt oki oi chig ich iln etlning chiiqli o lchmlri v rim qismlri o lchni. Kronsirkul iln etl silinr qismlrining imetrlri, ESKIZ chim. e

91 nutromer iln hr il teshiklr o lchni. itt shtngensirkul hmm o lchsh solrining o rnini osign universl so hisolni. ulrn tshqri, ju ko p hr il o lchsh solri hm mvju, msln, urchk o lchgich, rius o lchgich v hoko chim shtngensirkul tshqi, ichki silinr imetrlrini v chuqurlikni o lchsh ko rstilgn chim etlgi ir sirtn ikkinchisig o tishgi kichikroq riuslrni o lchign so iln o lchsh ko rstilgn. Kttroq riuslrni so iln o lchshning imkoni o lmgn, etl konturi qog og chii olini oki qog o u konturg qo i eili. Shun konturning ii qoli. Kontur itiori ucht nuqt tnl olini v ulr vtr ko rinishi ir-iri iln tutshtirili. osil qilingn kesmlrning o rtsin ulrg perpenikulr qili o tkilgn ormchi chiiqlrning o ro kesishgn nuqtsi o sh oning mrki 0 o li (32.6-chim). Kronsirkul Nutromer 32.4-chim. 6, ,5 6 6, chim chim chim. 91

92 1. Eski qn trti jrili? 2. lchm qo ish uchun tnlngn sos tekisligi nim eili? 3. Grit o lchmlrg qn o lchmlr kiri? Detlning slig qr uning eskiini chiing. r il teshiklr imetri qn o lchsh soi o lchni?. Kronsirkul.. Nutromer.. iusomer. D. urchko lchgich. 8-grfik ish. Moelg qr uning eskii v tenik rsmini chiish. qituvchi topshirig i sosi jrili QUV MDELLINING ESKIZINI IZIS u rs olingi rsning vomi hisolni, eskilr jrishni musthkmlsh mqsi moelning slig qr uning eskii chiili. Ushu rs mli mshg ulot tri o tkili, o quvchilr o qituvchi norti moelning eskiini mustqil jrishi. himchilik kinetigi moellrni o quvchilrg trqti ergnn kein ulrn iri o quvchilrg nmoish etili v uning eskiini osqichlr chiilishi n ir mrt qisq tushuntiri erili. quvchilr o qo llrigi moelning eskiini plktg qr mustqil chiishi v o qituvchi o quvchilr qn chiishotgnini kuti ori. Kerk o lgn jo orm hm qili. Moel eni, lnligi v uunligini o ro tqqosl, nistlrini niql chiishlrig o rgtish rur. Eski chiish pti chiish solrin folnishg o l qo mslik loim. Lekin lnlrni sirkul ingichk qili chii, uning ustin qo l iln urgii chiishg rust erish mumkin. 1. Tenik trqqioti eski qn rol o ni? 2. Eski chiish jroni nimlrg hmit erili? himchilik onsigi 33.1-chimgig o shgnlrn irining eskiini chiing chim TEXNIK SM IZIS Turli chimlrni o qishni osonlshtirish mqsi, ngi itiro qilinotgn uumlrning shklini te qo l chii, uum nistlrini sqlgn hol chimchilik solrisi chiilgn ksonometrik tsvir tenik rsm eili. Detlning tenik rsmi, sosn, iometri oki frontl imetri jrili. quv jroni tenik rsm evosit moelning o ig qr oki uning erilgn ko rinishlrig qr chiili. Tenik rsmni ktklngn vrqlr chiish tvsi etili chim iometrik v frontl imetrik o qlrning ktk ftrg chiilishi erilgn. Ulrning soslrini iometri v frontl imetri

93 Z Z X Y X Y 34.1-chim. chiilishi iln olinroq tnishilgn ei. Tenik rsmlr ulrning chiilishi olingilr ki ir il. Fqt u er ulr ko chml qo l chiili. Tekis shkl (ln)ning tenik rsmini iometri chiish. Tenik rsm ln elliðs shkli tsvirlni, uni chiish osqichlr ko rstili (34.2-ñhim). Detlning erilgn ko rinishlri (34.3-chim, ) sosi uning tenik rsmini frontl imetri chiish uchun olin frontl imetri o qlri chii olini. So ngr etlning olingi og i uning osh ko rinishin ko chml ko chirili (34.3-chim, ). Ko chiri chiish ktklrn folnish tvsi etili. So ngr etlning orq tomoni o q o nlishi niqlni v rsm tt qilini (34.3-chim, ). e f 34.2-chim chim. Qn rsmlr tenik rsmlr eili? U nimg soslni chiili? 93