2011-ei-圆弧形柔性铰链柔度计算公式的推导与结构优化设计

supported by the NSFC project (No. 50805008) Derivation of the 3recise &alculation )ormula of &ompliance and 2ptimal 'esign�of &ircular )lexure +inge XIE Zhiyong , QIU Lifang , BIAN Xinxiao , DUAN Lei School of Mechanical Engineering University of Science and Technology Beijing Beijing,100083,China yongzi86@163.com qlf@me.ustb.edu.cn Abstract—Choosing and designing of the flexure hinges are the keys for the compliant mechanisms.This paper deduced the precise calculation formula of the compliance of circular flexure hinge. The structure of flexure hinge in the fully compliant micro-mechanisms of five-link was optimized with optimization toolbox of MATLAB. The performance of the mechanism was improved after optimization. Keywords- flexure hinge; compliance; MATLAB; optimization ೚೚ᓻᔶᶨᗻ䫄䫒ᶨᑺ㊒⹂䅵ㅫ݀ᓣⱘ᥼ᇐϢ㒧ᵘӬ࣪䆒䅵 ᵘӊϢ䖤ࡼࡃᰃᵘ៤ᴎᵘⱘ෎ᴀܗ㋴DŽϢӴ㒳ᴎᵘϡ ৠˈᶨᗻᴎᵘᇚӴ㒳ⱘ䖤ࡼࡃ⫼ϢПⳌᇍᑨⱘᶨᗻ䫄䫒ᴹ ҷ᳓ˈᑊᇚᵘӊϢᶨᗻ䫄䫒䲚៤Ўϔԧ࣪ⱘ㒧ᵘˈ䗮䖛ᶨ ᗻ䫄䫒ⱘᔍᗻবᔶᅲ⦄ᖂᇣⱘ䖤ࡼDŽᶨᗻ䫄䫒ᰃܼᶨᗻᴎ ᵘⱘ䞡㽕㒘៤䚼ߚˈ݋᳝ԧ⿃ᇣǃ᮴ᴎẄᨽ᪺ǃ᮴䯈䱭ǃ 䖤ࡼ♉ᬣᑺ催ǃᇐ৥㊒ᑺ催ㄝ䇌໮⡍⚍ˈ೼㊒ᆚᴎẄǃ㊒ ᆚ⌟䞣ǃᖂ㒇㉇ᡔᴃㄝ乚ඳᑨ⫼ᑓ⊯ˈᑊ㦋ᕫњࠡ᠔᳾᳝ ⱘ催㊒ᑺ੠〇ᅮᗻ[1-3]DŽ� ᶨᗻ䫄䫒԰Ўᶨᗻᴎᵘⱘ݇䬂䚼ӊˈⳈ᥹ᕅડⴔᴎᵘ ⱘ᳔㒜ᗻ㛑DŽ಴ℸᇍѢᶨᗻ䫄䫒ⱘᗻ㛑ⷨおᇸЎ䞡㽕DŽᶨ ᗻ䫄䫒ⱘᗻ㛑Џ㽕ࣙᣀᶨᑺǃ㊒ᑺǃᑨ࡯ㄝᮍ䴶ˈ݊Ёᶨ ᑺࣙᣀࡳ㛑ᮍ৥ⱘᶨᑺ੠䴲ࡳ㛑ᮍ৥ⱘᶨᑺ[4]DŽ� ᶨᗻ䫄䫒ⱘᶨᑺ⡍ᗻ㸼⼎Ў೼ᶤ⚍ᮑࡴऩԡ࡯᠔ᓩ䍋 ⱘԡ⿏䞣៪ᮑࡴऩԡ䕀ⶽ᠔ᓩ䍋ⱘ䕀㾦䞣DŽ⧚䆎ϞᏠᳯࡳ 㛑ᮍ৥ⱘᶨᑺ䍞໻䍞དˈ䴲ࡳ㛑ᮍ৥݋᳝䕗ᇣⱘᶨᑺDŽ⬅ Ѣᶨᗻᴎᵘᰃ䗮䖛ᶨᗻ䫄䫒ⱘবᔶᴹᅲ⦄䖤ࡼⱘˈ಴ℸᶨ ᗻ䫄䫒ⱘ৘乍ᗻ㛑Ёᶨᑺᗻ㛑䴲ᐌ䞡㽕DŽ� ᶨᗻ䫄䫒ⱘ㊒ᑺ⡍ᗻ㸼⼎Ў䕀ࡼЁᖗأ⿏݊ॳԡ㕂ⱘ أ⿏䞣ˈأ⿏䞣䍞ᇣ㊒ᑺ䍞催DŽ೼䆒䅵䖛⿟Ёˈ㊒ᑺ㽕⒵ 䎇ϔᅮⱘ㽕∖DŽ� ᑨ࡯⡍ᗻᰃ߸ᮁᶨᗻ䫄䫒ᢉᡫ⸈ണⱘ㛑࡯ˈᔧᑨ࡯催 Ѣᴤ᭭ⱘ䆌⫼ᑨ࡯ᯊˈᶨᗻ䫄䫒ህӮ༅ᬜ[5]DŽ� ᭛⤂>�@ҹޣᇣᑨ࡯ЎӬ࣪Ⳃᷛˈᇍᶨᗻ䫄䫒䖯㸠њ Ӭ࣪䆒䅵ˈ᭛⤂>�@>�@>�@�ᇍ⬅ᶨᗻ䫄䫒᠔ᵘ៤ⱘϡৠᶨ ᗻᴎᵘ䖯㸠њӬ࣪DŽᴀ᭛᥼ᇐњ೚ᓻᔶᶨᗻ䫄䫒ᶨᑺ䅵ㅫ ݀ᓣˈᑊҹᖂൟᇍ⿄ܼᶨᗻѨᴚᴎᵘЁⱘᶨᗻ䫄䫒Ў՟ˈ ᓎゟњᶨᗻ䫄䫒ⱘӬ࣪῵ൟ�߽⫼ MATLAB Ӭ࣪Ꮉ݋ㆅˈ ᇍᶨᗻ䫄䫒䖯㸠Ӭ࣪DŽ� I. ೚ᓻᔶᶨᗻ䫄䫒㒩 Z䕈䕀ࡼᶨᑺⱘ䅵ㅫ݀ᓣⱘ᥼ᇐ ೒ 1 㸼ᯢњᶨᗻ䫄䫒ⱘ޴ԩ㒧ᵘDŽᶨᗻ䫄䫒ⱘ޴ԩሎ ᇌЎ䭓ᑺ lǃ᳔ᇣ८ᑺ tˈᆑᑺ wҹঞߛࡆ೚ᓻⱘञᕘ rDŽ ᶨᗻ䫄䫒Ꮊッফ࡯ⶽЎ zM ˈ؛䆒ᶨᗻ䫄䫒ⱘেッЎ೎ᅮ ッˈ߭ᶨᗻ䫄䫒ᎺッⱘবᔶЎ zθ DŽ೒ 2 Ў೚ᓻᔶᶨᗻ䫄䫒 ⱘᑇ䴶῵ൟDŽ ᶨᗻ䫄䫒⊓ z 䕈ᮍ৥ⱘ䕀ࡼᶨᑺᰃ䆒䅵ᶨᗻ䫄䫒᳔䞡 㽕ⱘখ᭄DŽ䅵ㅫᶨᗻ䫄䫒⊓ z 䕈ᮍ৥ⱘ䕀ࡼᶨᑺᯊˈ⬅Ѣ ᶨᗻ䫄䫒ⱘবᔶ䲚Ё೼ᶨᗻ䫄䫒ⱘ೚ᓻ䚼ߚˈ᠔ҹᗑ⬹ᶨ ᗻ䫄䫒೚ᓻҹ໪ⱘবᔶDŽ ೒ 1 ೚ᓻᔶᶨᗻ䫄䫒ⱘ޴ԩ㒧ᵘ 978-1-4244-8039-5/11/$26.00 ©2011 IEEE liuqing 高亮 liuqing 高亮 liuqing 高亮 liuqing 高亮 � ೒ � ೚ᓻᔶᶨᗻ䫄䫒ⱘᑇ䴶῵ൟ 䆒ᶨᗻ䫄䫒ⱘᣴ᳆㒓ᮍ⿟੠䕀㾦ᮍ⿟ߚ߿Ў )(xyy = ੠ )(xθθ = ˈ݊㒩 z 䕈ⱘᔃⶽЎ zM ˈ߭⬅ᴤ ᭭࡯ᄺⶹ䆚ৃⶹ˖� " ( ) z x My EI = ��� )()( ' xyx =θ ������������ ᓣЁ�� 3 ( ) [ ( )] 12x w t xI = üüᶨᗻ䫄䫒㒩 z 䕈ᮍ৥ⱘᛃᗻ ⶽ˗� ⬅Ѣᶨᗻ䫄䫒ⱘ䭓ᑺ l Ⳍᇍ↨䕗ᇣˈৃҹ䅸Ў԰⫼೼ ᶨᗻ䫄䫒ܼ䚼䭓ᑺϞⱘ zM ব࣪ϡ໻ˈᇚ zM ⳟ԰ᐌ᭄ M ˈᬙ˖� " 3 ( ) 12 [ ( )] z x M My EI Ew t x = = �������������������������������������������� ' 3 3 12( ) ( ) [ ( )] 12 1 [ ( )] Mx y x dx Ew t x M dx Ew t x θ = = = ³ ³ ������������������ ⬅೒ � ৃҹᕫࠄ˖� ���� )(xt t + �� −r 22 ) 2 ( xlr −− ���������������������������������� ᇍѢ೚ᓻൟᶨᗻ䫄䫒ˈ݊ᶨᑺЎ˖� dx xtEwMM c l z z ³=== 0 3max )]([ 112θθ ��������������� ᇚᓣ���ҷܹᓣ˄�˅ᑊ߽⫼ mathematica ⿃ߚᕫࠄ೚ ᓻᔶᶨᗻ䫄䫒ᶨᑺⱘ㊒⹂㸼䖒݀ᓣЎ˖� 2 2 2 2 2 2 2 2 2 2 2 2 2 3 2 2 2 2 2 2 2 2 2 2 5/2 (2 (2 ) (4 ) (12 4 )(4 )) 4 2 (4 ) (4 ) 12 6 (2 ) (2 ) (4 ) (4 ) (4 )(4 ) 1 (2 )6 (2 )(arctan arctan ) 4 4 4 [ (4 )] l t r t r t r rt t rt t l r l t r t rt t l r l r t l r tc Ew t r t rt t l t r t rt t l l r tr r t t r t t r t r l t r t ­° + + + + + + + − + + + + + = + +® + + + + + + + + + + + −+ + ½°° °° °° °° °¾° °° °° °° °° °¯ ¿ (6) II. ೚ᓻᔶᶨᗻ䫄䫒ⱘӬ࣪䆒䅵 ೒ � ᠔⼎ⱘᖂൟᇍ⿄ܼᶨᗻѨᴚᴎᵘˈℸ㒧ᵘЁᶨᗻ 䫄䫒ⱘᔶᓣЎ೚ᓻᔶDŽᴚ � ੠ᴚ � ফࠄ䲚Ё䕑㥋 F2੠ F5 䗮䖛ᇍ䆹ᴎᵘϸ䖍ᮑࡴ䕑㥋ᴹᅲ⦄ N ⚍ԡ⿏ⱘ䕧ߎDŽ� ೒ ��ᖂൟᇍ⿄ܼᶨᗻѨᴚᴎᵘঞ݊ফ࡯೒� 䆹ᴎᵘⱘ෎ᴀሎᇌབ㸼 � ᠔⼎ˈ㸼Ё l1~ l5 ߚ߿㸼⼎ ᴚ 1~ᴚ 5 ⱘ䭓ᑺˈw 㸼⼎ᴎᵘⱘᆑᑺˈlˈt ߚ߿㸼⼎䫄䫒 ⱘ䭓ᑺǃ᳔ᇣ८ᑺDŽ� 㸼 ��ᖂൟᇍ⿄ܼᶨᗻѨᴚᴎᵘⱘ෎ᴀሎᇌ� ৘ᵘӊᴚ䭓˄μm˅ ᶨᗻ䫄䫒ሎᇌ˄μm˅ l1 l2= l5 l3= l4 l t w 1610 500 880 200 20 75 � ߽⫼ ANSYS ᅠ៤ᖂൟᇍ⿄ܼᶨᗻѨᴚᴎᵘⱘᓎ῵ˈ ᇍᴎᵘ䖯㸠䴭࡯ᄺߚᵤˈߚᵤ䕑㥋԰⫼ϟᴎᵘⱘবᔶDŽ⬅ Ѣᴎᵘᰃᇍ⿄ⱘˈ಴ℸপϔञ䖯㸠䴭࡯ᄺߚᵤDŽᔧᮑࡴ �����1 ⱘ԰⫼࡯ᯊˈᴎᵘⱘবᔶབ೒ � ᠔⼎DŽ⬅೒ � ৃ ⶹˈℸᯊᴎᵘ 1 ⚍ⱘԡ⿏Ў ������ȝmDŽЎњᅲ⦄ 1 ⚍ⱘ 䕧ߎԡ⿏᳈໻ˈᇍ䫄䫒䖯㸠Ӭ࣪䆒䅵DŽ� 1 MN MXX YZ -.26111 .784972 1.831 2.877 3.923 4.969 6.015 7.061 8.108 9.154 SEP 28 2010 16:34:45 NODAL SOLUTION STEP=1 SUB =1 TIME=1 UX (AVG) RSYS=0 DMX =9.154 SMN =-.26111 SMX =9.154 ೒ �������N ⱘ䕑㥋԰⫼ϟᴎᵘⱘবᔶ� Ӭ࣪῵ൟⱘᓎゟ� ˄�˅䆒䅵ব䞣� ᶨᗻ䫄䫒ⱘᴤ᭭੠޴ԩ㒧ᵘᰃއᅮᶨᗻ䫄䫒ᗻ㛑ⱘ݇ 䬂಴㋴DŽᴀ᭛؛䆒ᶨᗻ䫄䫒ⱘᴤ᭭Ꮖ㒣⹂ᅮˈेᔍᗻ῵䞣 E ੠ᆚᑺ ȡ Ꮖⶹˈᇍ݊㒧ᵘখ᭄䖯㸠Ӭ࣪䆒䅵DŽ೚ᓻᔶᶨ ᗻ䫄䫒㒧ᵘখ᭄བ೒ 1 ᠔⼎ˈ rˈtˈw ߚ߿㸼⼎ᶨᗻ䫄䫒 ⱘञᕘǃ᳔ᇣ८ᑺϢᆑᑺˈ䫄䫒ⱘ䭓ᑺЎ lDŽ⹂ᅮ೚ᓻᔶ ᶨᗻ䫄䫒ⱘ䆒䅵ব䞣Ў˖X=[x1ˈx2ˈx3]=[rˈtˈl]DŽ ˄�˅Ⳃᷛߑ᭄� ᶨᗻ䫄䫒ⱘ෎ᴀᗻ㛑Џ㽕ࣙᣀᶨᑺǃ㊒ᑺঞᑨ࡯⡍ᗻ ㄝ޴ᮍ䴶ˈ݊Ёᶨᑺᗻ㛑Ⳉ᥹ড᯴њᶨᗻ䫄䫒ᢉᡫ໪䕑ⱘ 㛑࡯ˈгԧ⦄њ䖤ࡼࡃⱘᶨᗻ⿟ᑺˈᰃЏ㽕ⱘⷨお಴㋴DŽ� ೼໪䕑㥋԰⫼ϟˈᶨᗻ䫄䫒᠔ѻ⫳ⱘ㒩 z 䕈ⱘ䕀ࡼᰃ ៥Ӏ᠔䳔㽕ⱘ䖤ࡼˈ䍞໻㸼⼎݊ᶨᑺ䍞དˈ಴ℸᏠᳯ䍞໻ 䍞དDŽ಴ℸ⹂ᅮӬ࣪䆒䅵ⱘⳂᷛߑ᭄Ў˖� ����������� c XF 1)(min = ����������������������� ᓣЁ� cЎᶨᗻ䫄䫒ⱘᶨᑺˈᓣ���ेЎᶨᑺⱘ㸼䖒ᓣDŽ� ˄3˅㑺ᴳᴵӊ� ķ 䖍⬠㑺ᴳᴵӊ min max min max min max min max l l l r r r t t t w w w ≤ ≤­° ≤ ≤°® ≤ ≤°° ≤ ≤¯ (8) ⬅೒ 2 ৃҹᕫࠄ rˈtˈl ϝ㗙П䯈ⱘ݇㋏Ў˖ 2 2 2( ) ( ) 2 2 h t lr r−− + = (9) ĸ ᗻ㛑㑺ᴳ ᇍѢᖂൟᇍ⿄ܼᶨᗻѨᴚᴎᵘˈ䫄䫒ⱘফ࡯བ೒ 3 ᠔⼎ˈ ⬅Ѣ䫄䫒ফࠄᔃⶽⱘ԰⫼ˈ⬅ᴤ᭭࡯ᄺৃᕫߎ݊԰⫼ⱘॅ䰽⚍Ў ᳔ᇣ៾䴶˄x=l/2˅䖍㓬Ϟⱘᶤϔ⚍ˈ݊Ёϔջফࠄᢝᑨ࡯ˈϔ ջফࠄय़ᑨ࡯DŽॅ䰽⚍໘ⱘᔃ᳆ℷᑨ࡯Ў˖ ( ) (10)b o M I σ = ᓣЁ� ( ) ( ) 2y lM M z F b= = + üü䆹⚍໘ⱘᔃⶽ˗�� � 3 ( ) 12o wtI = üü῾៾䴶ᇍЁᗻ䕈ⱘᛃᗻⶽDŽ�� ᠔ҹᕫࠄ᳔໻ℷᑨ࡯Ў˖� �� max 3 6 ( ) 2y b lF b k wt σ + = × �������������������� ᓣЁ� 2.7 5.4 0.325 8 t rk r t + = + + üüᑨ࡯䲚Ё㋏᭄DŽ� ⹂ᅮӬ࣪䆒䅵ⱘᗻ㛑㑺ᴳᴵӊЎ˖� ������������ [ ] max 1 0 σ σ − ≥ ������������������������� � ೒ ��ᶨᗻ䫄䫒ⱘফ࡯೒� III. MATLAB Ӭ࣪䖛⿟ᅲ⦄ MATLAB Ӭ࣪Ꮉ݋ㆅ�optimization toolbox�ᰃ෎ѢⳌ ᑨ MATLAB ⠜ᴀⱘ䴶৥᳔Ӭ࣪䯂乬∖㾷ⱘϧ⫼Ꮉ݋ㆅˈ ৿᳝ϔ㋏߫ⱘӬ࣪ㅫ⊩ߑ᭄ˈᇍѢ䴲㒓ᗻ㑺ᴳ᳔Ӭ࣪䯂 乬ˈৃҹՓ⫼ MATLAB Ӭ࣪Ꮉ݋ㆅЁⱘ fmincon ߑ᭄䖯 㸠∖㾷DŽ೼ MATLAB Ӭ࣪Ꮉ݋ㆅЁˈ᳝㑺ᴳⱘ䴲㒓ᗻ᳔ ᇣ࣪ߑ᭄ fmincon ⱘ᭄ᄺ῵ൟ䞛⫼ҹϟᔶᓣ㸼⼎˖� ����������� °° °° ¯ °° °° ® ­ ≤≤ = ≤ = ≤ ubxlb beqxAeq bxA xCeq xCts xf )( )( 0)( )0(.. )(min �������������������� ᓣЁ )(xf ЎⳂᷛߑ᭄˗ lbbeqbx ,,, ੠ ub Ў৥䞣˗ A ੠ Aeq Ўⶽ䰉˗ )(xC ੠ )(xCeq ߚ߿㸼⼎䴲㒓ᗻϡㄝ ᓣ㑺ᴳ੠䴲㒓ᗻㄝᓣ㑺ᴳ˗� ᇍѢᴀ᭛ⷨおⱘᖂൟᇍ⿄ܼᶨᗻѨᴚᴎᵘˈ䆒䅵ⱘሎ ᇌᑨ⒵䎇ࡴᎹЁᖗᷛޚⱘࡴᎹᎹ㡎⌕⿟ˈ䖭ḋৃҹᦤ催఼ ӊࡴᎹⱘ៤ક⥛ˈ䰆ℶ䆒䅵఼ӊⱘࡴᎹᎹ㡎⌕⿟㽕∖䍙ߎ њᅲ偠ᅸⱘᅲ䰙ࡴᎹ㛑࡯㗠ՓࡴᎹ༅䋹DŽ݊㒧ᵘ䆒䅵খ᭄ гফࠄ䰤ࠊˈৠᯊḍ᥂ᗻ㛑㽕∖⹂ᅮӬ࣪ሎᇌ㣗ೈDŽ liuqing 高亮 ᇍѢ೚ᓻᔶᶨᗻ䫄䫒ˈ݊Ӭ࣪῵ൟЎ˖� 3 2 2 2 1min ( ) 2 0 6501 02.7 5.4( 0.325)(500 ) 8 100( ) ( ) 2 2 160 20 f x c l r t t r l r t t lr r r t ­ =°° − ≤°°° − ≤ +° + +® +° −° − + =°° ≤°° ≤¯ (14)� ೼ MATLAB にষЁ䕧ܹҹϟ⿟ᑣ˖� clear all;clc; format long x0=[145,20,200]; lb=[145,5,180]; ub=[160,14,210]; [x,fval]=fmincon(@mubiaofun,x0,[ ],[ ],[ ],[ ],lb,ub,@no nlincon) 䖤㸠ҹϞ⿟ᑣˈᕫࠄⱘӬ࣪㒧ᵰབ㸼 2 ᠔⼎DŽ⬅㸼 2 ৃⶹˈӬ࣪ৢ䫄䫒ⱘᶨᑺᕫࠄњᦤ催DŽ 㸼 2 ᶨᗻ䫄䫒Ӭ࣪ࠡৢሎᇌঞᗻ㛑ᇍ↨ খ᭄ ߱ྟؐ Ӭ࣪ৢⱘؐ r/ȝm 145 149.6 t/ȝm 20 14 l/ȝm 200 210 ᶨᑺ(c)/rad/N*m 0.007 41 0.023 97 � ḍ᥂Ӭ࣪ৢⱘ䫄䫒ሎᇌˈ೼ ANSYS Ёˈᇍᖂൟᇍ⿄ ܼᶨᗻѨᴚᴎᵘ䖯㸠䞡ᮄᓎゟ῵ൟˈᑊ䖯㸠䴭࡯ᄺߚᵤˈ ᮑࡴⳌৠⱘ䕑㥋������1�ˈᕫࠄᴎᵘⱘবᔶབ೒ � ᠔⼎DŽ ⬅೒ � ৃⶹˈӬ࣪ৢᴎᵘ N ⚍ԡ⿏Ў �������ȝmDŽ㗠Ӭ ࣪ПࠡˈᮑࡴⳌৠ䕑㥋ᯊˈᴎᵘ N ⚍ⱘԡ⿏Ў 9.154 ȝmˈ ৃ㾕ˈӬ࣪ৢᴎᵘⱘᗻ㛑ᕫࠄњᦤ催DŽ 1 MN MXX YZ -1.099 3.288 7.675 12.062 16.449 20.836 25.223 29.61 33.997 38.384 SEP 26 2010 09:20:24 NODAL SOLUTION STEP=1 SUB =1 TIME=1 UX (AVG) RSYS=0 DMX =38.384 SMN =-1.099 SMX =38.384 ೒ 5 Ӭ࣪ৢ 0.02N ⱘ䕑㥋԰⫼ϟᴎᵘⱘবᔶ IV. 㒧䆎 (1) ᥼ᇐњ೚ᓻᔶᶨᗻ䫄䫒ᶨᑺⱘ㊒⹂䅵ㅫ݀ᓣDŽ (2)ҹᦤ催ᶨᗻ䫄䫒ⱘ䕀ࡼᗻ㛑ЎⳂᷛˈᓎゟњᶨᗻ䫄 䫒Ӭ࣪䆒䅵ⱘ᭄ᄺ῵ൟˈᇍ೚ᓻᔶᶨᗻ䫄䫒䖯㸠њӬ࣪ˈ Ӭ࣪ৢ䫄䫒ⱘᶨᑺᕫࠄњᦤ催DŽ (3)ҹᖂൟᇍ⿄ܼᶨᗻѨᴚᴎᵘЎ՟ˈ䖤⫼ ANSYS ᇍ ݊䖯㸠䴭࡯ᄺߚᵤˈ䗮䖛ᇍᴎᵘӬ࣪ࠡৢ N ⚍䕧ߎԡ⿏ⱘ ↨䕗ˈ㸼ᯢ䫄䫒Ӭ࣪ৢᴎᵘⱘᗻ㛑ᕫࠄњᦤ催DŽ References [1] Huang J Y㧘Wei Y D㧘Zhang W.Optimal design of the flexure hinge parameter based on space micro-displacement worktable.Mech Electr Eng Mag,2006,23(1):55.( in chinese) [2] Lobontiu N㧚Design of symmetric conic㧚section flexure hinges based on closed-form compliance equations㧚Mech Mach Theory㧘2002㧘 37(5)㧦47. [3] Lobontiu N㧘Paine J SN㧘O’MalhyE㧘et a1.Parabolic and hyper-bolic flexure hinges::flexibility㧘motion precision and stress char· acterization based on compliance closed-form equations㧚 Precis Eng㧘 2002㧘 26(2):183. [4] DU Z J㧘DONG W㧘SUN L N.Flexure hinge and its application in precision parallel manipulators 㧚 Journal of Harbin Institute of Technology㧚2006㧘9:1469-1473㧚(in chinese) [5] CHEN G M㧘JIA J Y㧘LIU X Y㧘GOU Y J㧚Study on the accuracy of flexure hings. Chinese journal of scientific instrument㧚2004㧘 4:107-109㧚(in chinese) [6] ZHOU W W㧘HE G P㧚Optimizing flexure hings of a planar full compliant parellel mechanism㧚Journal of north China university of technology㧚2007㧘19(1):20-27㧚(in chinese) [7] CHEN S J㧘YANG Y H㧘SUN X Z㧚Performance analysis and optimal design of micro-displacement working table㧚 Journal of machine design㧚 2004㧘21(7):46-49㧚(in chinese) [8] YU J J,ZHOU Q,BI S S.Optimal design of a fully compliant mechanism based on its dynamic charactristics㧚Chinese journal of mechanical engineering㧚2003㧘39(8)㧦32-35㧚(in chinese) [9] Nicolae Lobontiu.Analytical model of displacement amplification and stiffness optimization for a class of flexure-based compliant mechanisms.Computers and Structures 2003:2797-281. << /ASCII85EncodePages false /AllowTransparency false /AutoPositionEPSFiles false /AutoRotatePages /None /Binding /Left /CalGrayProfile (Gray Gamma 2.2) /CalRGBProfile (sRGB IEC61966-2.1) /CalCMYKProfile (U.S. Web Coated \050SWOP\051 v2) /sRGBProfile (sRGB IEC61966-2.1) /CannotEmbedFontPolicy /Warning /CompatibilityLevel 1.7 /CompressObjects /Off /CompressPages true /ConvertImagesToIndexed true /PassThroughJPEGImages true /CreateJobTicket false /DefaultRenderingIntent /Default /DetectBlends true /DetectCurves 0.0000 /ColorConversionStrategy /LeaveColorUnchanged /DoThumbnails false /EmbedAllFonts true /EmbedOpenType false /ParseICCProfilesInComments true /EmbedJobOptions true /DSCReportingLevel 0 /EmitDSCWarnings false /EndPage -1 /ImageMemory 1048576 /LockDistillerParams true /MaxSubsetPct 100 /Optimize true /OPM 0 /ParseDSCComments false /ParseDSCCommentsForDocInfo false /PreserveCopyPage true /PreserveDICMYKValues true /PreserveEPSInfo false /PreserveFlatness true /PreserveHalftoneInfo true /PreserveOPIComments false /PreserveOverprintSettings true /StartPage 1 /SubsetFonts true /TransferFunctionInfo /Remove /UCRandBGInfo /Preserve /UsePrologue false /ColorSettingsFile () /AlwaysEmbed [ true ] /NeverEmbed [ true ] /AntiAliasColorImages false /CropColorImages true /ColorImageMinResolution 200 /ColorImageMinResolutionPolicy /OK /DownsampleColorImages true /ColorImageDownsampleType /Bicubic /ColorImageResolution 300 /ColorImageDepth -1 /ColorImageMinDownsampleDepth 1 /ColorImageDownsampleThreshold 1.50000 /EncodeColorImages true /ColorImageFilter /DCTEncode /AutoFilterColorImages false /ColorImageAutoFilterStrategy /JPEG /ColorACSImageDict << /QFactor 0.76 /HSamples [2 1 1 2] /VSamples [2 1 1 2] >> /ColorImageDict << /QFactor 0.76 /HSamples [2 1 1 2] /VSamples [2 1 1 2] >> /JPEG2000ColorACSImageDict << /TileWidth 256 /TileHeight 256 /Quality 15 >> /JPEG2000ColorImageDict << /TileWidth 256 /TileHeight 256 /Quality 15 >> /AntiAliasGrayImages false /CropGrayImages true /GrayImageMinResolution 200 /GrayImageMinResolutionPolicy /OK /DownsampleGrayImages true /GrayImageDownsampleType /Bicubic /GrayImageResolution 300 /GrayImageDepth -1 /GrayImageMinDownsampleDepth 2 /GrayImageDownsampleThreshold 1.50000 /EncodeGrayImages true /GrayImageFilter /DCTEncode /AutoFilterGrayImages false /GrayImageAutoFilterStrategy /JPEG /GrayACSImageDict << /QFactor 0.76 /HSamples [2 1 1 2] /VSamples [2 1 1 2] >> /GrayImageDict << /QFactor 0.76 /HSamples [2 1 1 2] /VSamples [2 1 1 2] >> /JPEG2000GrayACSImageDict << /TileWidth 256 /TileHeight 256 /Quality 15 >> /JPEG2000GrayImageDict << /TileWidth 256 /TileHeight 256 /Quality 15 >> /AntiAliasMonoImages false /CropMonoImages true /MonoImageMinResolution 400 /MonoImageMinResolutionPolicy /OK /DownsampleMonoImages true /MonoImageDownsampleType /Bicubic /MonoImageResolution 600 /MonoImageDepth -1 /MonoImageDownsampleThreshold 1.50000 /EncodeMonoImages true /MonoImageFilter /CCITTFaxEncode /MonoImageDict << /K -1 >> /AllowPSXObjects false /CheckCompliance [ /None ] /PDFX1aCheck false /PDFX3Check false /PDFXCompliantPDFOnly false /PDFXNoTrimBoxError true /PDFXTrimBoxToMediaBoxOffset [ 0.00000 0.00000 0.00000 0.00000 ] /PDFXSetBleedBoxToMediaBox true /PDFXBleedBoxToTrimBoxOffset [ 0.00000 0.00000 0.00000 0.00000 ] /PDFXOutputIntentProfile (None) /PDFXOutputConditionIdentifier () /PDFXOutputCondition () /PDFXRegistryName () /PDFXTrapped /False /CreateJDFFile false /Description << /CHS /CHT /DAN /DEU /ESP /FRA /ITA (Utilizzare queste impostazioni per creare documenti Adobe PDF adatti per visualizzare e stampare documenti aziendali in modo affidabile. 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