䋳䋮ฦ䊁䊷䊙䈱ᚑᨐ⹦⚦㩷 /'/5 ᛛⴚࠍ↪޿ߚዊဳᄙゲࡈࠜ࡯ࠬ࡮ࡕ࡯ࡔࡦ࠻࠮ࡦࠨߩ㐿⊒㩷䋨䋱䋩⎇ⓥ᭎ⷐ㩷ㄭᐕ‫ޔ‬ᱠⴕࡠࡏ࠶࠻ߩ⎇ⓥᚑᨐߩ⊒⴫ߥߤߦࠃࠅ‫ߩ࠻࠶ࡏࡠޟ‬਎♿‫ߩߡߒߣޠ‬ㄭᧂ᧪߇࡝ࠕ࡝࠹ࠖ
࡯ࠍჇߔߣ౒ߦ‫ੱޔ‬㑆ဳ⥄ᓞࡠࡏ࠶࠻ߩታ⃻᥉෸߇ᦼᓙߐࠇߡ޿ࠆ‫ࠍ࠻࠶ࡏࡠߥ߁ࠃߩߘޕ‬ታ⃻ߔࠆ਄ߢ㊀ⷐߥᛛⴚߣߒߡ‫ੱޔ‬㑆ߩᚻߣห᭽ߥᯏ⢻ࠍ஻߃ߚࡠࡏ࠶࠻ࡂࡦ࠼ߦࠃࠆ㜞ᐲߥࡂࡦ࠼࡝ࡦࠣᛛ
ⴚ߇᜼ߍࠄࠇࠆ‫ࠍࠇߎޕ‬ታ⃻ߔࠆߚ߼ߩ㧟ߟߩⷐ⚛ᛛⴚߣߒߡ‫࠼ࡦࡂ࠻࠶ࡏࡠޔ‬ᯏ᭴‫ޔࠨࡦ࠮ޔ‬ᖱႎ
ಣℂ೙ᓮᛛⴚ߇޽ࠆ‫ߩߎޕ‬ਛߢ࠮ࡦࠨߪࡂࡦ࠼૞ᬺߔࠆ਄ߢᔅⷐߥⅣႺߩᖱႎࠍᓧࠆ߽ߩߣ‫ߥ↪ེޔ‬૞ᬺࠍߎߥߔߚ߼ߩᗵⷡᖱႎࠍ⸘᷹ߔࠆ߽ߩ߇޽ࠆ‫⎇ᧄޕ‬ⓥߪᗵⷡᖱႎࠍ⸘᷹ߔࠆߚ߼ߩ⸅ⷡ࠮ࡦࠨ
ߦߟ޿ߡ‫ߩ࠼ࡦࡂ࠻࠶ࡏࡠޔ‬ᜰవ࠮ࡦࠨߦ߽៞タน⢻ߥᨵエធ⸅ㇱࠍ᦭ߔࠆᨵエߥᜰవ⸅ⷡ࠮ࡦࠨߩ
㐿⊒ߦ㑐ߔࠆ߽ߩߢ޽ࠆ‫ޕ‬ߎࠇ߹ߢ‫⎇ᧄޔ‬ⓥࠣ࡞࡯ࡊߢߪ‫ⶄޔ‬㔀ߥㆇേ߿૞ᬺࠍน⢻ߣߔࠆ೙ᓮᛛⴚߦ↪޿ࠆ  ゲࡈࠜ࡯ࠬ࠮ࡦࠨߩ⎇ⓥ㐿⊒ࠍⴕߞߡ߈ߚ‫ ޕ‬ゲࡈࠜ࡯ࠬ࠮ࡦࠨߣߪ‫ޔ‬㨄㧙㨅㧙㨆ߩゲᣇะߦ૞↪ߔࠆജߩ ᚑಽߣฦゲ࿁ࠅߩࡕ࡯ࡔࡦ࠻  ᚑಽࠍᬌ಴ߔࠆ࠮ࡦࠨߢ޽ࠆ‫ࡏࡠࡊࠗ࠲࠼ࠗࡁࡑ࡯ࡘࡅ߫߃଀ޕ‬࠶࠻ߥߤ‫ޔ‬Ყセ⊛ዊဳߩࡠࡏ࠶࠻ߩⶄ㔀ߥㆇേࠍᬌ಴ߔࠆߚ߼ߦߪ‫ޔ‬ᬌ಴ኻ⽎߳ߩᓇ㗀ࠍน⢻ߥ㒢ࠅዋߥߊߔࠆዊဳߩ࠮ࡦࠨ߇ᔅⷐߣߥࠆ‫ߩ࠻࠶ࡏࡠޕ‬േ૞ⅣႺ╬ߦࠃߞߡߪ‫ޔ‬ಽᏓ⊛ߦ㈩⟎ߒ⸘᷹ߔࠆᔅⷐ߇޽ࠆߚ߼‫ޔ‬ᓥ᧪ߩᄢ߈ߐߦᲧߴᩰᲑߦዊߐ޿ 6 ゲࡈࠜ࡯ࠬ࠮ࡦࠨࠍ㐿⊒ߒ‫࠻࠶ࡏࡠޔ‬೙ᓮ⎇ⓥߦଏߒ‫᦭ߩߘޔ‬ലᕈࠍ⹏ଔߔࠆߎߣߦ㊀ὐࠍ⟎߈ㅴ߼ߡ߈ߚ‫ޕ‬ᧄ⎇ⓥߪ‫ޔ‬࿖ౝߩ MEMS ࡈࠔ࠙ࡦ࠼࡝࡯⹜૞ࠨ࡯ࡆࠬࠍᵴ↪ߒ‫ߩߢ߹ࠇߎޔ‬ᢙ୘㨪ᢙච୘න૏ߩ⎇ⓥ⹜૞߆ࠄᢙ⊖୘㨪ජ୘ߩࠝ࡯࠳࡯ߩታ↪⹜૞ࠍታᣉߔࠆߎߣ߽⋡⊛ߦߒߡ޿ࠆ‫⵾ߩ߼ߚߩߘޕ‬૞ࡊࡠ࠮ࠬ਄ߩ⺖㗴ߩ᛽಴ߣߘߩ⸃᳿ߦ㑐ߔࠆᬌ⸛߽㊀ⷐߥ࠹࡯ࡑߢ޽ࠆ‫ߢߎߎޕ‬ᓧࠄࠇߚ⚿ᨐߪ‫ޔ‬࿖ౝMEMS ࡈࠔ࠙ࡦ࠼࡝࡯ߩᛛⴚജߩะ਄ߩߺߢߥߊ‫⹜ޔ‬૞୘ᢙߩᢙჇߒߦࠃߞߡ‫࠻࠶ࡏࡠޔ‬ᔕ↪⎇ⓥߩ
▸࿐᜛ᄢߣଦㅴߦߟߥ߇ࠆ߽ߩߢ޽ࠆ‫ޕ‬ᧄ⎇ⓥߢߪ‫ޔ‬MEMS ࡈࠔ࠙ࡦ࠼࡝࡯⹜૞ࠨ࡯ࡆࠬࠍᵴ↪ߒ‫⎇ᧄߢ߹ࠇߎޔ‬ⓥࠣ࡞࡯ࡊ߇㐿⊒ߒߡ߈ߚ  ゲࡈࠜ࡯ࠬ࠮ࡦࠨߩ࠴࠶ࡊኸᴺࠍ 3mm ⷺ߆ࠄ 2mm ⷺߦߐࠄߦ❗ዊߒߚ࠴࠶ࡊߩ㐿⊒ࠍⴕߞߚ‫ޕ‬߹ߚⵝ⌕߇ኈᤃߢ⸘᷹߇቟ቯߥࡄ࠶ࠤ࡯ࠫ᭴ㅧࠍណ↪ߒࡠࡏ࠶࠻ࡂࡦ࠼↪ᨵエᜰవ⸅ⷡ࠮ࡦࠨߩታ↪
ൻ⹜૞ࠍⴕߞߚ‫ߩࠨࡦ࠮ޕ‬ඨ⃿ធ⸅ㇱߦශടߐࠇߚജ㧔Fx̉‫ޔ‬Fỷ‫ޔ‬Fz̉㧕ߣࡕ࡯ࡔࡦ࠻㧔Mz̉㧕ߩ㧠ᚑಽࠍᬌ಴น⢻ߢ޽ࠆ‫⎇ᧄޕ‬ⓥߩ⹏ଔߣߒߡᜰవ⸅ⷡ࠮ࡦࠨࠍࡠࡏ࠶࠻ࠣ࡝࠶ࡄ࡯ߦ៞タߒ‫‛ޔ‬૕ߩᛠᜬታ㛎ࠍⴕ޿ࡠࡏ࠶࠻↪⸅ⷡ࠮ࡦࠨߣߒߡߩ᦭↪ᕈࠍ⏕⹺ߒߚ‫⎇ᧄޕ‬ⓥߢᓧࠄࠇߚᚑᨐߪ‫੹ޔ‬ᓟ‫࠶ࡏࡠޔ‬࠻↥ᬺߩߺߥࠄߕࡀ࠶࠻ࡢ࡯ࠢ࠮ࡦࠪࡦࠣ߿࡙ࡆࠠ࠲ࠬ࠮ࡦࠪࡦࠣߥߤ߳ߩᔕ↪ዷ㐿߽฽߼ᐢߊ↥ᬺ
ߦ⽸₂ߔࠆ߽ߩߣ⠨߃ࠆ‫ޕ‬㩷θ㧙1䋨䋲䋩ᚑᨐ⹦⚦㩷㩷Ԙ ⋡⊛⸅ⷡ࠮ࡦࠨߩᱧผߪ㐳ߊ‫ޔ‬ዉ㔚ࠧࡓᑼ‫࠱ࠛࡇޔ‬㔚᳇ᑼ‫⏛ޔ‬᳇ᑼ‫ޔ‬㕒㔚ኈ㊂ᑼ‫ޔ‬㖸㗀ᑼߥߤ᭽‫ߩޘ‬⒳㘃
ߩේℂߩ࠮ࡦࠨ߇㐿⊒ߐࠇߡ߈ߚ[1]‫[ޔ‬2]‫[ޔ‬3]‫ޕ‬1980 ઍߦߪ↥ᬺ↪ࡠࡏ࠶࠻߳ߩᔕ↪ࠍ⋡⊛ߣߒߚᄙߊ
ߩ⸅ⷡ࠮ࡦࠨߦ㑐ߔࠆ⎇ⓥᚑᨐ߇⊒⴫ߐࠇߡ޿ࠆ‫ޕ‬਎⇇⊛ߦ⷗ߡ߽ຠ⾰ߩ⦟޿Ꮏᬺ⵾ຠࠍᄢ㊂ߦ↢↥ߔࠆߎߣߢ㜞޿෼⋉ࠍᓧࠃ߁ߣߒߡ޿ߚᤨઍߢ޽ࠅ‫ޔ‬቟ቯߒߚല₸ߩ⦟޿૞ᬺࠍ↥ᬺ↪ࡠࡏ࠶࠻ߦⴕࠊߔ
ߚ߼‫ޔ‬ㇱຠߩᛠᜬ‫ޔ‬ㆇ៝‫߼ߪޔ‬ㄟߺߥߤߩ⥄േൻ߇ᔅⷐߣߐࠇߡ޿ߚ‫ࡠߚ޿↪ࠍࠨࡦ࠮ⷡ⸅ޔߒ߆ߒޕ‬ࡏ࠶࠻ࡂࡦ࠼ߪ↥ᬺ↪ࡠࡏ࠶࠻ߦᔕ↪ߐࠇࠆߎߣߪዋߥ߆ߞߚ‫ߩߘޕ‬ℂ↱ߪ⸅ⷡ࠮ࡦࠨߘߩ߽ߩߩ㐿⊒߅ࠃ߮ߘࠇࠍ↪޿ߚࡂࡦ࠼࡝ࡦࠣᛛⴚࠍ೑↪ߔࠆࠃࠅߪ૞ᬺㇱຠߩ᭴ㅧ‫ޔ‬૞ᬺᎿ⒟‫ޔ‬ⅣႺߩᡷ⦟ߩᣇ߇
◲න⏕ታߢ޽ߞߚߚ߼ߢ޽ࠆ‫ޕ‬1990 ᐕઍߩೋ߼ߦߪᄙຠ⒳ዋ↢↥ߩᤨઍߦߥࠅ‫৻ޔ‬บߩࡠࡏ࠶࠻ߦࠃ
ࠅ᭽‫ߥޘ‬૞ᬺࠍታ⃻ߐߖߚ޿ߣ޿߁ⷐ᳞߇ᄙߊߥࠅ‫ੱޔ‬㑆ߩᧃ┵ེߩࠃ߁ߥ⸅ⷡ࠮ࡦࠨߦࠃࠆ࠮ࡦࠪࡦ
ࠣࠍ೑↪ߒߚ㜞ᐲߥࡂࡦ࠼࡝ࡦࠣᛛⴚߩᔕ↪߇ᵈ⋡ߐࠇߚ߇‫ޔ‬ᄙߊߩࡠࡏ࠶࠻㐿⊒⠪ߪⷞⷡ࠮ࡦࠨ߿೙
ᓮᛛⴚߦࠃߞߡߎࠇࠍ⸃᳿ߒࠃ߁ߣߒߚ‫ߡߞࠃߦ࠻࠶ࡏࡠޕ‬૞ᬺߐߖࠆࠕࡊࡠ࡯࠴ߣߒߡᔅߕߒ߽ੱ㑆ߩ૞ᬺࠍᮨ୮ߐߖࠆᔅⷐߪߥߊ‫ߩ᦭․࠻࠶ࡏࡠࠈߒ߻ޔ‬૞ᬺᣇᴺࠍᮨ⚝ߔࠆߣ޿ߞߚᚻᴺ߇৻⥸⊛ߦߣࠄࠇߡ޿ߚ‫ ߎߎ߇ࠈߎߣޕ‬10 ᐕ‫ࠍࠨࡦ࠮ⷡ⸅ޔ‬ขࠅᏎߊߘߩࠃ߁ߥⅣႺߪᄌࠊࠅߟߟ޽ࠆ‫↥ޕ‬ᬺಽ㊁
ߢߪᄙຠ⒳ዋ㊂↢↥ߦኻᔕߔࠆߚ߼‫ࠆࠃߦ࠼ࡦࡂ࠻࠶ࡏࡠޔ‬㜞ᐲߥࡂࡦ࠼࡝ࡦࠣߩ⎇ⓥ߇⋓ࠎߦߥߞߡ
޿ࠆ‫ߩߘޕ‬⢛᥊ߦߪ‫ޔ‬૞ᬺߦࠃߞߡ᦭೑ߥࡂࡦ࠼ᯏ᭴ߦขࠅᦧ߃ࠆ‫ޟࠆࠁࠊ޿ޔ‬ઃߌᦧ߃ဳࡂࡦ࠼‫[ޠ‬4]ߪ㒢⇇ߦߥߞߡ߅ࠅ‫ߺ⚵ࠍࠨࡦ࠮ⷡ⸅ޔ‬ㄟࠎߛࡂࡦ࠼ᯏ᭴ߩᔅⷐᕈ߇⹺⼂ߐࠇߪߓ߼ߡ޿ࠆ‫␩⑔ޕ‬ಽ㊁ߢߪᣣᧄࠍߪߓ߼ߣߔࠆవㅴ⻉࿖ߢߪ㜞㦂ൻ߇ㅴࠎߢ߅ࠅ੺⼔ࡠࡏ࠶࠻ߩ࠾࡯࠭߇㜞߹ߞߡ޿ࠆ‫⼔੺ޕ‬ࡠࡏ࠶࠻ߩࠃ߁ߥੱ㑆ߩዬ૑ⓨ㑆ߢ૞ᬺߔࠆ႐ว‫ੱޔ‬㑆߿๟ࠅߩⅣႺߦෂኂࠍട߃ߥ޿ࠃ߁⸅ⷡࠍోりߢⷒ߁ᔅⷐ߇޽ࠆ[5]‫ޕ‬ක≮ಽ㊁ߦ߅޿ߡߪㄭᐕࡠࡏ࠶࠻ࡂࡦ࠼ߦࠃࠆᚻⴚߩታ⃻[6]‫⥄ޔ‬ᓞဳࠞ࠹࡯࠹
࡞‫ޔ‬ౝⷞ㏜ߦࠃࠆૐଚⷅᚻⴚ[7]ߩ⎇ⓥ߇ⴕࠊࠇߡ޿ࠆ߇‫ߩߎޔ‬ᛛⴚߦ߅ߌࠆ⃻࿷⺖㗴ߪ‫ޔ‬ធ⸅⴫㕙ߩ⎬ߐ߿᧚⾰‫ⷡ⸅ߩߤߥࡖ࠴ࠬࠢ࠹ޔ‬ᖱႎࠍᓧࠆߎߣߢ޽ࠆ‫⃻ޕ‬Ბ㓏ߢߪᚻⴚߪⷞⷡᖱႎࠍၮߦࡠࡏ࠶࠻ࡂ
ࡦ࠼ࠍ↪޿ᚻⴚࠍⴕߞߡ޿ࠆ߇‫ޔ‬ᚻⴚߦ߅ߌࠆജⷡᖱႎߩࡈࠖ࡯࠼ࡃ࠶ࠢ߇޽ࠆߎߣ߇ᦸ߹ߒ޿‫ޕ‬ࡠࡏ࠶࠻ߦ⸅ⷡ࠮ࡦࠨࠍ૶↪ߔࠆ⋡⊛ߪ⴫㧝㧚㧝ߦ␜ߔࠃ߁ߦᄢ߈ߊੑߟߦಽߌࠄࠇࠆ[8]‫⋡ߩ৻╙ޕ‬⊛ߪⵍᛠᜬ‛ߩหቯߢ޽ࠅ‫ޔ‬ᥧᚲ߿ㆤ߳޿‛ߩᓇߥߤⷞⷡᖱႎࠍᓧࠆߎߣߩߢ߈ߥ޿⁁ᴫ‫ޔ‬ⅣႺߢߩ‛૕ߩᒻ⁁⹺⼂‫ߤߥ⾰᧚߿ߐ⎬߮ࠃ߅ޔ‬ធ⸅ߒߡೋ߼ߡࠊ߆ࠆⵍᛠᜬ‛ߦ㑐ߔࠆᖱႎࠍᓧࠆߎߣߢ޽ࠆ‫ޕ‬╙ੑߩ⋡⊛ߪࡠࡏ࠶࠻ࡂࡦ࠼߇‛૕ࠍᛠᜬߒᠲ૞ߔࠆ㓙ߦ‫ޔ‬቟ቯߒߚ೙ᓮࠍⴕ߁ߚ߼ߩ೙ᓮࠍⴕ߁ߚ߼
ߩᖱႎࠍᓧࠆߎߣߢ޽ࠆ‫ߩࠄࠇߎޕ‬ᖱႎߣߒߡߪ‫ⵍޔ‬ᛠᜬ‛ߦടࠊࠆᛠᜬജ‫ⵍޔ‬ᛠᜬ‛ߣࡂࡦ࠼ߩ㑆ߦ↢ߓࠆߔߴࠅ‫ⵍޔ‬ᛠᜬ‛ߩ⥄㊀ߦࠃࠅࡂࡦ࠼ߦ෸߷ߔࡕ࡯ࡔࡦ࠻ߥߤ߇޽ࠆ‫ޕ‬ߘࠇߙࠇߩ⋡⊛ߦᔕߓߡ⸅ⷡ࠮ࡦࠨߦኻߔࠆⷐ᳞੐㗄߽⇣ߥࠅ‫ߦ⊛⋡ߩ৻╙ޔ‬ኻߒߡߪ㜞ᗵᐲ‫ޔ‬㜞ኒᐲ‫ޔ‬ᐢ޿㕙Ⓧߣ޿ߞߚⷐ᳞߇‫╙ߚ߹ޔ‬ੑߩ⋡⊛ߦኻߒߡߪ㧟ಽജᬌ಴߇น⢻‫߇✢࠼࡯࡝ޔ‬ዋߥ޿‫ޔ‬㜞ㅦಣℂߣ޿ߞߚⷐ᳞߇⸅ⷡ࠮ࡦࠨߦኻߒߡߥߐࠇߡ޿ࠆ‫ޕ‬⴫㧝㧚㧝 ⸅ⷡ࠮ࡦࠨߩ૶↪⋡⊛ߣⷐ᳞੐㗄⋡⊛⸅ⷡ࠮ࡦࠨᖱႎ

⸅ⷡ࠮ࡦࠨ߳ߩⷐ᳞੐㗄ⵍᛠᜬ‛ߩหቯ

ᒻ⁁‫⾰᧚ޔߐ⎬ޔ‬㜞ᗵᐲ‫ޔ‬㜞ኒᐲ‫ޔ‬ᐢ޿㕙Ⓧ቟ቯߥᛠᜬജ೙ᓮ

ᛠᜬജ‫࠻ࡦࡔ࡯ࡕޔࠅߴߔޔ‬ᄙゲജ࡮ࡕ࡯ࡔࡦ࠻ᬌ಴‫ޔ‬቟ቯߥࠦࡦ࠲ࠢ࠻‫ޔ‬シ޿‫ޔ‬ዋߥ޿࡝࡯࠼✢
㜞ㅦಣℂ

θ㧙2

ᧄ⎇ⓥߩ⋡⊛ߪ╙ੑߩ⋡ᮡߦኻߒ‛૕ߩ቟ቯߥᛠᜬࠍ⋡⊛ߣߒߚࡠࡏ࠶࠻ࡂࡦ࠼↪‫ޟ‬ᜰవ⸅ⷡ࠮ࡦ
ࠨ‫ࠍޠ‬㐿⊒ߒ‫↪᦭ߩߘޔ‬ᕈࠍᬌ⸽ߔࠆߎߣߢ޽ࠆ‫ޕ‬ᧄࡊࡠࠫࠚࠢ࠻ߢߪන⚿᥏ࠪ࡝ࠦࡦࠍ᭴ㅧ᧚ᢱߣߒ‫࠱ࠛࡇޔ‬ᛶ᛫ലᨐࠍᬌ಴ේℂߣߒߚ㧞ࡒ࡝ⷺߩജ࡮ࡕ࡯ࡔࡦ࠻࠮ࡦࠨ࠴࠶ࡊࠍඨ⃿⁁ߩᨵエߥធ⸅ㇱߢⷒ߁ߎߣߢታⵝᓟߩᄢ߈ߐ㧔࠮ࡦࠪࡦࠣㇱ㧕߇553.3mm ߩ⿥ዊဳ⸅ⷡ࠮ࡦࠨߩ㐿⊒ࠍⴕ߁‫ߪࠨࡦ࠮ᧄޕ‬ਗㅴ㧟ゲߩઁߦធ⸅ജߩ๟ࠅߩࡕ࡯ࡔࡦ
࠻ߩᬌ಴߇น⢻ߢ޽ࠆ‫ޕ‬ធ⸅๟ࠅߩࡕ࡯ࡔࡦ࠻߇ᬌ಴น⢻ߢ޽ࠇ߫ᛠᜬ‛૕ߩ㊀ᔃ߹ߢߩ〒㔌ᖱႎࠍᓧࠄࠇࠆߚ߼‫ޔ‬㧟ゲജ࠮ࡦࠨࠃࠅ቟ቯߥᛠᜬ೙ᓮ߇น⢻ߦߥࠆ‫⎇ᧄޕ‬ⓥߢߪߐࠄߦߎࠇࠍࡠࡏ࠶࠻ࡂࡦ࠼ߦ៞タ‫‛ޔ‬૕ߩᛠᜬࠍⴕ߁ߎߣߢࡠࡏ࠶࠻↪⸅ⷡ࠮ࡦࠨߣߒߡߩ᦭↪ᕈࠍᬌ⸽ߔࠆ‫ޕ‬ᒁ↪ᢥ₂[1] ዊୀᔀ㧦ེ̌↪ߥᚻ̍‫ޔ‬ᣣᧄࡠࡏ࠶࠻ቇળ‫ޔ‬vol.18‫ޔ‬no.6‫ޔ‬pp.2-4‫ޔ‬2000[2] H.R.Nicholls and M.H.Lee: “A saurvey of robotto tactile sensing technology ,Int .Robotics
research,”vol.8,no.3,pp3-30,1989[3] M.H.Lee and H.R.Nicholls: “ Tactile sensing for mechatorinics –a statesurvey, ”Mechatoronics

of artvol.9,pp1-31,1999[4] 㥲⮮ผ୶‫ޔ‬᳗↰๺ᒄ㧦̌ࡐ࡯࠲ࡉ࡞ࡑ࠾ࡇࡘ࡟࡯࡚ࠪࡦࠪࠬ࠹ࡓߩ⎇ⓥ㧙න㚟േജนᄌ㚟േࡂࡦ࠼ࠪࠬ࠹ࡓߩឭ᩺̍╙ 17 ࿁ᣣᧄࡠࡏ࠶࠻ቇળቇⴚ⻠Ṷળ੍Ⓜ㓸‫ޔ‬pp.937-938,1999[5] Takayuki Hoshi,Hiroyuki Shinoda: “A Tactile Element Based on Nonliner Elasticity to Sense
Contact Area” Proceedings of the 22nd Sensor Symposium,pp.375-379,2005[6] G.S.Guthart and J.K. Salisbury, Jr.: “The Intuitive Telesurgery System: Overview andApplication,” Proc.IEEE Int.Conf. on Robotics and automation, pp.618-621,2000[7] ࠝ࡝ࡦࡄࠬశቇᎿᬺ㧦̌ࠞ࠹࡯࠹࡞̍ࡑࠗࠢࡠࡑࠪࡦ/MEMS ᔕ↪࠺ࡃࠗࠬ‫ޔ‬2003 ࡑࠗࠢࡠࡑࠪࡦ/㧹㧱㧹㧿ᛛⴚᄢో pp.38-40‫ޔ‬2003[8] ዊᨋశ↵‫ޔ‬㣕ᴛᔋ㧦̌ࠪ࡝ࠦࡦࠍ᭴ㅧ᧚ᢱߣߔࠆ㧟ゲ⸅ⷡ࠮ࡦࠨ̍‫ޔ‬㔚ሶᖱႎㅢାቇળ⺰ᢥ⹹‫ޔ‬CΤ,vol.J74-C-Τ‫ޔ‬vol.5‫ޔ‬pp.427-433,1995

θ㧙3ԙ ᜰవ࠮ࡦࠨߩ᭴ㅧߣᛠᜬේℂ
ԙ-1 ᜰవ࠮ࡦࠨߩ᭴ㅧ
࿑㧞㧚㧝ߪᜰవ࠮ࡦࠨߩ᭴ㅧ࿑ߢ޽ࠆ‫ޕ‬࿑ߦ␜ߔࠃ߁ߦᜰవ࠮ࡦࠨߪ࠮ࡦࠪࡦࠣࠛ࡝ࠕߣࠦࡀࠢ࠲߆
ࠄ᭴ᚑߐࠇࠆ‫ో ޕ‬૕ߩࠨࠗ࠭ߪ 5113.3 mm3(᏷u㐳ߐuෘߺ)ߢ޽ࠆ‫࡯ࠨޔߪࠕ࡝ࠛࠣࡦࠪࡦ࠮ޕ‬ࠠ࠶࠻ࡏ࡯࠼㧔࿑ਛ PCB㧙Printed circuit board㧕ᄙゲᬌ಴น⢻ߥࡑࠗࠢࡠࡈࠜ࡯ࠬࡕ࡯ࡔࡦ࠻࠮ࡦࠨ
㧔MFMS㧕‫ޔ‬ㆊ⽶⩄଻⼔↪ࡌ࡯ࠬ(Overload protection base)‫ޔ‬ജવ㆐↪ࡇ࡜࡯(Transmission pillar)‫ޔ‬ࠤ࡯ࠬ(Case)‫ޔ‬ᨵエߥඨ⃿૕ធ⸅ㇱ㧔Soft hemisphere force-receiver㧕ߢ᭴ᚑߐࠇߡ޿ࠆ‫ߪ࠲ࠢࡀࠦޕ‬ࡑࠗࠢࡠࡈࠜ࡯ࠬࡕ࡯ࡔࡦ࠻࠮ࡦࠨ㧔એਅ࠮ࡦࠪࡦࠣ࠴࠶ࡊ㧕ߣࡈ࡟ࠠࠪࡉ࡞ࡢࠗࡗ࡯ߩធ⛯ࠍⴕ߁ᓎഀࠍᨐߚߔ‫ߪ࡯ࡗࠗࡢ࡞ࡉࠪࠠ࡟ࡈޕ‬ᄖㇱᯏེߣ࠮ࡦࠪࡦࠣ࠴࠶ࡊ߳ߩ㔚࿶ߩ౉಴ജࠍⴕߞߡ޿ࠆ‫‛ޕ‬૕ߩᛠᜬ߿ធ⸅ߦࠃࠅ‫ޔ‬ඨ⃿૕ធ⸅ㇱߦജ߿ࡕ࡯ࡔࡦ࠻߇ශടߐࠇࠆߣߘࠇࠄߪജવ㆐↪ࡇ࡜࡯ࠍ੺ߒ
ߡ࠮ࡦࠪࡦࠣ࠴࠶ࡊߦવ㆐ߔࠆ‫ߪࡊ࠶࠴ࠣࡦࠪࡦ࠮ޕ‬ශടߐࠇߚജ߿ࡕ࡯ࡔࡦ࠻ࠍ㔚࿶ߩᄌൻ㊂ߦᄌ឵
ߔࠆ․ᕈࠍ߽ߞߡ߅ࠅ‫ߩߘޔ‬ᄌൻ㊂߿ᄌൻߒߚ࠴ࡖࡀ࡞ߦࠃߞߡශടߒߚജ߿ࡕ࡯ࡔࡦ࠻ߩ㊂෸߮ᣇะࠍᬌ಴ߔࠆߎߣ߇ߢ߈ࠆ‫ޕ‬Soft hemisphere force-receiver
Transmission pillar
4-DOF MFMS chipOverload
protection baseConnector

PCB
Flexible cable࿑㧞㧚㧝 ᜰవ⸅ⷡ࠮ࡦࠨߩ᭴ㅧ࿑
ԙ-2 ᜰవ࠮ࡦࠨᛠᜬේℂ
ԙ-2-1 ࡠࡏ࠶࠻ࡂࡦ࠼ߦࠃࠆ‛૕ߩᛠᜬࡠࡏ࠶࠻ࡂࡦ࠼ߦࠃߞߡ⾰㊂‫៺ޔ‬ᡂଥᢙ߇ᧂ⍮ߩ‛૕ࠍᛠᜬߔࠆߣ޿߁⺖㗴ߦኻߒߡᄙߊߩ⎇ⓥ߇ⴕ
ࠊࠇߡ޿ࠆ[17]㨪[19]‫⁁ߥ߁ࠃ޿ߥ߈ߢ↪૶߇ࠨࡦ࠮ⷡⷞߪࠄࠇߎޕ‬ᴫߦ߅޿ߡ‫ࡈߩࠄ߆ࠨࡦ࠮ⷡ⸅ޔ‬ࠖ࡯࠼ࡃ࠶ࠢࠍၮߦ‛૕ߩ቟ቯߥ‛૕ߩᛠᜬ߇ⴕ߃ࠆ߆ߦߟ޿ߡ‛૕ߩᛠᜬജߣ៺ᡂജߩ㑐ଥߦߟ޿ߡ⸒෸ߒߡ޿ࠆ[20]‫⎇ᧄޕ‬ⓥߢߪߎࠇߦኻߒ‫ޔ‬ᛠᜬ‛૕ߩ㊀ᔃߣᛠᜬὐߩ〒㔌‫ޔ‬ᛠᜬᤨߩ௑ᢳⷺߦߟ޿
ߡ㧞ߟߩᜰవ࠮ࡦࠨࠍ↪޿ࠆߎߣߦࠃߞߡߎࠇࠄᬌ಴ߔࠆᣇᴺࠍ␜ߔ‫ޕ‬ᛠᜬ‛૕ߩ㊀ᔃߣᛠᜬὐߩ〒㔌ࠍ⹺⼂ߢ߈ࠇ߫ᛠᜬὐ๟ࠅߩࡕ࡯ࡔࡦ࠻ࠍ࠯ࡠߦߔߴߊ೙ᓮߔࠆߎߣ߇น⢻ߢ޽ࠆߒ‫ޔ‬ᛠᜬᤨߩᜰవ࠮
ࡦࠨߩ௑ᢳⷺ߇ᬌ಴ߢ߈ࠇ߫௑߈ࠍ઻߁ᛠᜬേ૞ߦᔅⷐߥᖱႎ߽ⶄ㔀ߥࠪࠬ࠹ࡓࠍ᭴ᚑߔࠆߎߣߥߊ
ᓧࠆߎߣ߇ߢ߈ࠆ‫ߪߢߎߎޕ‬࿑㧞㧚㧞ߦ␜ߔࠃ߁ߦ㧞ߟߩᜰవ࠮ࡦࠨ߇ߘࠇߙࠇะ߈ว߁ࠃ߁ߦࡠࡏ࠶
࠻ࡂࡦ࠼ߩ㧞ᜰߦⵝ⌕ߐࠇ‫‛ޔ‬૕ࠍᛠᜬߔࠆߣ߈ߩജߩ㊒ࠅว޿ࠍ⠨߃ࠆ‫‛ߢߎߎޕ‬૕ߪ৻᭽ߥ⾰㊂ࠍᜬߟ೰૕ߩ⋥ᣇ૕ߣߔࠆ‫ޕ‬θ㧙4ࡠࡏ࠶࠻ࡂࡦ࠼ߦࠃࠅᜰవ࠮ࡦࠨ‛૕ࠍធ⸅㕙ߦኻߒߡု⋥ߥᛠᜬജ Fgrip ߢᛠᜬߔࠆߣ߈‫ޔ‬෻૞↪ߩ
ജ Fn’㧔ធ⸅㕙ߦኻߒߡု⋥ߥജ㧕߇ᜰవ࠮ࡦࠨߦኻߒ૞↪ߔࠆ‫ޕ‬㕙ߦ៺ᡂ߇޽ࠆߣ߈ߪߐࠄߦ៺ᡂജ Ft’߇ធ⸅㕙ߩធ✢ᣇะߦ௛ߊ‫ޕ‬㧔Ft’ߪធ⸅㕙ౝߢ‫ޔ‬Ftx’‫ ޔ‬Fty’‫ޔ‬ߦಽ⸃ߢ߈ࠆ㧕ߘߩᄢ߈ߐߪ Fgrip ߦ㑐ଥߔࠆ‫‛ޕ‬૕߇േ߈಴ߘ߁ߣߒߡ޿ࠆߣ߈‫ޔ‬Po ࠍ㕒ᱛ៺ᡂଥᢙ
㧔Ft’= PoFgrip ߪᦨᄢ៺ᡂജ㧕߹ߚ‛૕ߩ⾰㊂ࠍ M‫ޔ‬㊀ജടㅦᐲࠍ g ߣߔࠆߣߔࠆߣ Ft’ dPoFgrip ߢ޽ࠆ‫ޕ‬ߣ‫ޔ‬Ft’=Mg ߢ޽ࠆ‫‛ߪߢߎߎޕ‬૕ࠍᛠᜬߒߡ޿ࠆ⁁ᘒߔߥࠊߜ‫ޔ‬FgripdPo/Mg ߩᛠᜬജ߇‛૕ߦ૞↪ߒߡ޿ࠆ߽ߩߣߔࠆ‫ࠆࠃߦ࠼ࡦࡂ࠻࠶ࡏࡠޔߚ߹ޕ‬ᛠᜬὐߣ‛૕ߩ㊀ᔃߩ〒㔌߇ l ߢ޽ࠆ႐ว‫ޔ‬ᛠᜬὐ߹ࠊࠅߦࡕ࡯ࡔࡦ࠻ Mn’㧔=Mgul㧕߇⊒↢ߔࠆ‫ޕ‬ߎࠇࠄᜰవ࠮ࡦࠨߦශടߐࠇߚ Fn’‫ ޔ‬Ftx’‫ ޔ‬Fty’‫ ޔ‬Mn’ߩ㧠ᚑಽߪᄌ឵ࡑ࠻࡝࠶ࠢࠬࠍ↪޿ߡᰴߩࠃ߁ߦ㔚࿶ VFtx’, VFty’ , VFn’ , VMn’ߣߒߡߘࠇߙࠇ⁛┙ߦᬌ಴ߔࠆߎߣ߇ߢ߈ࠆ‫ޕ‬§V c ·¨ Ftx ¸¨V c ¸¨ Fty ¸¨ VFnc ¸¨¨ c ¸¸© VMn ¹

§ S Ftx c
¨
¨ 0
¨ 0
¨
¨ 0
©

0

0

S Fty c00

S Fn c000 ·§ Ftxc ·¸¨¸
0 ¸¨ Ftyc ¸             
0 ¸¨ Fnc ¸¸¨¸S Mn c ¸¹¨© Mnc ¸¹

㧔㧞㧚㧝㧕

߹ߚߪ
V

   S (F )

㧔㧞㧚㧞㧕

(V)‫(ޔ‬F)ߪ৻㓏ߩ࠹ࡦ࠰࡞ߢߘࠇߙࠇ㔚࿶࠹ࡦ࠰࡞‫ޔ‬ജ࡮ࡕ࡯ࡔࡦ࠻࠹ࡦ࠰࡞ߢ޽ࠆ‫(ޕ‬S)ߪ㧞㓏ߩᗵᐲ࠹ࡦ࠰࡞ߢ޽ࠆ‫ߚ߹ޕ‬ᑼ㧔㧞㧚㧝㧕ߪ
F

S

1

(V )                          㧔㧞㧚㧟㧕ߢ޽ࠆ߆ࠄ‫ࠨࡦ࠮ޔ‬಴ജ㔚࿶(V)ߦࠃߞߡᜰవ࠮ࡦࠨߦශടߐࠇߚജ࡮ࡕ࡯ࡔࡦ࠻(F)ࠍ᳞߼ࠆߎߣ߇
ߢ߈ࠆ‫ޕ‬
ߎߩߣ߈ᛠᜬ‛૕ߩ⾰㊂ M‫ߩ࠼ࡦࡂ࠻࠶ࡏࡠޔ‬ᛠᜬജ Fgrip‫ޔ‬ᛠᜬὐߣ‛૕ߩ㊀ᔃ߹ߢߩ〒㔌 l ߪߘࠇߙࠇᰴߩࠃ߁ߦ᳞߼ࠄࠇࠆ‫ޕ‬Mg

2 u Ftyc 㧔 Ftxc

Fgrip

Fnc                                㧔㧞㧚㧡㧕

l

2

Mnc
Mg

0 㧕                        㧔㧞㧚㧠㧕Mnc
                         
Ftyc 㧔㧞㧚㧢㧕

ᑼ㧔㧞㧚㧟㧕ࠃࠅ‫ޔ‬ᑼ㧔㧞㧚㧣㧕㨪㧔㧞㧚㧥㧕߇ᓧࠄࠇࠆ‫ޕ‬1Mg

2 u S Fty ' VFtyc                          

Fgrip

S Fnc VFnc                            㧔㧞㧚㧤㧕S M1nc u VMnc
                         
1
S Fty' u VFtyc   㧔㧞㧚㧥㧕

l

1

㧔㧞㧚㧣㧕

ࠃߞߡ㧞ߟߩะ߆޿ว߁ᜰవ࠮ࡦࠨߦࠃߞߡ‛૕ࠍᛠᜬߒߚߣ߈‫ߩߘޔ‬಴ജ㔚࿶㧔V㧕ߦࠃࠅ‫‛ޔ‬૕ࠍᛠᜬߔࠆജ Fgrip‫⾰ޔ‬㊂ M‫ޔ‬ᛠᜬὐ߆ࠄ‛૕ߩ㊀ᔃ߹ߢߩ〒㔌 l ࠍ᳞߼ࠆߎߣ߇ߢ߈ࠆ‫ޕ‬θ㧙5࿑㧞㧚㧞 㧞ߟߩᜰవ࠮ࡦࠨࠍ↪޿ߚᛠᜬේℂᰴߦ࿑㧞㧚㧟ߩࠃ߁ߦ⸳ቯߒߚ O-x-y-z ᐳᮡ♽ߦ߅޿ߡ x ゲ๟ࠅߦȀ‫ޔ‬y ゲ๟ࠅߦǰ௑ᢳߒߚ⁁ᘒߢߩᛠᜬേ૞ߦߟ޿ߡ⠨߃ࠆ‫ޕ‬ะ߆޿ว߁㧞ߟߩᜰవ࠮ࡦࠨ㧔ᜰవ࠮ࡦࠨ i‫(ޔ‬i=1,2)㧕ߩߘࠇߙࠇߩജࡕ
࡯ࡔࡦ࠻㧙㔚࿶․ᕈߪએਅߩࠃ߁ߦਈ߃ࠄࠇࠆ‫ޕ‬§ Ftx c ·¨ i ¸¨ Fty c ¸
¨ i ¸
¨ Fni c ¸¨¨
c ¸¸© Mni ¹

§V c ·¨ Ftxi ¸¨c¸
1 V
S i ¨ Ftyic ¸  (i=1,2)                 㧔㧞㧚㧝㧜㧕¨V ¸¨ Fni ¸¨ VMn c ¸
© i ¹
Y

Fgrip
Fgrip

Z

Mg

X

࿑㧞㧚㧟 Z ゲ๟ࠅߦȀ௑ᢳߒߚ⁁ᘒߢߩᛠᜬേ૞

Z ゲ߆ࠄȀ௑޿ߚ႐ว㧔࿑㧞㧚㧠㧕‫ޔ‬ะ߆޿ว߁࠮ࡦࠨߦ෸߷ߔ X‫ޔ‬Y ᣇะߩജ Ftx c ‫ ޔ‬Fty c ߪߘࠇߙࠇ╬ߒߊ‫ޔ‬ᑼ㧔㧞㧚㧝㧝㧕㧔㧞㧚㧝㧞㧕ߩࠃ߁ߦ⴫ߔߎߣ߇ߢ߈ࠆ‫ޕ‬

Ftxi
Ftyi

c
c

1

1

2

Mg cosȀ (i=1,2)                       㧔㧞㧚㧝㧝㧕2

Mg sinȀ (i=1,2)                       㧔㧞㧚㧝㧞㧕ࠃߞߡȀߪᑼ㧔㧞㧚㧝㧟㧕ߩࠃ߁ߦ᳞߼ࠄࠇࠆ‫ޕ‬Ȁ arctan(

Ftyi
Ftxi

c
c

)  (i=1,2)                        㧔㧞㧚㧝㧟㧕θ㧙6߹ߚᑼ㧔㧞㧚㧝㧝㧕㧘㧔㧞㧚㧝㧞㧕ࠃࠅᑼ㧔㧞㧚㧝㧠㧕߇ᓧࠄࠇࠆ‫ޕ‬
Fti

c

2

2

Ftxic  Ftyic  㧔i=1,2)                      㧔㧞㧚㧝㧠㧕࿑㧞㧚㧠 Z ゲ߆ࠄȀ௑޿ߚ႐วߩജߩߟࠅ޽޿
એ਄ࠍ߹ߣ߼ࠆߣ‫ޔ‬Z ゲ߹ࠊࠅߩ௑ᢳⷺȀ‫ޔ‬෸߮ᛠᜬ‛૕ߩ⾰㊂ M‫ߩ࠼ࡦࡂ࠻࠶ࡏࡠޔ‬ᛠᜬജ Fgrip‫ޔ‬ᛠᜬὐߣ‛૕ߩ㊀ᔃ߹ߢߩ〒㔌 l ߪߘࠇߙࠇᑼ㧔㧞㧚㧝㧜㧕ࠃࠅએਅߩࠃ߁ߦ᳞߼ࠄࠇࠆ‫ޕ‬

Fgrip

1
S Fn
' (VFn c  VFn c ) / 2                      1

Ȁ arctan(2

1
S Ftyi' u VFty ci

1
S Ftxi' u VFtx c㧔㧞㧚㧝㧡㧕)  (i=1,2)                     㧔㧞㧚㧝㧢㧕

i

M

l

2

1
2 S Ftxi' u VFtxi ' / g cos(Ȁ)  (i=1,2)        㧔㧞㧚㧝㧣㧕Mn'    Mg㧔㧞㧚㧝㧤㧕

ࠃߞߡ㧞ߟߩะ߆޿ว߁ᜰవ࠮ࡦࠨߦࠃߞߡ‛૕ࠍᛠᜬߒߚߣ߈‫ߩߘޔ‬಴ജ㔚࿶ߦࠃࠅ‫ޔ‬ᛠᜬ‛૕ࠍᛠᜬߔࠆജ Fgrip‫⾰ޔ‬㊂ M‫ޔ‬௑ᢳⷺȀ‫ޔ‬ᛠᜬὐ߆ࠄᛠᜬ‛૕ߩ㊀ᔃ߹ߢߩ〒㔌 l ࠍ᳞߼ࠆߎߣ߇ߢ߈ࠆ‫ޕ‬
ԙ-2-2 ඨ⃿ធ⸅ㇱߣ࠮ࡦࠪࡦࠣ࠴࠶ࡊߩജቇ⊛㑐ଥᰴߦᜰవ࠮ࡦࠨធ⸅ㇱߦශടߐࠇߚജ࡮ࡕ࡯ࡔࡦ࠻ߣ࠮ࡦࠪࡦࠣ࠴࠶ࡊߦવࠊࠆജ࡮ࡕ࡯ࡔࡦ࠻ߩ㑐ଥߦߟ޿ߡ␜ߔ‫ޕ‬࿑㧞㧚㧡ߦ␜ߔࠃ߁ߦ‫ޔ‬ᜰవ࠮ࡦࠨធ⸅ㇱߦශടߐࠇߚ Fn’‫ ޔ‬Ftx’‫ ޔ‬Fty’‫ ޔ‬Mn’ߩ㧠ᚑಽߪߘࠇߙࠇ Fnz‫ޔ‬Mty‫ޔ‬Mtx‫ޔ‬Mnz ߣߒߡ࠮ࡦࠨ࠴࠶ࡊߦශടߐࠇࠆ‫ߢߎߎޕ‬ធ⸅ㇱߦශടߐࠇ
ߚਗㅴജ Ftx’‫ ޔ‬Fty’ߪࡇ࡜࡯ㇱ஥㕙ߦ૞↪ߔࠆߎߣߦࠃߞߡߘࠇߙࠇ y ゲ߹ࠊࠅ‫ޔ‬㨤ゲ߹ࠊࠅߩࡕ࡯ࡔ
ࡦ࠻ߣߒߡ࠮ࡦࠪࡦࠣ࠴࠶ࡊߦශടߐࠇࠆߎߣߦᵈᗧߐࠇߚ޿‫߈ߣߩߎޕ‬ඨ⃿ធ⸅ㇱߦടࠊࠆജ෸߮ࡕ
࡯ࡔࡦ࠻ߣ࠴࠶ࡊߦടࠊࠆജߪᑼ㧔㧞㧚㧝㧥㧕ߢ⴫ߐࠇࠆ‫ޕ‬θ㧙7§ Ftxc ·¨¸¨ Ftyc ¸¨ c¸¨ Fn ¸¨ Mnc ¸©
¹

§ C1 0¨¨ 0 C2
¨0 0
¨
¨0 0
©

0
0
C3
0

0 ·§ My ·¸¨¸
0 ¸¨ Mx ¸                    㧔㧞㧚㧝㧥㧕0 ¸¨ Fz ¸¸¨¸
C4 ¸¹¨© Mz ¸¹

߹ߚߪF'C ( F )                              㧔㧞㧚㧞㧜㧕ߎߎߢ F ' , ( F ) ߪធ⸅ㇱ‫ߩࡊ࠶࠴ࠣࡦࠪࡦ࠮ޔ‬ਛᔃߘࠇߙࠇߦශടߔࠆ৻㓏ߩജࡕ࡯ࡔࡦ࠻࠹ࡦ࠰࡞‫ޕ‬(C ) ߪ㧞㓏ߩᄌ឵ࡑ࠻࡝࠶ࠢࠬߢ޽ࠆ‫ޕ‬

Fn'

Z
Mn'

Ftx'

₧

Fty'
⁓

Ft'

⁞

Mz
Mx

My

X
Y
࿑㧞㧚㧡 ᜰవ࠮ࡦࠨធ⸅ㇱߦශടߐࠇߚജ‫ߩ߳ࡊ࠶࠴ࠣࡦࠪࡦ࠮ߩ࠻ࡦࡔ࡯ࡕޔ‬વ㆐ߎࠇએ㒠‫◲ޔ‬නߩߚ߼ᜰవ࠮ࡦࠨធ⸅ㇱߦශടߐࠇࠆജ Fn’‫ ޔ‬Ftx’‫ ޔ‬Fty’‫ ޔ‬Mn’ߪߘࠇߙࠇ Fz’‫ ޔ‬Fx’‫ޔ‬

Fy’‫ ޔ‬Mz’ߣ⴫⸥ߔࠆ‫ߦࡊ࠶࠴ࠣࡦࠪࡦ࠮ޔߚ߹ޕ‬ශടߐࠇࠆജ Fnz‫ޔ‬Mty‫ޔ‬Mtx‫ޔ‬Mnz ߪ‫ޔ‬Fz‫ޔ‬My‫ޔ‬
Mx‫ޔ‬Mz ߣ⴫⸥ߔࠆ‫ޕ‬ᒁ↪ᢥ₂=? ጊ↰ర㧦̌ᛠᜬ߹ߢߩ࠮ࡦࠪࡦࠣᚢ⇛̍ᣣᧄࡠࡏ࠶࠻ቇળ‫ޔ‬XQNPQRR
=?ጊ↰ర㧦̌⸅ⷡ࠮ࡦࠨ⎇ⓥߩᣂߒ޿ዷ㐿̍‫ޔ‬ᯏ᭴⺰‫ޔ‬PQ$RR
=?)%CPGRC&&4QUUKGVCN̌&GVGEVKQPQH+PEKRKGPV1DLGEV5NKRRCIGD[5MKP.KMG5GPUKPI
CPF0GWTCN0GVYQTM2TQEGUUKPI̍+'''6TCPUU[UVGO/CP%[DGTPGVKEU2CTV$XQNPQ
RR
=?೨㊁㓉ม㧦̌ᦛ㕙⁁ᒢᕈࡈࠖࡦࠟߩ࿕⌕࡮ṖࠅಽᏓផቯߦၮߠߊᛠᜬജߩ೙ᓮ̍‫ޔ‬ᣣᧄࡠࡏ࠶࠻ቇળ
⹹‫ޔ‬XQN‫ޔ‬PQ‫ޔ‬RR‫ޔ‬



θ㧙8

Ԛ ࠮ࡦࠪࡦࠣ࠴࠶ࡊߩ᭴ㅧߣᬌ಴ේℂԚ ࠮ࡦࠪࡦࠣ࠴࠶ࡊߩ᭴ㅧ
࿑㧟㧚㧝ߦ␜ߔߩߪߘࠇߙࠇ᭴ㅧߩ⇣ߥࠆන⚿᥏ࠪ࡝ࠦࡦࠍ᭴ㅧ᧚ᢱߣߒߚዊဳ࠮ࡦࠪࡦࠣ࠴࠶ࡊߢ
޽ࠆ‫ޕ‬න⚿᥏ࠪ࡝ࠦࡦߪዊဳൻߦ᦭೑‫߇ࠬ࠮ࡠࡊ࠴࠶ࡃޔ‬น⢻‫߇ࠬࠪ࡝࠹ࠬࡅޔ‬ᭂ߼ߡዋߥ޿㧔ቢోᒢᕈ૕㧕‫ޔ‬+% ࡊࡠ࠮ࠬߣߩⷫ๺ᕈ߇⦟޿ߥߤߩ⸅ⷡ࠮ࡦࠨߩ᭴ㅧ᧚ᢱߣߒߡఝࠇߚ․ᕈࠍᜬߞߡ޿ࠆ‫࠮ޕ‬ࡦࠪࡦࠣ࠴࠶ࡊߪ࠮ࡦ࠲࡯ࡊ࡟࡯࠻‫࠭ࠗࠨߣࡓ࡯࡟ࡈޔ‬㧔㐳ߐ N‫ޔ‬᏷ Y‫ޔ‬ෘߺ V㧕ߩ╬ߒ޿㧠ߟߩࡆ࡯ࡓ
߆ࠄ᭴ᚑߐࠇߘࠇߙࠇࡆ࡯ࡓ਄ߦߪࡇࠛ࠱ᛶ᛫⚛ሶ߇᜛ᢔߐࠇߡ޿ࠆ‫࠻࡯࡟ࡊ࡯࠲ࡦ࠮ߪࡓ࡯ࡆޕ‬෸߮ࡈ࡟࡯ࡓߦ࿕ቯߐࠇߡ޿ࠆ‫ߩࡓ࡯ࡆޕ‬ෘߺߪ࠮ࡦ࠲࡯ࡊ࡟࡯࠻෸߮ࡈ࡟࡯ࡓߩෘߺߦᲧߴචಽ⭯ߊߥߞߡ޿ࠆߚ߼‫ޔ‬ജ߿ࡕ࡯ࡔࡦ࠻ࠍශടߔࠆߣࡆ࡯ࡓߦᔕജ߇㓸ਛߔࠆ‫ࡓ࡯ࡆ߈ߣߩߎޕ‬਄ߦᒻᚑߐࠇߚࡇ
ࠛ࠱ᛶ᛫⚛ሶߩᛶ᛫ᄌൻ₸߇ᄌൻߔࠆ‫࠱ࠛࡇࠍࠇߎޕ‬ᛶ᛫⚛ሶߦធ⛯ߐࠇߚࡉ࡝࠶ࠫ࿁〝ߦࠃࠅ㔚࿶ߩᄌൻߣߒߡᬌ಴ߔࠆ‫ޕ‬(/5 ߪࡆ࡯ࡓߩ

ᣇ߇࠮ࡦ࠲࡯ࡊ࡟࡯࠻ߦ߽߁

ᣇ߇ࡈ࡟࡯ࡓߦ࿕ቯߐࠇߡ޿ࠆ‫(ޕ‬/5 ߪ৻ߟߩࡆ࡯ࡓߩਔ┵߇ࡈ࡟࡯ࡓߦ࿕ቯߐࠇ‫ߩࡓ࡯ࡆߦࠄߐޔ‬ਛᄩㇱ߇࠮ࡦ࠲࡯ࡊ࡟࡯࠻ߦ࿕ቯߐࠇߡ޿ࠆ‫ޕ‬(/5 ߪࡆ࡯ࡓߩਔ┵ߪ (/5 ߣห᭽ߦ৻ߟߩࡆ࡯ࡓߩਔ┵ߪࡈ࡟࡯ࡓߦ࿕ቯߐࠇߡ޿ࠆ߇‫ߦઁߩߘޔ‬࠮ࡦ࠲࡯ࡊ࡟࡯࠻ߦ㧞▎ᚲ‫ߦࡓ࡯࡟ࡈޔ‬㧝▎ᚲ࿕ቯߐࠇߡ޿ࠆ‫ޕ‬ฦ࠮ࡦࠨߣ߽㨄ゲ‫ޔ‬㨅ゲߦኻߒߡኻ⒓ߥ᭴ㅧߦߥߞߡ޿ࠆ‫(ޕ‬/5 ߪ㧢ゲ㧔(Z([(\/Z/[/\㧕ߩ⁛┙ߒߚ಴ജ㔚࿶ࠍᬌ಴ߔࠆߚ߼㧢ߟߩࡉ࡝࠶ࠫ࿁〝߇‫(ޔ‬/5(/5 ߪ㧔(\/Z/[㧕ߩ⁛┙ߒߚ಴ജ㔚࿶ࠍᬌ಴ߔࠆߚ߼㧟ߟߩࡉ࡝࠶ࠫ࿁〝߇࠮ࡦࠪࡦࠣ࠴࠶ࡊߩ⴫㕙ߦᒻᚑߐࠇߡ޿ࠆ‫ޕ‬ฦ࠮ࡦࠨߪන⚿᥏ࠪ࡝ࠦࡦߩ  㕙ࠍ૶↪ߒߡ޿ࠆ‫ޕ‬C (/5           D (/5                  ࿑㧟㧚㧝 ࠮ࡦࠪࡦࠣ࠴࠶ࡊߩ᭴ㅧ
θ㧙9
E (/5

Ԛ ࠮ࡦࠪࡦࠣ࠴࠶ࡊߩ᭴ㅧ⸃ᨆ
Ԛ ᭴ㅧ⸃ᨆߩ⋡⊛ࡆ࡯ࡓߩ਄ߦࡇࠛ࠱ᛶ᛫⚛ሶߩᦨㆡߥ૏⟎෸߮ᦨᄢශടജ෸߮ᦨᄢශടࡕ࡯ࡔࡦ࠻ࠍ⺞ߴࠆߚ߼ߦ
࠮ࡦࠨ࠴࠶ࡊߩ᭴ㅧ⸃ᨆࠍ߅ߎߥߞߚ‫ᦨߢߎߎޕ‬ᄢශടജ෸߮ᦨᄢශടࡕ࡯ࡔࡦ࠻ߣߪࡆ࡯ࡓㇱߦ߆߆ࠆᦨᄢᔕജ 8QPOKUUGUUVTGUU=㧞㧝? ߇ࠪ࡝ࠦࡦߩ㒢⇇⎕უᔕജߩ⚂  ߢ޽ࠆߦߥࠆߣ߈ߩജ

Fx max  Fy max  Fz max ෸߮ࡕ࡯ࡔࡦ࠻ Mx max  My max  Mz max ߢ޽ࠆ‫ޕ‬Ԛ ᭴ㅧ⸃ᨆߩᣇᴺ
ᒢᕈജቇߩ⸃ᨆߪ‫ޔ‬ᔕജ㧙߭ߕߺ㑐ଥᑼ‫ࠅߟޔ‬ว޿ᣇ⒟ᑼ߅ࠃ߮߭ߕߺߩㆡวᣇ⒟ᑼࠍਈ߃ࠄࠇߚႺ
⇇᧦ઙߩ߽ߣߢ⸃ߊߣ޿߁஍ᓸಽᣇ⒟ᑼߩ໧㗴ߦᏫ⌕ߐࠇࠆ‫ޕ‬㒢ࠄࠇߚ႐วߦߪ‫⸃ߪ⸃ߩߘޔ‬ᨆ⊛ߦ᳞߼ࠄࠇࠆ߇‫⸃ޔߪߦ⊛⥸৻ޔ‬ᨆ⸃ࠍ㐽ߓߚᒻߢ᳞߼ࠆߎߣߪ࿎㔍ߢ޽ࠆ႐ว߇ᄙ޿‫ޔߢߎߘޕ‬ㄭૃ⊛ߥᢙ୯⸃ࠍ᳞߼ࠆᚻᴺߣߒߡ᦭㒢ⷐ⚛ᴺ㧔㧲㧱㧹㧕ࠍ↪޿ࠆ‫ޕ‬㧲㧱㧹ߪ⸃ᨆኻ⽎‛ࠍ᦭㒢ߥᄢ߈ߐߩછᗧߩᒻ⁁ߩⷐ⚛ߩ㓸ว૕ߣߺߥߒ‫ߢߎߘޔ‬ᚑ┙ߔࠆ஍ᓸಽᣇ⒟ᑼࠍઍᢙᣇ⒟ᑼߢㄭૃߒߡ‫ޔ‬ᒢᕈ⊛ߥㄭૃ໧㗴ࠍᢙ୯⊛ߦ⸃ߊᣇᴺߢ޽ࠆ‫᦭ߩߢߎߎޕ‬㒢ⷐ⚛ߪਃᰴరߢ޽ࠆߩߢ⋥ᣇ૕ࠍ↪޿ࠆ‫᦭ߩߎޕ‬㒢ⷐ⚛ߩ㓸ว૕ߦኻߔࠆઍᢙᣇ⒟ᑼࠍዉߊᚻ㗅ߪ‫ޔ‬ᢙቇ⊛ߦߪᄌಽᴺߦၮߠ޿ߡ޿ࠆ‫⎇ᧄޕ‬ⓥߢߪ᦭㒢ⷐ⚛⸃ᨆߪ #05;5 ߦࠃࠅ ('/ ⸃ᨆࠍⴕߞߚ‫ޕ‬࿑㧟㧚㧞ߦ૞ᚑߒߚ (/5㨪 ߩ ('/ ⸃ᨆࡕ࠺࡞ࠍ␜ߔ‫⸃ߢߎߎޕ‬ᨆࡕ࠺࡞ߩࡆ࡯ࡓㇱߩኸᴺߪ

l u w u t 500 u 60 u 45(Pm3 ) ߢ޽ࠆ‫ ޕ‬N‫ޔ‬Y‫ޔ‬V ߪ࿑㧟㧚㧝ෳᾖ C (/5    
D (/5           E (/5࿑㧟㧚㧞 ᦭㒢ⷐ⚛ࡕ࠺࡞
θ㧙10




Ⴚ⇇᧦ઙߩ⸳ቯߦߟ޿ߡߪ‫ޔ‬࿕ቯ┵ߩ⸳ቯࠍⴕ߁‫ࠍ┵ߩࡓ࡯ࡆߪߢߎߎޕ‬࿕ቯ┵ߣߔࠆߚ߼ᜰቯߒߚ
ࠛ࡝ࠕߩోߡߩਗㅴᄌ૏߅ࠃ߮࿁ォᄌ૏ࠍ᜔᧤ߔࠆ‫ޕ‬ᰴ‫ޔ‬ജ࡮ࡕ࡯ࡔࡦ࠻ߩශട૞ᚑߒߚࡕ࠺࡞ߦജࠍශടߔࠆ‫࠻࡯࡟ࡊ࡯࠲ࡦ࠮ࡊ࠶࠴ࠨࡦ࠮ޕ‬ਛᄩㇱߩࠠ࡯ࡐࠗࡦ࠻ࠍᜰቯߒജ߿ࡕ࡯ࡔࡦ࠻ߩᄢ߈ߐะ߈ࠍᜰቯߔࠆ‫ޕ‬ᦨᓟߦ ('/ ߦࠃࠆᔕജ⸃ᨆࠍⴕߞߚ‫ޕ‬࿑㧟㧚㧟ߦ (/5 ߦ (\ ࠍශടߒߚߣ߈ߩ࠮ࡦࠪࡦࠣ࠴࠶ࡊࡆ࡯ࡓߩᄌᒻߩ᭽ሶ‫ޔ‬࿑㧟㧚㧠ߦ /[ ࠍශടߒߚߣ߈ߩ࠮ࡦࠪࡦࠣ࠴࠶ࡊࡆ࡯ࡓߩᄌᒻߩ᭽ሶࠍߘࠇߙࠇ଀ߣߒߡ␜ߔ‫ޕ‬


Z
D
C

Fz
B
A

X

Y


          C            D ࿑㧟㧚㧟 C (/5 ߦ (\ ࠍශടߒߚߣ߈ߩ࠮ࡦࠪࡦࠣ࠴࠶ࡊࡆ࡯ࡓߩᄌᒻ D (\O0 ࠍශടߒߚߣ
߈ߩࡆ࡯ࡓߦ߆߆ࠆ⌀ᔕജ V 1 ‫ ޔ‬V 2 ‫ ޔ‬V 3  



θ㧙11

Z

RMy4
2D

4

Y

X

C

RMy2
1

RMy3

B
3

RMy1
A


C 


D 

࿑㧟㧚㧠 C (/5 ߦ /[ ࠍශടߒߚߣ߈ߩ࠮ࡦࠪࡦࠣ࠴࠶ࡊࡆ࡯ࡓߩᄌᒻ D /[0ǴO ࠍශടߒߚ
ߣ߈ߩࡆ࡯ࡓߦ߆߆ࠆ⌀ᔕജ V 1 ‫ ޔ‬V 2 ‫ ޔ‬V 3  ᭴ㅧ⸃ᨆߦࠃߞߡᓧࠄࠇߚ (/5㨪 ߩࡆ࡯ࡓㇱߦ߆߆ࠆᦨᄢᔕജ 8QPOKUUGUUVTGUU ߇ࠪ࡝ࠦࡦߩ
㒢⇇⎕უᔕജߩ⚂  ߢ޽ࠆ /2C ߦߥࠆߣ߈ߩශടജ‫⴫ࠍ࠻ࡦࡔ࡯ࡕޔ‬㧟㧚㧝ߦ␜ߔ=㧞㧞?‫ޕ‬⴫㧟㧚㧝 ᦨᄢශടജ‫ᦨޔ‬ᄢශടࡕ࡯ࡔࡦ࠻㧔(/5㨪㧕(QTEG O0 
5GPUKPIEJKR/QOGPV 0࡮ǴO 

Fx max 

Fy max Fz max  Mx max  My max 

Mz max (/5













(/5

 

 







 

(/5

 

 







 




θ㧙12

Ԛ ࡇࠛ࠱ᛶ᛫ലᨐ
ඨዉ૕ߦ࿶ജࠍട߃ࠆߣ⚿᥏ߦ߭ߕߺࠍ↢ߓߡࠛࡀ࡞ࠡ࡯᭴ㅧ૕߇ᄌࠊࠅ‫ࠕ࡝ࡖࠠޔ‬ᢙ߿⒖േᐲ߇ᄌ
ൻߔࠆߎߣߢ⚿ᨐ⊛ߦᛶ᛫୯߇ᄌൻߔࠆ‫ߩߎޕ‬㔚᳇⊛․ᕈᄌൻߩߎߣࠍࡇࠛ࠱ᛶ᛫ലᨐߣ޿߁‫ߩߎޕ‬ല
ᨐߪ㊄ዻߦᲧߴ 㨪 ୚ᄢ߈ߊ‫⇣ޔ‬ᣇᕈ߇ᭂ߼ߡ㜞޿‫⎇ᧄޕ‬ⓥߢߪ࠮ࡦࠨ࠴࠶ࡊߦශടߐࠇߚജ߿ࡕ
࡯ࡔࡦ࠻ߪ࿑㧟㧚㧡ߦ␜ߔࠃ߁ߦ‫ޔ‬㔚ᵹኒᐲࡌࠢ࠻࡞ J ‫ޔ‬㔚⇇ࡌࠢ࠻࡞ E ߇หᣇะߩ㧞ߟߩ࠲࡯ࡒ࠽
࡞ࠍᜬߟࡇࠛ࠱ᛶ᛫⚛ሶߦࠃߞߡᬌ಴ߐࠇࠆ‫ߩߎޕ‬႐วࡇࠛ࠱ᛶ᛫ലᨐߪᑼ㧔㧟㧚㧝㧕ߩࠃ߁ߦ⴫ߐࠇ
ࠆ‫ޕ‬㧔ᑼ㧔㧟㧚㧝㧕ߩዉ಴ߪઃ㍳㧯ෳᾖ㧕

'R
R

6

¦ S V  L                      㧔㧟㧚㧝㧕
,
1j

j

j 1

ߎߎߢ 'R R ߪᲧᛶ᛫‫ޔ‬V j ߪᔕജ෸߮ߖࠎᢿᔕജ‫ ޔ‬S 1, j ߪ⚿᥏ᣇ૏ߦࠃߞߡ᳿ቯߐࠇࠆࡇࠛ࠱ᛶ

᛫ଥᢙߢ޽ࠆ‫ޕ‬⴫㧟㧚㧞ߪ        㕙ߦ߅ߌࠆ㐳ᚻᣇะ෸߮ᮮᚻᣇะߩࡇࠛ࠱ᛶ᛫ଥᢙࠍ⴫ߒߚ߽
ߩߢ޽ࠆ‫⎇ᧄޕ‬ⓥߢߪන⚿᥏ࠪ࡝ࠦࡦߩ⚿᥏㕙  㕙਄ߩ ෸߮ ࠍ㐳ᚻᣇะ޽ࠆ޿ߪᮮᚻᣇ
ะߣߔࠆߚ߼⴫㧟㧚㧞ࠃࠅ‫ޔ‬ᑼ㧔㧟㧚㧝㧕ߪᑼ㧔㧟㧚㧞㧕ߩࠃ߁ߦ◲⇛ൻߢ߈ࠆ‫ޕ‬'R
R

S 11, V 1  S 12, V 2  S 13, V 3                        㧔㧟㧚㧞㧕S 11,72 ‫ ޔ‬S 12,

66 ‫ ޔ‬S 13,1 ࿑㧟㧚㧡 ࡇࠛ࠱ᛶ᛫⚛ሶߦടࠊࠆᔕജ
⴫㧟㧚㧞 ⚿᥏ᣇ૏ߣࡇࠛ࠱ᛶ᛫ଥᢙ    ࡇࠛ࠱ᛶ᛫ଥᢙ u 10

⚿᥏ᣇ૏
㕙







Ǒ’12

Ǒ’13

12

(cm 2 / dyne) 

 ゲ

㧞ゲ

Ǒ’11

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θ㧙13

Ǒ’14

Ǒ’15

Ǒ’16

Ԛ ࡇࠛ࠱ᛶ᛫⚛ሶߩ㈩⟎࿑㧟㧚㧢ߪߘࠇߙࠇ (/5㨪㧟ߩ࠮ࡦࠨ࠴࠶ࡊߩࡆ࡯ࡓ਄ߩࡇࠛ࠱ᛶ᛫⚛ሶߩ㈩⟎ࠍ⴫ߒߡ޿ࠆ‫(ޕ‬/5ߢߪ㧢ᚑಽ㧔(Z([(\/Z/[/\㧕ࠍᬌ಴ߔࠆߚ߼‫ ޔ‬RFx1 , RFx 2 㧔(Z ᬌ಴↪㧕‫ ޔ‬RFy1 , RFy 2 㧔([ ᬌ಴↪㧕‫ޔ‬

RFz1 , RFz 2 , RFz 3 , RFz 4㧔(\ ᬌ಴↪㧕‫ޔ‬RMx1 , RMx 2 , RMx 3 , RMx 4㧔/Z ᬌ಴↪㧕‫ޔ‬RMy1 , RMy 2 , RMy 3 , RMy 4㧔/[ ᬌ಴↪㧕‫ޔ‬

RMz1 , RMz 2 , RMz 3 , RMz 4 㧔/\ ᬌ಴↪㧕ߩ⸘㧞㧞୘ߩࡇࠛ࠱ᛶ᛫⚛ሶ߇㈩⟎ߐࠇߡ޿ࠆ‫(ޕ‬/5 ߢߪ㧟ゲ‫ޔ‬㧔(\/Z/[㧕ࠍᬌ಴ߔࠆߚ߼‫ ޔ‬RFz1 , RFz 2 , RFz 3 , RFz 4 ‫ ޔ‬RFz '1 , RFz ' 2 , RFz '3 , RFz ' 4 㧔(\ ᬌ಴↪㧕

RMx1 , RMx 2 , RMx 3 , RMx 4 㧔/Z ᬌ಴↪㧕‫ ޔ‬RMy1 , RMy 2 , RMy 3 , RMy 4 㧔/[ ᬌ಴↪㧕ߩ⸘㧝㧢୘ߩࡇࠛ࠱ᛶ᛫⚛ሶ߇ߘࠇߙࠇ㈩⟎ߐࠇߡ޿ࠆ‫'( ߪࠄࠇߎޕ‬/ ⸃ᨆߩ⚿ᨐߦၮߠ߈‫ޔ‬ജ‫ߩ࠻ࡦࡔ࡯ࡕޔ‬ශടᤨ‫ࡓ࡯ࡆޔ‬਄ߦ߅޿ߡᦨ߽ᄢ߈ߥᔕജ߇⊒↢ߔࠆ૏⟎ߦ㈩⟎ߒߚ‫ޕ‬C Y <110>RX2 RZ1

RZ2

RZ3

RX4 RZ4

RY3

RY4

X <110>RY1

RY2
RX1 R'Z1

R'Z2

R'Z3

RX3 R'Z4


D 
θ㧙14

Y <110>RZ1RZ2 RZ3

RZ4

RY4

RY2

RX4

RX3

X <110>

RX2

RX1
RY1

RY3

R'Z1 R'Z2

R'Z3

R'Z4


E 
࿑㧟㧚㧢 ࡇࠛ࠱ᛶ᛫⚛ሶߩ㈩⟎Ԛ ᬌ಴࿁〝Ԛ (/5 ߩᬌ಴࿁〝ฦᚑಽࠍ⁛┙ߒߡᬌ಴ߔࠆߚ߼࿑㧟㧚㧣ߩࠃ߁ߦ (/5 ߢߪ㧢ߟߩ⁛┙ߒߚࡉ࡝࠶ࠫ࿁〝߇ᒻᚑߐࠇߡ
޿ࠆ‫ޕ‬㧔(Z‫ \(ޔ[(ޔ‬ᬌ಴↪ߪࡂ࡯ࡈࡉ࡝࠶ࠫ࿁〝 /Z‫ޔ‬/[㧘/\ ߪࡈ࡞ࡉ࡝࠶ࠫ࿁〝㧕([‫ޔ‬/[ᬌ಴↪࿁〝ߪߘࠇߙࠇ (Z‫ޔ‬/Zᬌ಴↪࿁〝ߣหߓ᭴ᚑߢ޽ࠆߚ߼⋭⇛ߒߚ‫ޕ‬


Vin
RFx1

Vin
RFz1

RRef
VoutFxVoutFz
RFz2

RRef

RFx2

RRef

RFz4

RRef

RFz3

ground     ground

Vin

Vin(RMy2)
RMx2(RMy1)RMx1

RMz1

VoutMx(VoutMy)
RMx4(RMy4)RMz2
VoutMz

RMx3(RMy3)
groundRMz4
     ࿑㧟㧚㧣 (/5 ߩࡉ࡝࠶ࠫ࿁〝


θ㧙15

RMz3
groundߎߩߣ߈‫(ޔ‬Z‫ޔ\(ޔ[(ޔ‬/Z‫ޔ‬/[‫ޔ‬/\ ߩᬌ಴↪ࡉ࡝࠶ࠫߩ಴ജ㔚࿶ VoutFx ‫ ޔ‬VoutFy ‫ ޔ‬VoutFz ‫ ޔ‬VoutMx ‫ ޔ‬VoutMy ‫ޔ‬

VoutMz ߪߘࠇߙࠇᑼ㧔㧟㧚㧟㧕㨪㧔㧟㧚㧤㧕ߢ⴫ߐࠇࠆ‫ޕ‬

VoutFx

1 'RFx1 'RFx 2()Vin                        㧔㧟㧚㧟㧕
4 RFx1
RFx 2

VoutFy1 'RFy1 'RFy 2
()Vin                        㧔㧟㧚㧠㧕RFy 2
4 RFy1

VoutFz

1 'RFz1  'RFz 4 'RFz 2  'RFy 3()Vin                 㧔㧟㧚㧡㧕
4 RFz1  RFz 4
RFz 2  RFy 3

VoutMx

1 'RMx1 'RMx 3 'RMx 2 'RMx 4()Vin                㧔㧟㧚㧢㧕
4 RMx1
RMx 3
RMx 2
RMx 4

VoutMy1 'RMy1 'RMy 3 'RMy 2 'RMy 4()Vin                㧔㧟㧚㧣㧕
RMy 3
RMy 2
RMy 4
4 RMy1

VoutMz

1 'RMz1 'RMz 3 'RMz 2 'RMz 4()Vin                 㧔㧟㧚㧤㧕
4 RMz1
RMz 3
RMz 2
RMz 4


⴫㧟㧚㧟ߦ (/5 ߩࡇࠛ࠱ᛶ᛫⚛ሶߩᛶ᛫୯ߩჇᷫ⴫ࠍ␜ߔ‫⴫ޕ‬ਛ̈ ̉‫ޔ‬̈̉ߪߘࠇߙࠇჇ‫ޔ‬ᷫࠍ⴫ߒ‫ޔ‬̈̉ߪᄌൻ߇ߥ޿ߎߣࠍ␜ߒߡ޿ࠆ‫⴫ޕ‬ਛߩ✂ដߌㇱߪ‫ࠫ࠶࡝ࡉߩࠇߙࠇߘޔ‬࿁〝ߦ߅޿ߡ಴ജ߇޽
ࠆߎߣࠍ␜ߒߡ޿ࠆ‫ޕ‬⴫㧟㧚㧟 ࡇࠛ࠱ᛶ᛫⚛ሶߩᛶ᛫୯ߩჇᷫ⴫ (/5 
Fx-Bridge Fy-Bridge

Fz-Bridge

RFx1 RFx2

RFz2 RFz3 RFz4 RMy1 RMy2 RMy3 RMy4 RMx1 RMx2 RMx3 RMx4 RMz1 RMz2 RMz3 RMz4

RFy1 RFy2 RFz1

Fx +
- 0
Fy 0 0 +Fz +/- +/- +/My 0 0 0
Mx 0 0 0
Mz + + +

0
+/0
0
+

My-Bridge

+

+

-

-

+ +

0
+
+
0
+

0
0
+

0
+
0
+

0
+
0
+

0 0
+ + 0 0+ +Mx-Bridge- - 0 0 0
0 0 + + - + + - + - 0 0 0
0 0 + - ++ + + + +Mz-Bridge

0 + - - + - 0 0 0- - + - +

-

+

+ +
- 0 0
+ +
- + 

ߎߩ⴫ߦࠃߞߡฦශടജߣࡕ࡯ࡔࡦ࠻ߩᬌ಴ߪਅ⸥ߩࠃ߁ߦ⺑᣿ߔࠆ‫ޕ‬Ԛ (Z ([ ߩᬌ಴ශടജ (Z ߇࠮ࡦ࠲࡯ࡊ࡟࡯࠻ㇱߦടࠊߞߚ႐ว‫(ޔ‬Z ᬌ಴↪ࡉ࡝࠶ࠫ࿁〝ߩ  ߟߩࡇࠛ࠱ᛶ᛫⚛ሶߦ૞↪ߔࠆᔕജߪᰴߩࠃ߁ߦ⴫ߐࠇࠆ‫ޕ‬

θ㧙16

VR

Fx 1

V R                               㧔㧟㧚㧥㧕Fz 2

ࠃߞߡ (Z ᬌ಴↪ࡉ࡝࠶ࠫ࿁〝ߩᛶ᛫ᄌൻߪ

'RFx1

 'RFx 2                             㧔㧟㧚㧝㧜㧕ߣߥࠅ‫ޔ‬એਅߦ␜ߔ಴ജࠍᓧࠆߎߣ߇ߢ߈ࠆ‫ޕ‬

VoutFx

1 'RFx1
Vin                            㧔㧟㧚㧝㧝㧕2 RFx1ߎߩߣ߈‫ࡊ࠶࠴ࠨࡦ࠮ޔ‬਄ߦ߅ߌࠆኻ⒓ߥ㈩⟎ߣ࠮ࡦࠨ࠴࠶ࡊߩ᭴ㅧ߆ࠄ (㨥ᬌ಴↪ࡉ࡝࠶ࠫ࿁〝ߩ'RFy1ߣ'RFy 2 ߪ╬ߒߊߚ߼‫ [(ޔ‬ᬌ಴↪ࡉ࡝࠶ࠫ࿁〝ߩ಴ജߪ࠯ࡠߦߥࠆ‫ޕ‬ห᭽ߦ‫ޔ\(ޔ‬/Z‫ޔ‬/[‫ߡߒߘޔ‬/\ ᬌ಴↪ࡉ࡝࠶ࠫ࿁〝ߩᛶ᛫ᄌൻߪ

'RFz1'RFz 2

 'RFz 3

 'RFz 4 ‫' ޔ‬RMx1'RMx 4'RMx 2'RMy1'RMy 2

 'RMy 3

 'RMy 4 ‫' ޔ‬RMz1'RMz 3

 'RMz 2'RMx 3  'RMz 4 ߣߥࠅ‫ࠇߙࠇߘޔ‬ᑼ㧔㧟㧚㧟㧕㨪㧔㧟㧚㧤㧕ࠃࠅ ([‫ޔ\(ޔ‬/Z‫ޔ‬/[‫ޔ‬/\ ᬌ಴↪ࡉ࡝࠶ࠫ࿁〝ߩ಴ജߪߘ
ࠇߙࠇ࠯ࡠߣߥࠆ‫ޕ‬([ ߦߟ޿ߡߪ (Z ߣห᭽ߩᬌ಴ᣇᴺߢ޽ࠆ‫ޕ‬Ԛ (\ ߩᬌ಴ශടജ (\ ߇࠮ࡦ࠲࡯ࡊ࡟࡯࠻ㇱߦടࠊߞߚ႐ว‫ \(ޔ‬ᬌ಴↪ࡉ࡝࠶ࠫ࿁〝ߩ㧠ߟߩࡇࠛ࠱ᛶ᛫⚛ሶߦ૞↪ߔࠆᔕജߪᰴߩࠃ߁ߦ⴫ߐࠇࠆ‫ޕ‬


VR

Fz 1

V R

Fz 2

V R

Fz 3

V R                      㧔㧟㧚㧝㧞㧕Fz 4


ࠃߞߡ (\ ᬌ಴↪ࡉ࡝࠶ࠫ࿁〝ߩᛶ᛫ᄌൻߪ


'RFz1

 'RFz 2

 'RFz 3'RFz 4                     㧔㧟㧚㧝㧟㧕ߣߥࠅ‫ޔ‬એਅߦ␜ߔ಴ജࠍᓧࠆߎߣ߇ߢ߈ࠆ‫ޕ‬

VoutFz

1 'RFz1
Vin                           㧔㧟㧚㧝㧠㧕2 RFz1ߎߩߣ߈‫(ޔ‬Z‫ޔ[(ޔ‬/Z‫ޔ‬/[‫ ߡߒߘޔ‬/\ ᬌ಴↪ࡉ࡝࠶ࠫ࿁〝ߩᛶ᛫ᄌൻߪߘࠇߙࠇ‫' ޔ‬RFy1
θ㧙17'RFy 2 ‫ޔ‬'RFy1'RFy 2 ‫' ޔ‬RMx1'RMx 2'RMy1'RMy 2'RMy 4 ‫'ޔ‬RMz1'RMy 3'RMx 3'RMx 4 'RMz 2'RMz 3'RMz 4 ߣߥࠅ‫ࠇߙࠇߘޔ‬ᑼ㧔㧟㧚㧟㧕㨪㧔㧟㧚㧤㧕ࠃࠅ ([‫ޔ\(ޔ‬/Z‫ޔ‬/[‫ޔ‬/\ ᬌ಴↪ࡉ࡝࠶ࠫ࿁〝ߩ಴ജߪߘࠇߙࠇ࠯ࡠߣߥࠆ‫ޕ‬Ԛ /[ /Z ߩᬌ಴ශടജ /[ ߇࠮ࡦ࠲࡯ࡊ࡟࡯࠻ㇱߦടࠊߞߚ႐ว‫ޔ‬/[ ᬌ಴↪ࡉ࡝࠶ࠫ࿁〝ߩ㧠ߟߩࡇࠛ࠱ᛶ᛫⚛ሶߦ૞↪ߔࠆᔕജߪᰴߩࠃ߁ߦ⴫ߐࠇࠆ‫ޕ‬


VR

My 1

V R

DV R

My 4

DV R

My 2

My 3

                    㧔㧟㧚㧝㧡㧕ࠃߞߡ /[ ᬌ಴↪ࡉ࡝࠶ࠫ࿁〝ߩᛶ᛫ᄌൻߪ


'RMy1

 'RMy 4

D'RMy 2

D'RMy 3                    㧔㧟㧚㧝㧢㧕ߣߥࠅ‫ޔ‬એਅߦ␜ߔ಴ജࠍᓧࠆߎߣ߇ߢ߈ࠆ‫ޕ‬

VoutMy1 (1  D ) 'RMy1
Vin                         㧔㧟㧚㧝㧣㧕
RMy1
2



ߎߩߣ߈‫(ޔ‬Z‫ ߡߒߘ \(ޔ[(ޔ‬/\ ᬌ಴↪ࡉ࡝࠶ࠫ࿁〝ߩᛶ᛫ᄌൻߪోߡ࠯ࡠߢ޽ࠅ‫ޔ‬࿁〝ߩ಴ജߪ࠯ࡠ
ߢ޽ࠆ‫ޕ‬/[ ᬌ಴↪ࡉ࡝࠶ࠫ࿁〝ߪ 'RMy1

 'RMy 4 ‫' ޔ‬RMy 2

'RMy 3 ߣߥࠅ‫ޔ‬಴ജߪ࠯ࡠߢ޽ࠆ‫ޕ‬/[ߦߟ޿ߡߪ /Z ߣห᭽ߩᬌ಴ᣇᴺߢ޽ࠆ‫ޕ‬Ԛ /\ ߩᬌ಴ශടജ /\ ߇࠮ࡦ࠲࡯ࡊ࡟࡯࠻ㇱߦടࠊߞߚ႐ว‫ޔ‬/\ ᬌ಴↪ࡉ࡝࠶ࠫ࿁〝ߩ㧠ߟߩࡇࠛ࠱ᛶ᛫⚛ሶߦ૞↪ߔࠆᔕജߪᰴߩࠃ߁ߦ⴫ߐࠇࠆ‫ޕ‬


VR

Mz 1

VR

Mz 3

V R

Mz 2

V R

Mz 4

                     㧔㧟㧚㧝㧤㧕ࠃߞߡ /\ ᬌ಴↪ࡉ࡝࠶ࠫ࿁〝ߩᛶ᛫ᄌൻߪ


'RMy1

'RMy 3

 'RMy 2

 'RMy 4                     㧔㧟㧚㧝㧥㧕θ㧙18ߣߥࠅ‫ޔ‬એਅߦ␜ߔ಴ജࠍᓧࠆߎߣ߇ߢ߈ࠆ‫ޕ‬

VoutMy'RMz1
Vin                             㧔㧟㧚㧞㧜㧕
RMz1
ߎߩߣ߈‫(ޔ‬Z‫ޔ\(ޔ[(ޔ‬/[‫ޔ‬/\ ᬌ಴↪ࡉ࡝࠶ࠫ࿁〝ߩᛶ᛫ᄌൻߪߘࠇߙࠇ 'RFx1'RFz1'RFz 2'RFz 3'RFz 4 ‫' ޔ‬RMx1'RMx 2'RMx 3'RMx 4 ‫' ޔ‬RMy1'RFx 2 ‫'ޔ‬RFy1'RMy 2'RMy 3'RFy 2 ‫ޔ‬'RMy 4 ߣߥࠅ‫ࠇߙࠇߘޔ‬ᑼ㧔㧟㧚㧟㧕㨪㧔㧟㧚㧤㧕ࠃࠅ (Z‫ޔ\(ޔ[(ޔ‬/Z‫ޔ‬/\ ᬌ಴↪ࡉ࡝࠶ࠫ࿁〝ߩ಴ജߪߘࠇߙ
ࠇ࠯ࡠߣߥࠆ‫ޕ‬Ԛ (/5(/5 ߩᬌ಴࿁〝
(/5 ߢߪ࿑㧟㧚㧝㧜㧚ߩࠃ߁ߦ㧟ߟߩ⁛┙ߒߚࡈ࡞ࡉ࡝࠶ࠫ࿁〝߇ᒻᚑߐࠇߡ޿ࠆ‫ޕ‬/Zࡉ࡝࠶ࠫ
ߪ /[ࡉ࡝࠶ࠫߣหߓ᭴ᚑߢ޽ࠆߚ߼⋭⇛ߒߚ‫ޕ‬Vin(RMx3)
RMy3

Vin(RMx2)RMy2

RZ2+R'Z2

VoutMy(Mx)
RMy4(RMx4)

RZ1+R'Z1
VoutFz

RMy1(RMx1)
groundRZ4+R'Z4      ࿑㧟㧚㧤㧚ࡉ࡝࠶ࠫ࿁〝

RZ3+R'Z3
groundߎߩߣ߈‫ޔ\(ޔ‬/Z‫ޔ‬/[ ߩᬌ಴↪ࡉ࡝࠶ࠫߩ಴ജ㔚࿶ VoutFz ‫ ޔ‬VoutMx ߪߘࠇߙࠇᑼ㧔㧟㧚㧞㧝㧕㨪㧔㧟㧚㧞㧟㧕ߢ⴫ߐࠇࠆ‫ޕ‬

VoutFz

1 'RFz1  'R 'Fz1 'RFz 3  'R 'Fz 3 'RFz 2  'R 'Fz 2 'RFz 4  'R 'Fz 4()Vin 㧔㧟㧚㧞㧝㧕

4 RFz1  R 'Fz1
RFz 3  R 'Fz 3
RFz 2  R 'Fz 2
RFz 4  R 'Fz 4

VoutMx

1 'RMx1 'RMx 3 'RMx 2 'RMx 4()Vin               㧔㧟㧚㧞㧞㧕
4 RMx1
RMx 3
RMx 2
RMx 4



VoutMy1 'RMy1 'RMy 3 'RMy 2 'RMy 4()Vin               㧔㧟㧚㧞㧟㧕
RMy 3
RMy 2
RMy 4
4 RMy1θ㧙19⴫㧟㧚㧠ߦ (/5‫࠱ࠛࡇߩ ޔ‬ᛶ᛫⚛ሶߩᛶ᛫୯ߩჇᷫ⴫ࠍ␜ߔ‫⴫ޕ‬ਛ̈ ̉‫ࠇߙࠇߘߪ̉̈ޔ‬Ⴧ‫ޔ‬ᷫࠍ⴫ߒ‫ޔ‬
̈̉ߪᄌൻ߇ߥ޿ߎߣࠍ␜ߒߡ޿ࠆ‫⴫ޕ‬ਛߩ✂ដߌㇱߪ‫ࠫ࠶࡝ࡉߩࠇߙࠇߘޔ‬࿁〝ߦ߅޿ߡ಴
ജ߇޽ࠆߎߣࠍ␜ߒߡ޿ࠆ‫ޕ‬⴫㧟㧚㧠 ࡇࠛ࠱ᛶ᛫⚛ሶߩᛶ᛫୯ߩჇᷫ⴫㧔(/5‫ޔ‬㧕Ԛ (\ ߩᬌ಴ශടജ (\ ߇࠮ࡦ࠲࡯ࡊ࡟࡯࠻ㇱߦടࠊߞߚ႐ว‫ \(ޔ‬ᬌ಴↪ࡉ࡝࠶ࠫ࿁〝ߩ㧤ߟߩࡇࠛ࠱ᛶ᛫⚛ሶߦ૞↪ߔࠆᔕജߪᰴߩࠃ߁ߦ⴫ߐࠇࠆ‫ޕ‬


VR

Fz 1

V Rc

Fz 1

VR

Fz 4

V Rc

Fz 4

V R Fz 2

V RFzc 2

V R cFz 3

V R cFz 3        㧔㧟㧚㧞㧠㧕ࠃߞߡ (\ ᬌ಴↪ࡉ࡝࠶ࠫ࿁〝ߩᛶ᛫ᄌൻߪ


'RFz1

'RFzc 1

'RFz 4'RFzc 4

 'RFz 2

 'RFzc 2

 'RFz 3

 'RFzc 3      㧔㧟㧚㧞㧡㧕ߣߥࠅ‫ޔ‬એਅߦ␜ߔ಴ജࠍᓧࠆߎߣ߇ߢ߈ࠆ‫ޕ‬

VoutFz'RFz1
Vin                             㧔㧟㧚㧞㧢㧕RFz1ߎߩߣ߈‫ ޔ‬/Z‫ޔ‬/[ ᬌ಴↪ࡉ࡝࠶ࠫ࿁〝ߩᛶ᛫ᄌൻߪߘࠇߙࠇ‫' ޔ‬RMx1'RMy1'RMy 2'RMy 3'RMx 2 'RMx 3'RMx 4 ‫ޔ‬'RMy 4 ߣߥࠅ‫ࠇߙࠇߘޔ‬ᑼ㧔㧟㧚㧞㧝㧕㨪㧔㧟㧚㧞㧟㧕ࠃࠅ /Z‫ޔ‬/[ ᬌ಴↪ࡉ࡝࠶ࠫ࿁〝ߩ಴ജߪߘࠇߙࠇ࠯ࡠߣߥࠆ‫ޕ‬Ԛ /Z ߩᬌ಴ශടജ /Z ߇࠮ࡦ࠲࡯ࡊ࡟࡯࠻ㇱߦടࠊߞߚ႐ว‫ޔ‬/Z ᬌ಴↪ࡉ࡝࠶ࠫ࿁〝ߩ㧠ߟߩࡇࠛ࠱ᛶ᛫⚛ሶߦ૞↪ߔࠆᔕജߪᰴߩࠃ߁ߦ⴫ߐࠇࠆ‫ޕ‬


VR

Mx 1

VR

Mx 3

V RMx 2

V RMx 4               㧔㧟㧚㧞㧣㧕θ㧙20ࠃߞߡ /Z ᬌ಴↪ࡉ࡝࠶ࠫ࿁〝ߩᛶ᛫ᄌൻߪ


'RMx1

'RMx 3

 'RMx 2

 'RMx 4             㧔㧟㧚㧞㧤㧕ߣߥࠅ‫ޔ‬એਅߦ␜ߔ಴ജࠍᓧࠆߎߣ߇ߢ߈ࠆ‫ޕ‬

1 'RMx1
Vin                    㧔㧟㧚㧞㧥㧕
2 RMx1

VoutMxߎ ߩ ߣ ߈ ‫ ޔ \( ޔ‬/[ᬌ ಴ ↪ ࡉ ࡝ ࠶ ࠫ ࿁ 〝 ߩ ᛶ ᛫ ᄌ ൻ ߪ ߘ ࠇ ߙ ࠇ ‫ޔ‬'RFz1  'RFzc 1'RFz 2  'RFzc 2'RFz 4  'RFzc 4'RFz 3  'RFzc 3

0 V RMy 1

VR

My 2

V RMy 3

V RMy 4 ‫ߥߣޔ‬ࠅ‫ޔ‬಴ജߪ࠯ࡠߢ޽ࠆ‫ޕ‬/[ ߦߟ޿ߡߪ /Z ߣห᭽ߩᬌ಴ᣇᴺߢ޽ࠆ‫ޕ‬Ԛ ᗵᐲߩ⸘▚Ԛ ᬌ಴࿁〝ߦ߅޿ߡ‫(ޔ‬/5㨪 ߩฦゲߩ಴ജ㔚࿶ࠍࡆ࡯ࡓㇱߦ߆߆ࠆᔕജߦࠃࠅ▚಴ߒߚ‫ߞࠃޕ‬ߡ ('/ ⸃ᨆߢ᳞߼ߚ࠮ࡦࠨߦශടߒߚജ෸߮ࡕ࡯ࡔࡦ࠻ߣߘߩߣ߈ߩࡆ࡯ࡓߦ⊒↢ߔࠆᔕജ୯ߩኻᔕߦ
ࠃߞߡᑼ㧔㧟㧚㧟㧜㧕㧔㧟㧚㧟㧝㧕ߦቯ⟵ߔࠆࠃ߁ߥജᗵᐲ S F ‫࠻ࡦࡔ࡯ࡕޔ‬ᗵᐲ S M ࠍ᳞߼ࠆߎߣ߇ߢ
߈ࠆ‫ޕ‬
SF

VoutF
                               㧔㧟㧚㧟㧜㧕
F



SM

VoutM
                              㧔㧟㧚㧟㧝㧕M⴫㧟㧚㧡ߪᑼࠍ↪޿ߡ᳞߼ߚ (/5㨪 ߩฦゲߩᗵᐲߢ޽ࠆ‫౉ޕ‬ജ㔚࿶ Vin ߪ 8 ߣߒߡ⸘▚ࠍⴕߞߡ޿ࠆ‫ޕ‬⴫㧟㧚㧡 ᭴ㅧ⸃ᨆࠍၮߦ▚಴ߒߚ (/5㨪 ߩᗵᐲ l u w u t

500 u 60 u 45(Pm3 ) ‫ ޔ‬Vin 5( O8O0 

5/ O80ǴO  

5(Z5([5(\5/Z5/[5/\(/5









(/5

 







(/5

 








θ㧙21

5(V ) Ԛ ⠨ኤ࿑㧟㧚㧥ߪ⴫㧟㧚㧝ߢ␜ߒߚᦨᄢශടജ‫⴫ޔ࠻ࡦࡔ࡯ࡕޔ‬㧟㧚㧡ߢ␜ߒߚᗵᐲࠍၮߦ (/5㨪 ߩ․ᕈ
ࠍᲧセߒߚ߽ߩߢ޽ࠆ‫ޔ\(ޕ‬/[ /Z ߣ߽ߦ (/5(/5(/5 ߩ㗅ߦශടߢ߈ࠆജ㧔ࡆ࡯ࡓߦ⊒↢ߔࠆᦨᄢᔕജ߇ /2C ߔࠆߣ߈ߩ (\㧕߇ᄢ߈ߊߥߞߡ߅ࠅ‫(ޔ‬/5 ߩ Fz max ߪ O0 My max Mx max
ߪ 0ǴO ߣ㧟ߟߩਛߢߪᦨ߽ᄢ߈ߥ୯ࠍ␜ߒߚ‫ޔ\(ޔߚ߹ޕ‬/[ /Z ߩᗵᐲߣ߽ߦ (/5(/5(/5ߩ㗅ߦᗵᐲߪ㜞ߊߥߞߡ߅ࠅ‫(ޔ‬/5 ߩ (\ ᗵᐲ㧔 Vin 8㧕ߪ O8O0‫ޔ‬/[㧔/Z㧕ᗵᐲߪ O80ǴOߣ  ߟߩਛߢᦨ߽㜞޿ᗵᐲ߇ᓧࠄࠇߚ‫ޕ‬ߎࠇࠄߩ⚿ᨐ߆ࠄหߓࡆ࡯ࡓߩኸᴺߢ߆ߟᦨ߽ᔕജߩ⊒↢ߔࠆ૏⟎ߦࡇࠛ࠱ᛶ᛫⚛ሶࠍ㈩⟎ߒߚߣ߈‫ߩࡓ࡯ࡆߩߘޔ‬ᡰᜬὐᢙߩჇടߦ઻޿ᦨᄢශടജ㧔ࡕ࡯ࡔࡦ࠻㧕ߪჇടߒ‫ߚ߹ޔ‬ᗵᐲߪૐਅߔࠆ‫ߟޕ‬߹ࠅ‫ᦨޔ‬ᄢශടജ㧔ࡕ࡯ࡔࡦ࠻㧕ߣᗵᐲߪ࠻࡟࡯࠼ࠝࡈߩ㑐ଥߦ޽ࠆߣ޿߃ࠆ‫ޕ‬㪩㪸㫅㪾㪼㩿㪝㫑㪀㪤㪸㫏㫀㫄㫌㫄㩷㫆㪽㩷㪙㪼㪸㫄㩷㫊㫋㫉㪼㫊㫊㩷䋼㪌㪇㪇㪤㪧㪸
㪉㪇㪇㪇
㪈㪍㪇㪇

㪝㫆㫉㪺㪼㩿㫄㪥㪀

㪈㪍㪇㪇
㪈㪉㪇㪇
㪏㪇㪇
㪏㪇㪇
㪋㪇㪇

㪉㪇㪇

㪇
㪝㪤㪪㪄㪈

㪝㪤㪪㪄㪉



㪝㪤㪪㪄㪊

C 
㪩㪸㫅㪾㪼㩿㪤㫏㪃㪤㫐㪀㪤㪸㫏㫀㫄㫌㫄㩷㫆㪽㩷㪙㪼㪸㫄㩷㫊㫋㫉㪼㫊㫊㩷䋼㪌㪇㪇㪤㪧㪸㪤㫆㫄㪼㫅㫋㩿㪥㱘㫄㪀

㪊㪇㪇

㪉㪋㪇

㪉㪌㪇
㪉㪇㪇
㪈㪌㪇
㪈㪇㪇

㪈㪈㪇

㪏㪇

㪌㪇
㪇
㪝㪤㪪㪄㪈

㪝㪤㪪㪄㪉

㪝㪤㪪㪄㪊



D 
㪊㪌
㪊㪈㪅㪍㪈
㪊㪇

㪝㫑㩿㫄㪭㪆㫄㪥㪀㪉㪌㪤㫐㩿㪤㫏㪀㩿㫄㪭㪆㪥㱘㫄㪀

㪉㪇
㪈㪌
㪐㪅㪏㪌

㪈㪇
㪌

㪋㪅㪏㪈
㪈㪅㪍㪈

㪉㪅㪏㪇
㪇㪅㪋㪈

㪇

㪝㪤㪪㪄㪈

㪝㪤㪪㪄㪉

㪝㪤㪪㪄㪊



E ᗵᐲߩᲧセ࿑㧟㧚㧥 (/5㨪 ߩᦨᄢශടജ C ࡮ᦨᄢශടࡕ࡯ࡔࡦ࠻ D ‫ޔ‬ᗵᐲ E ߩᲧセθ㧙22Ԛ ౣ⸳⸘ߎࠇ߹ߢ࠮ࡦࠨߩ᭴ㅧߦࠃࠆᕈ⢻Ყセߩߚ߼ (/5㨪 ߩࡆ࡯ࡓኸᴺࠍߘࠇߙࠇ╬ߒߊ NYV
3 ( Pm ) ߣߒߡ޿ߚ‫ߢߎߎޕ‬᳞߼ߚᦨᄢශടജ‫ᦨޔ‬ᄢශടࡕ࡯ࡔࡦ࠻‫ޔ‬ᗵᐲࠍၮߦౣ⸳⸘ࠍⴕߞ
ߚ‫⴫ޕ‬㧟㧚㧢‫⴫ޔ‬㧟㧚㧣ߦౣ⸳⸘ߒߚ (/5㨪 ߩᦨᄢශടജ࡮ᦨᄢශടࡕ࡯ࡔࡦ࠻‫ޔ‬ᗵᐲࠍ␜ߔ‫߹ޕ‬ߚ‫ޔ‬ઃ㍳ (㧚㧝ߦౣ⸳⸘ߒߚ (/5㨪 ߩ࿑㕙ࠍ␜ߒߚ‫ޕ‬





⴫㧟㧚㧢 ౣ⸳⸘ߒߚ࠮ࡦࠨߩᦨᄢශടജ࡮ᦨᄢශടࡕ࡯ࡔࡦ࠻(QTEG O0 

/QOGPV 0࡮ǴO 

5GPUKPIEJKR
l u w u t , ( Pm ) Fx max  Fy max 

Fz max 

Mx max  My max 

Mz max (/5  









(/5  









(/5  









3



⴫㧟㧚㧣 ౣ⸳⸘ߒߚ࠮ࡦࠨߩᗵᐲ Vin
5( O8O0 

5(V ) 5/ O80ǴO 

5GPUKPIEJKR
l u w u t , ( Pm ) 5(Z5([

5(\

5/Z5/[5/\

(/5  









(/5  











(/5  









3






ᒁ↪ᢥ₂

[13]
[14]

 F.Brinson: Engineered Materials Handbook Vol3 ‫ޔ‬ASM International, 1990
 A.S.Tetelman: Fracture Of Structural Materials, Wiley & Sons, 1967




θ㧙23

ԛ ࠮ࡦࠨ࠴࠶ࡊߩ⵾૞ߣ⹏ଔ
ԛ ⵾૞ࡊࡠ࠮ࠬߩᵹࠇ
࿑㧠㧚㧝ߪ࠮ࡦࠪࡦࠣ࠴࠶ࡊߩ⵾૞ࡊࡠ࠮ࠬߩᵹࠇ‫⴫ޔ‬㧠㧚㧝ߦ⵾૞ࡊࡠ࠮ࠬߩᎿ⒟ࠍ␜ߔ‫ޕ‬࿑㧠㧚㧞ߪ⵾૞ߒߚ࠮ࡦࠨߩ౮⌀ࠍ␜ߔ‫ޕ‬ ၮ᧼ߦߪ  㕙ߩ࠺ࡃࠗࠬጀ ǴO‫㉄ޔ‬ൻጀ Ǵ‫ޔ‬ၮ᧼ ǴO ߩ 51+ ࠙ࠛࡂࠍ↪޿ࠆ‫ޕ‬ ᾲ㉄ൻߦࠃߞߡ Ǵෘߩ 5K1 ࠍ⴫㕙ߩ਄ߦᒻᚑߔࠆ‫ޕ‬ ⚿᥏ᣇ૏  ߇ਥゲߣߥࠆࠃ߁ߦ 5K1㧞ߦࡇࠛ࠱ᛶ᛫⚛ሶߩࡄ࠲࡯ࡦ࠾ࡦࠣࠍⴕ߁‫ࡦࡠࡏޕ‬ߩ  Ბ㓏᜛ᢔ㧔࠺ࡐ࡚ࠫࠪࡦߣ࠼࡜ࠗࡉࠗࡦ㧕ߦࠃࠅ Rဳࡇࠛ࠱ᛶ᛫⚛ሶࠍᒻᚑߔࠆ‫ޕ‬㧕 ࡇࠛ࠱ᛶ᛫⚛ሶߣ #N ㈩✢㈩✢ࠍࠦࡦ࠲ࠢ࠻ߔࠆߚ߼ߦࠦࡦ࠲ࠢ࠻ࡎ࡯࡞ࠍࡄ࠲࡯ࡦ࠾ࡦࠣ‫࠴࠶ࠛޔ‬ࡦࠣߦࠃࠅᒻᚑߔࠆ‫ޕ‬ ǴO ෘߩ #N ㈩✢ࠍ⌀ⓨ⫳⌕‫ࠖࡈ࡜ࠣ࠰࡝࠻ࠜࡈޔ‬෸߮ࠛ࠶࠴ࡦࠣߦࠃߞߡᒻᚑߔࠆ‫ޕ‬#N ㈩✢ߣࡇࠛ࠱ᛶ᛫⚛ሶߩࠝ࡯ࡒ࠶ࠢធ⸅ࠍᓧࠆߚ߼ߦ‫ޔ‬㧺㧞㔓࿐᳇ਛߢࠪࡦ࠲࡝ࡦࠣࠍⴕ߁‫ޕ‬ ࠙ࠛࡂߩ೨㕙ࠍࡄ࠲࡯ࡦ࠾ࡦࠣ‫⃻ޔ‬௝ߒ‫ࠍࠢࠬࡑߩ↪ࠣࡦ࠴࠶ࠛࠗ࡜࠼ޔ‬ᒻᚑߒ +%24+' ߦࠃߞߡ࠺ࡃࠗࠬጀߩࡆ࡯ࡓࠍᒻᚑߔࠆ‫ޕ‬ ࠙ࠛࡂߩ⢛㕙ࠍ㧔㧢㧕ߣห᭽ߦ +%24+' ߦࠃߞߡၮ᧼ጀࠍࠛ࠶࠴ࡦࠣߔࠆߎߣߦࠃߞߡࡆ࡯ࡓࠍᒻ
ᚑߔࠆ‫ޕ‬ 4+' ߦࠃߞߡ㉄ൻጀࠍ㒰෰ߔࠆ‫ޕ‬ ࡄࠗ࡟࠶ࠢࠬࠟ࡜ࠬࠍࡄ࠲࡯ࡦ࠾ࡦࠣ‫ޕࠆߔࠣࡦ࠴࠶ࠛޔ‬ 㧔㧥㧕ߢ⵾૞ߒߚࠟ࡜ࠬࠍ㧔㧤㧕ߩ⢛㕙ߦ㓁ᭂធวߔࠆ‫ޕ‬

















θ㧙24

SOI wafer:
Device layer: 80 Pm
Box layer: 0.5-1 Pm
Substrate: 420 Pm<011>

Wire (W x T)
5 x 0.5 Pm2<100>- Al evaporation- Wire patterning- Al etching- Annealing<011>

1. Starting material           

5. Wiring (interconnection)



SiO2 : 0.3Pm- Al evaporating- Backside DRIE
- Buried SiO2 removing- Frontside DRIE

- Thermal oxidization

2. Oxidization













6. Crossbeam formation
Piezoresistor
3 x 30 Pm2- Photoresist spincoating on glass- Overload protection hole patterning- Photoresist spincoating- Piezoresistor patterning- SiO2 etching- Boron ion diffusion- B2O3 removing- Drive in

3. p-type piezoresistor formation(boron ion diffusion)- SiO․ etching- Anodic Bonding

7. Glass bonding    Contact hole:2 x 2 Pm2

- Photoresist spincoating- Contact holes patterning- SiO2 etching

4. Contact hole opening࿑㧠㧚㧝 ࠮ࡦࠪࡦࠣ࠴࠶ࡊߩ⵾૞ࡊࡠ࠮ࠬ



θ㧙25

 

  


C 㧲㧹㧿㧙㧝     D 㧲㧹㧿㧙㧞 E 㧲㧹㧿㧙㧟࿑㧠㧚㧞 ⵾૞ߒߚ࠮ࡦࠪࡦࠣ࠴࠶ࡊ
หߓ࠙ࠛࡂౝߩࡇࠛ࠱ᛶ᛫⚛ሶߩᛶ᛫୯ߩಽᏓ㧔᷹ቯὐᢙ㧦㧝㧜㧜ὐ㧕ࡇࠛ࠱ᛶ᛫ጀߩᷓߐ㧦⚂㧝㧞Ǵ㨙⴫㕙Ớᐲ㧦 ⚂㧡'㧝㧤㨏㨙㧟ᛶ᛫୯     㧔⸳⸘୯㧦㧝㨗ǡ㧕ᮡḰ஍Ꮕ㧔ǻ㧕㧦㧝㧢㧡ǡ      㧔㧝㧚㧣㧣㧑㧕      㧟ǻ㧩㧡㧚㧟㧑






㪋㪇
䉰䊮䊒䊦୘ᢙ㪥ᐔဋ୯㧦  㧥㧟㧝㧞ǡ

㪊㪇
㪉㪇
㪈㪇
㪇
㪏㪐㪇

㪐㪊㪇
㪐㪎㪇
ᛶ᛫୯㩿㱅㪀

࿑㧠㧚㧟 ᛶ᛫୯ߩಽᢔ


θ㧙26

㪈㪇㪈㪇



ԛ ࠮ࡦࠪࡦࠣ࠴࠶ࡊߩ⸘᷹ࠪࠬ࠹ࡓ
࿑㧠㧚 C ߪ࠮ࡦࠨ࠴࠶ࡊߩ⹏ଔߦ↪޿ߚ⸘᷹ࠪࠬ࠹ࡓߩ᭴ᚑ࿑ࠍ D ߪߘߩ౮⌀ߢ޽ࠆ‫࠴ࠨࡦ࠮ޕ‬࠶ࡊ ࿑ਛߦ␜ߔ 5GPUQTEJKR ߦᚲᦸߩജࠍශടߐߖࠆߚ߼ߦ࿑㧠㧚㧠ߦ␜ߔፉ࿑⵾ᓸዊ࿶❗⹜㛎ᯏ*/8㧔/KETQ+PFGPVGT㧕ߢജࠍශടߒ࠮ࡦࠨ࠴࠶ࡊ߆ࠄߩ಴ജ㔚࿶ࠍ MG[GPEG ⵾ࠕ࠽ࡠࠣ࠺ࠫ࠲࡞ࠦ ࡦ ࡃ ࡯ ࠲ 04 #& EQPXGTVGT ߢ ࠕ ࠽ ࡠ ࠣ ߆ ࠄ ࠺ ࠫ ࠲ ࡞ ା ภ ߳ ᄌ ឵ ߒ ߚ ߽ ߩ ࠍ 0'% ⵾
2%.#8+'0:.9* %QORWVGT ߦࠃࠅࡕ࠾࠲࡝ࡦࠣߒߚ‫ޕ‬ᓸ ዊ ࿶ ❗ ⹜ 㛎 ᯏ ߪ ࠳ ࠗ ࡗ ࡕ ࡦ ࠼ ࠍ ᧚ ᢱ ߣ ߔ ࠆ ࡆ ࠶ ࠞ ࡯ ࠬ ࿶ ሶ ߦ ࠃ ߞ ߡO0 ߩജߩශട߇น⢻ߢ޽ࠅ‫࡞ࡉ࡯࠹࠻ࡦࡔࠗ࡜ࠕޔ‬਄ߩ࠮ࡦࠨࠍ :;ᣇะߦ⒖േߐߖࠆߎߣߢ‫ޔ‬ജࠍශടߔࠆ૏⟎᳿߼ࠍⴕߞߚ‫࠻ࠬ࠹ޕ‬㧝ߣߒߡ‫࡯࡟ࡊ࡯࠲ࡦ࠮ߩࠨࡦ࠮ޔ‬࠻ਛᄩㇱߦ࠮ࡦࠨ࠴࠶ࡊߩ㕙ߦኻߒߡု⋥ߥജࠍශടߒߚ߽ߩࠍ (\ ߣߒ‫ߩࡊ࠶࠴ࠨࡦ࠮ߩ߈ߣߩߎޔ‬಴ജ㔚࿶ࠍ⸘᷹ߒߚ‫ޕ‬ᰴߦ࠹ࠬ࠻㧞ߣߒߡ࠮ࡦࠨ࠴࠶ࡊߩ࠮ࡦ࠲࡯ࡊ࡟࡯࠻ߩ┵㧔ਛᔃㇱ߆ࠄ ǴO㧕ߩ૏⟎ߦ࠮ࡦࠨ࠴࠶ࡊߩ㕙ߦኻߒߡု⋥ߥജࠍශടߔࠆߎߣߢ‫ ߣ \(ޔ‬/Z ߹ߚߪ /[ ࠍหᤨߦශടߒߚ‫ޕ‬C                    㨎                    㧔㨏㧕࿑㧠㧚㧟 ࠮ࡦࠪࡦࠣ࠴࠶ࡊߩ⸘᷹ࠪࠬ࠹ࡓ C ‫ޔ‬ജߩශടᣇᴺ D ፉ࿑⵾ᓸዊ࿶❗⹜㛎ᯏ */8㧔㨏㧕





θ㧙27

ԛ ⸘᷹⚿ᨐԛ (/5 ߩ⸘᷹ԛ (\ ߩ⸘᷹(\ ߩ⸘᷹ߪ࠮ࡦࠪࡦࠣ࠴࠶ࡊߩਛᄩㇱߦࠗࡦ࠺ࡦ࠲࡯ߦࠃࠅ⋥ធജࠍශടߔࠆߎߣߦࠃߞߡⴕ߁ ࿑㧠㧚㧠 ‫ޕ‬ශടߔࠆജߪ O0 ߆ࠄ O0 ߹ߢ O0 ߩࠬ࠹࠶ࡊߢჇടߐߖࠆ‫ޕ‬C     D E ࿑㧠㧚㧠 (/5 ߳ߩ (\ ߩශടᣇᴺ C 6QRXKGY D 5KFGXKGYE ⸘᷹ᤨߩ࠮ࡦࠨ࠴࠶ࡊߩ᭽ሶ
࿑㧠㧚㧡ߪ⸘᷹⚿ᨐߢ޽ࠆ‫౉ߪߢߎߎޕ‬ജ㔚࿶ࠍ㧞V ߣߒߡ⸘᷹ࠍⴕߞߚ‫ߩߎޕ‬࿑߆ࠄ Fz ࡉ࡝࠶ࠫ࿁〝ߩ಴ജ㔚࿶ VoutFz ߪ✢ᒻߢ޽ࠅ‫ࠫ࡝࠶ࡉߩઁޔ‬࿁〝ߦᲧߴᄢ߈ߥ಴ജࠍ⏕⹺ߢ߈ࠆ‫ ߚ߹ޕ‬Mx ࡉ࡝࠶ࠫ࿁〝ߩ಴ജ㔚࿶ VoutMx ‫ޔ‬My ࡉ࡝࠶ࠫ࿁〝ߩ಴ജ VoutMy ߪ‫ޔ‬VoutFz ߦᲧߴ㕖Ᏹߦዊߐߥ಴ജߢ޽ࠆ
ߎߣ߇⏕⹺ߢ߈ࠆ‫ޔ߈ߣߩߎޕ‬Fz ߩᗵᐲ߅ࠃ߮ࠢࡠࠬ࠻࡯ࠢߪએਅߩࠃ߁ߦ⸘▚ߢ߈ࠆ‫ޕ‬

S Fz

V Fz
=0.14(mV/mN)                       㧔㧠㧚㧝㧕Fz
θ㧙28

[ FzMx

V Mx
My‫ [ ޔ‬Fz
V Fz

Mx

V My
V Fz

                       (㧠㧚㧞㧕Myߎߎߢ [ Fz ‫ [ ޔ‬Fz ߪߘࠇߙࠇ Fz ࠍශടߒߚߣ߈ߩ Mx,My ࡉ࡝࠶ࠫ࿁〝ߩࠢࡠࠬ࠻࡯ࠢߢ޽ࠆ‫ޕ‬Fz ශ
My

Output Voltage(mV)ടᤨߩࠢࡠࠬ࠻࡯ࠢߩᦨᄢ୯ߪ [ Fz max
80
70

VMy / VFz

1.12 / 32.3 u 100

3.63% ߢ޽ࠆ‫ޕ‬

VFz
VMx

60
50
40
30

VMy
VFz-theory

20
10
0
0

100

200
300
Load(mN)

400࿑㧠㧚㧡 ශടജߣ಴ജ㔚࿶㧔Fz ߩ⸘᷹⚿ᨐ㧕 Vin

500

2(V )

ԛ My㧔Mx㧕ߩ⸘᷹ࡕ࡯ࡔࡦ࠻ My ࠍ⸘᷹ߔࠆߚ߼ߦ‫ࠨࡦ࠮ޔ‬ਛᔃㇱ߆ࠄ㨤ᣇะߦ 250Ǵm ߩ૏⟎ߦ F ࠍශടߒߚ㧔࿑㧠㧚㧢㧕‫ޔ߈ߣߩߎޕ‬Y ゲ๟ࠅߩࡕ࡯ࡔࡦ࠻ My ߣ Fz ߇࠮ࡦࠨਛᄩㇱ࠮ࡦ࠲࡯ࡊ࡟࡯࠻ߦടࠊࠆ‫ޕ‬Fz ߩ⸘᷹ߣห᭽ߦශടߔࠆജ F ߪ 100mN ߆ࠄ 500mN ߹ߢ 100mN ߩࠬ࠹࠶ࡊߢჇടߐߖࠆ‫ޔ߈ߣߩߎޕ‬My
ߪ F230(mNǴm)ߣߒߡ⸘▚ߔࠆߎߣ߇ߢ߈ࠆ‫ޕ‬

(a)

(b)



࿑㧠㧚㧢 FMS-1 ߳ߩ My ߩශടᣇᴺ
(a) Top view (b) Side view࿑㧠㧚㧣ߦ⸘᷹⚿ᨐࠍ␜ߔ‫ ޕ‬VoutFz ‫ ޔ‬VoutMy ߪ VoutMx ߦᲧߴᄢ߈ߥ୯ࠍ␜ߔ‫ޔ߈ߣߩߎޕ‬My ߩᗵᐲ߅ࠃ߮Mx

My ශടᤨߩ Mx ߩࠢࡠࠬ࠻࡯ࠢᦨᄢ୯ [ My max ߪᰴߩࠃ߁ߦߥࠆ‫ޕ‬

θ㧙29

S My

My

=1.76(mV/NǴm)VMx
100=4.49(%)㩷
VFz
Output Voltage(mV)[ MyMx max

VMy

200

VFz
VMx

150

VMy
VMz

100

VMy-theory

50
0
0

100

200

300

400

500

Load(mN)࿑㧠㧚㧣 ශടജߣ಴ജ㔚࿶㧔My ߩ⸘᷹⚿ᨐ㧕 Vin

2(V )ࡕ࡯ࡔࡦ࠻ Mx ߩ⸘᷹ߪ My ߣห᭽ߦ࠮ࡦࠨਛᔃㇱ߆ࠄ Y ᣇะߦ㧞㧟㧜Ǵm ߩ૏⟎ߦ F ࠍශടߒߚ‫ޕ‬ߎߩߣ߈‫ޔ‬X ゲ๟ࠅߩࡕ࡯ࡔࡦ࠻ Mx ߣ Fz ߇࠮ࡦࠨਛᄩㇱ࠮ࡦ࠲࡯ࡊ࡟࡯࠻ߦടࠊࠆ‫ޕ‬Fz ߩ⸘᷹ߣห
᭽ߦශടߔࠆജ F ߪ 100mN ߆ࠄ 500mN ߹ߢ 100mN ߩࠬ࠹࠶ࡊߢჇടߐߖࠆ‫ޕ‬Mx ߪ F230(mNǴm)ߣߒߡ⸘▚ߔࠆߎߣ߇ߢ߈ࠆ‫ޕ‬࿑㧠㧚㧤ߪ⸘᷹⚿ᨐߢ޽ࠆ‫ ޕ‬VoutFz ‫ ޔ‬VoutMx ߪ VoutMy ߦᲧߴᄢ߈ߥ୯ࠍ
My

␜ߔ‫ޔ߈ߣߩߎޕ‬Mx ߩᗵᐲ S Mx ߅ࠃ߮ࠢࡠࠬ࠻࡯ࠢᦨᄢ୯ [ Mx max ߪᰴߩࠃ߁ߦߥࠆ‫ޕ‬[ MxMy max

VMx=1.66(mV/NǴm)
Mx

VMy
VMx

100=1.39 (%)㩷200
Output Voltage(mV)

S Mx

VFz

150

VMx
VMy

100

Mx-theory

50
0
0

100

200
300
Load(mN)

400

500

࿑㧠㧚㧤 ශടജߣ಴ജ㔚࿶㧔Mx ߩ⸘᷹⚿ᨐ㧕 Vin

θ㧙30

2(V )

ԛ FMS-2 ߩ⸘᷹ԛ Fz ߩ⸘᷹

Fz ߩ⸘᷹ߪ FMS-1 ߣห᭽ߦ 100mN ߆ࠄ 500mN ߹ߢ࠮ࡦࠪࡦࠣ࠴࠶ࡊߩਛᄩㇱߦࠗࡦ࠺ࡦ࠲࡯ߦ
ࠃࠅ⋥ធജࠍශടߔࠆߎߣߦࠃߞߡⴕ߁(࿑㧠㧚㧥)‫ޕ‬

(a)

(b)
࿑㧠㧚㧥 FMS-2 ߳ߩ Fz ߩශടᣇᴺ
(a) Top view (b) Side view࿑㧠㧚㧝㧜ߦ Fz ߩ⸘᷹⚿ᨐࠍ␜ߔ‫౉ߪߢߎߎޕ‬ജ㔚࿶ࠍ㧞V ߣߒߡ⸘᷹ࠍⴕߞߚ‫ߩߎޕ‬࿑߆ࠄ Fz ࡉ࡝

Output Voltage(mV)࠶ࠫ࿁〝ߩ಴ജ㔚࿶ VoutFz ߪ✢ᒻߢ޽ࠅ‫ࠫ࡝࠶ࡉߩઁޔ‬࿁〝ߦᲧߴᄢ߈ߥ಴ജࠍ⏕⹺ߢ߈ࠆ‫ޕ‬

140
120
100
80
60
40
20
0

VFz
VMx
VMy
VFz-theory

0

100

200
300
Load(mN)

400

500

࿑㧠㧚㧝㧜 ශടജߣ಴ജ㔚࿶㧔Fz ߩ⸘᷹⚿ᨐ㧕 Vin

2(V )Fz ߩᗵᐲ߅ࠃ߮ࠢࡠࠬ࠻࡯ࠢߪએਅߩࠃ߁ߦ⸘▚ߢ߈ࠆ‫ޕ‬

S Fz[ FzMx max

VFz=0.18(mV/mN)
Fz

VMx
100=0.76%
VFzԛ My㧔Mx㧕ߩ⸘᷹ࡕ࡯ࡔࡦ࠻ My ࠍ⸘᷹ߔࠆߚ߼ߦ‫ޔ‬࿑㧠㧚㧝㧝ߦ␜ߔࠃ߁ߦ࠮ࡦࠨਛᔃㇱ߆ࠄ X ゲ਄ 270Pm ߩ૏⟎ߦ F ࠍශടߒߚ‫ޔ߈ߣߩߎޕ‬Y ゲ๟ࠅߩࡕ࡯ࡔࡦ࠻ My㧔 F270Pm㧕ߣ Fz ߇࠮ࡦࠨਛᄩㇱ࠮ࡦ࠲࡯ࡊ࡟࡯࠻ߦടࠊࠆ‫ޕ‬ශടߔࠆജ F ߪ 100mN ߆ࠄ 500mN ߹ߢ 100mN ߩࠬ࠹࠶ࡊߢჇടߐߖࠆ‫ޕ‬θ㧙31

(a) Top view(b) Side view࿑㧠㧚㧝㧝 FMS-2 ߳ߩ My ߩශടᣇᴺ

࿑㧠㧚㧝㧞ߪ⸘᷹⚿ᨐߢ޽ࠆ‫ ޕ‬VoutFz ‫ ޔ‬VoutMy ߪ VoutMx ߦᲧߴᄢ߈ߥ୯ࠍ␜ߒߡ޿ࠆߎߣ߇⏕⹺ߢ߈ࠆ‫ޕ‬Mxߎߩߣ߈‫ޔ‬My ߩᗵᐲ߅ࠃ߮ My ශടᤨߩ Mx ߩࠢࡠࠬ࠻࡯ࠢᦨᄢ୯ [ My max ߪᰴߩࠃ߁ߦߥࠆ‫ޕ‬

S My

My

=1.70(mV/NPm)

VMx
100=1.43%㩷
VMy
Output Voltage(mV)[ MyMx max

VMy

300
250
200
150
100
50
0

VFz
VMx
VMy
VMy-theory

0

100

200

300

400

500

Load(mN)࿑㧠㧚㧝㧞 ශടജߣ಴ജ㔚࿶㧔My ߩ⸘᷹⚿ᨐ㧕 Vin

2(V )ࡕ࡯ࡔࡦ࠻ Mx ߩ⸘᷹ߪ My ߣห᭽ߦ࠮ࡦࠨਛᔃㇱ߆ࠄ Y ᣇะߦ 270Pm ߩ૏⟎ߦ F ࠍශടߔࠆ‫ߩߎޕ‬ߣ߈‫ޔ‬X ゲ๟ࠅߩࡕ࡯ࡔࡦ࠻ Mx(F270)ߣ Fz ߇࠮ࡦࠨਛᄩㇱ࠮ࡦ࠲࡯ࡊ࡟࡯࠻ߦടࠊࠆ‫ޕ‬࿑㧠㧚㧝㧟ߪ⸘᷹⚿ᨐߢ޽ࠆ‫ޕ‬VoutFz ‫ޔ‬VoutMx ߪ VoutMy ߦᲧߴᄢ߈ߥ୯ࠍ␜ߔ‫ޔ߈ߣߩߎޕ‬Mx ߩᗵᐲ S Mx ߅ࠃ߮ࠢࡠ
Myࠬ࠻࡯ࠢᦨᄢ୯ [ Mx max ߪᰴߩࠃ߁ߦߥࠆ‫ޕ‬

S Mx[ MxMy max

VMx=1.72(mV/NPm)
Mx
VMy
VMx

100=2.05 (%)θ㧙32

Output Voltage(mV)

300
250
200
150
100
50
0

VFz
VMx
VMy
VMx-theory

0

100

200

300

400

500

Load(mN)࿑㧠㧚㧝㧟 ශടജߣ಴ജ㔚࿶㧔/Z ߩ⸘᷹⚿ᨐ㧕 Vin

2(V ) ԛ (/5 ߩ⸘᷹ԛ (\ ߩ⸘᷹(\ ߩ⸘᷹ߪ (/5 ߣห᭽ߦ O0 ߆ࠄ O0 ߹ߢ࠮ࡦࠪࡦࠣ࠴࠶ࡊߩਛᄩㇱߦࠗࡦ࠺ࡦ࠲࡯ߦࠃࠅ
⋥ធജࠍශടߔࠆߎߣߦࠃߞߡⴕ߁ ࿑㧠㧚㧝㧠 ‫ޕ‬

C 6QRXKGY D 5KFGXKGY࿑㧠㧚㧝㧠 (/5 ߳ߩ (\ ߩශടᣇᴺ
࿑㧠㧚㧝㧡㧚ߪ⸘᷹⚿ᨐߢ޽ࠆ‫౉ߪߢߎߎޕ‬ജ㔚࿶ࠍ㧞8 ߣߒߡ⸘᷹ࠍⴕߞߚ‫ߩߎޕ‬࿑߆ࠄ (\ ࡉ࡝࠶ࠫ࿁〝ߩ಴ജ㔚࿶ VoutFz ߪ✢ᒻߢ޽ࠅ‫ࠫ࡝࠶ࡉߩઁޔ‬࿁〝ߦᲧߴᄢ߈ߥ಴ജࠍ⏕⹺ߢ߈ࠆ‫ޕ‬

Output V oltage(mV )


50

VFz
VMx
VMy
VFz-theory

40
30
20

SFz

10

=

0
0

100

200

300

400

500

Load(mN)࿑㧠㧚㧝㧡 ශടജߣ಴ജ㔚࿶㧔(\ ߩ⸘᷹⚿ᨐ㧕(Bias voltage: 2V).

Fz ߩᗵᐲ߅ࠃ߮ࠢࡠࠬ࠻࡯ࠢߪએਅߩࠃ߁ߦ⸘▚ߢ߈ࠆ‫ޕ‬

S Fz

VFz
=0.087(mV/mN)
Fz[ FzMx max

VMx
100=4.52%
VFz
θ㧙33

ԛ My㧔Mx㧕ߩ⸘᷹ࡕ࡯ࡔࡦ࠻ My ࠍ⸘᷹ߔࠆߚ߼ߦ‫ࠨࡦ࠮ޔ‬ਛᔃㇱ߆ࠄ X ゲ਄ 350Pm ߩ૏⟎ߦ F ࠍශടߒߚ㧔࿑㧠㧚㧝㧢㧕‫ޔ߈ߣߩߎޕ‬Y ゲ๟ࠅߩࡕ࡯ࡔࡦ࠻ My㧔 F350Pm㧕ߣ Fz ߇࠮ࡦࠨਛᄩㇱ࠮ࡦ࠲࡯ࡊ࡟࡯࠻ߦ
ടࠊࠆ‫ޕ‬ශടߔࠆജ F ߪ 100mN ߆ࠄ 500mN ߹ߢ 100mN ߩࠬ࠹࠶ࡊߢჇടߐߖࠆ‫ޕ‬(a) Top view(b) Side view࿑㧠㧚㧝㧢 FMS-3 ߳ߩ My ߩශടᣇᴺ

࿑㧠㧚㧝㧣ߪ⸘᷹⚿ᨐߢ޽ࠆ‫ ޕ‬VoutFz ‫ ޔ‬VoutMy ߪ VoutMx ߦᲧߴᄢ߈ߥ୯ࠍ␜ߒߡ޿ࠆߎߣ߇⏕⹺ߢ߈ࠆ‫ޕ‬Mxߎߩߣ߈‫ޔ‬Mx ߩᗵᐲ߅ࠃ߮ Mx ශടᤨߩ My ߩࠢࡠࠬ࠻࡯ࠢᦨᄢ୯ [ My max ߪᰴߩࠃ߁ߦߥࠆ‫ޕ‬

S Mx

VMy
VMx

100=1.87 (%)㩷Output Voltage(mV)[ MxMy max

VMx=0.412(mV/NPm)
Mx

300
250
200
150
100
50
0

SMx = 0.412mV/NPm

VFz
VMx
VMy
VMx-theory

0

100

200
Load(mN)

300

400

500


࿑㧠㧚㧝㧣 ශടജߣ಴ജ㔚࿶㧔/Z ߩ⸘᷹⚿ᨐ㧕 8KP8 ࡕ࡯ࡔࡦ࠻ Mx ߩ⸘᷹ߪ My ߣห᭽ߦ࠮ࡦࠨਛᔃㇱ߆ࠄ Y ᣇะߦ 350Pm ߩ૏⟎ߦ F ࠍශടߔࠆ‫ߩߎޕ‬ߣ߈‫ޔ‬X ゲ๟ࠅߩࡕ࡯ࡔࡦ࠻ Mx(F350)ߣ Fz ߇࠮ࡦࠨਛᄩㇱ࠮ࡦ࠲࡯ࡊ࡟࡯࠻ߦടࠊࠆ‫ޕ‬࿑㧠㧚㧝㧤ߪ⸘᷹⚿ᨐߢ޽ࠆ‫ ޕ‬VoutFz ‫ ޔ‬VoutMx ߪ VoutMy ߦᲧߴᄢ߈ߥ୯ࠍ␜ߔ‫ޔ߈ߣߩߎޕ‬Mx ߩᗵᐲ S Mx ߅ࠃ߮ࠢMyࡠࠬ࠻࡯ࠢᦨᄢ୯ [ Mx max ߪᰴߩࠃ߁ߦߥࠆ‫ޕ‬

θ㧙34

S My

My

=0.412(mV/NPm)

VMx
100=1.25%
VMy
Output Voltage(mV)[ MyMx max

VMy

300
250
200
150
100
50
0

VFz
VMx
VMy
VMy-theory

0

100

200

300

400

500

Load(mN)࿑㧠㧚㧝㧤 ශടജߣ಴ജ㔚࿶㧔My ߩ⸘᷹⚿ᨐ㧕 Vin

2(V )࠮ࡦࠨ࠴࠶ࡊ FMS-1㨪3 ߩ⸘᷹ߦࠃߞߡᓧࠄࠇߚᗵᐲࠍ⴫㧠㧚㧞ߦ␜ߔ‫ޔߚ߹ޕ‬FMS-1㨪3 ߩฦゲߣ߽ࠢࡠࠬ࠻࡯ࠢߪ 5%એౝߢ޽ߞߚ‫ޕ‬⴫㧠㧚㧞 FMS-1㨪3 ߩ⸘᷹⚿ᨐ߆ࠄ▚಴ߒߚᗵᐲ Vin
Sensing-chip
3

SF(mV/mN)2(V )SM(mV/NǍm)l u w u t , ( Pm )

SFz

SMx

SMy

FMS-1(500×120×80)

0.14

1.76

1.66

FMS-2(800×100×80)

0.18

1.70

1.72

FMS-3(1000×100×80)

0.087

0.41

0.412

ԛ-4 ⠨ኤ㧔⸃ᨆ୯ߣߩᲧセ㧕㧟㧚㧥ౣ⸳⸘ߢ▚಴ߒߚ⸃ᨆ୯ߩᗵᐲࠍ Vin

2(V ) ߣߒߡ⴫ߣᲧセߒߚ‫⸃߈ߣߩߎޕ‬ᨆ୯ߦࠃߞߡ▚಴ߒߚᗵᐲࠍ S Analysis ‫⸘ޔ‬᷹ߦࠃߞߡ▚಴ߒߚᗵᐲࠍ S Measure ߒ‫⸃ޔ‬ᨆ୯ߣ⸘᷹୯ߩᏅ⇣ߩഀว 4 ࠍ·§ S
4 ¨1  Measure ¸ u 100%                           㧔㧠㧚㧟㧕¸¨ S
Analysis ¹©

ߣቯ⟵ߔࠆߣ‫ޔ‬FMS-1㨪3 ߩฦゲߩ 4 ߪ⸃ᨆ୯ߣ⸘᷹୯ߩᏅ⇣ߩഀว 4 ߩᐔဋ୯ߪ 5%એౝߢ޽ߞߚ‫ޕ‬Ԝ ᜰవ࠮ࡦࠨߩ᭴ㅧ⸃ᨆ
Ԝ ᭴ㅧ⸃ᨆߩ⋡⊛╙㧠┨ߢ⊒⴫ߒߚ࠮ࡦࠨ࠴࠶ࡊߪᨵエߥඨ⃿૕ធ⸅ㇱࠍ᦭ߔࠆᜰవ࠮ࡦࠨ߳ߣታⵝߐࠇࠆ‫ߩߎޕ‬㓙‫ޔ‬․ᕈߦᓇ㗀ߔࠆਥߥࡄ࡜ࡔ࡯࠲࡯ߣߒߡߪ࿑㧡㧚㧝ߦ␜ߔ⋥ᣇ૕ߩ࠻࡜ࡦࠬࡒ࠶࡚ࠪࡦࡇ࡜࡯ߩ㜞ߐ h
θ㧙35

2

㧔ᢿ㕙Ⓧߪ 0.350.35 mm 㧕‫ޔ‬෸߮ඨ⃿૕ធ⸅ㇱߩඨᓘ a ߢ޽ࠆ‫৻ߩ₸ᦛޕ‬ቯߥඨ⃿ߩਛᔃߪ࠮ࡦࠪࡦ
ࠣ࠴࠶ࡊ਄㕙ߩਛᄩㇱߦ޽ࠆ‫⸃ᧄޕ‬ᨆߩ⋡⊛ߪ᭴ㅧ⸃ᨆߦࠃࠅ‫ߩߎޔ‬ੑߟߩࡄ࡜ࡔ࡯࠲࡯ߩᦨㆡൻࠍ࿑
ࠆߣߣ߽ߦ‫ޔ‬ඨ⃿૕ធ⸅ㇱࠍ᦭ߒߚᜰవ࠮ࡦࠨߩᗵᐲ․ᕈࠍ᳞߼ࠆߎߣߢ޽ࠆ‫ޕ‬࿑㧡㧚㧝 ᭴ㅧ⸃ᨆߩࡄ࡜ࡔ࡯࠲࡯
㧔࠻࡜ࡦࠬࡒ࠶࡚ࠪࡦࡇ࡜࡯h‫ޔ‬ඨ⃿૕ធ⸅ㇱߩඨᓘ a㧕Ԝ ⸃ᨆᣇᴺ
ᧄ⎇ⓥߢ⵾૞ߔࠆඨ⃿૕ធ⸅ㇱߩࠃ߁ߥ☼ᒢᕈߩ᭴ㅧ‛ࠍ⸃ᨆߔࠆ႐ว‫ߥ߁ࠃߩࡦࠦ࡝ࠪޔ‬ᒢᕈ૕᧚ᢱ㧔ࡈ࠶ࠢߩᴺೣߦᓥ߁㧕ߣ⇣ߥࠅ᭴ㅧജቇߦ߅ߌࠆ㧟ߟߩ㕖✢ᒻ․ᕈߢ޽ࠆ᧚ᢱ㕖✢ᒻ‫ޔ‬ᐞ૗ቇ㕖✢ᒻ‫ޔ‬ធ⸅ߦ߅ߌࠆ㕖✢ᒻࠍ⠨ᘦߔࠆᔅⷐ߇޽ࠆ‫᧚ޕ‬ᢱ㕖✢ᒻߣߪᒢᕈ߿☼ᕈߩ㕖✢ᒻߢ޽ࠅ‫ޔ‬㧔ᔕജ㧕/㧔߭ߕߺ㧕߇ᔕജߩჇടߣ౒ߦჇടߔࠆ․ᕈߢ޽ࠆ‫ޕ‬ᐞ૗ቇ㕖✢ᒻߣߪኈᤃߦᄢᄌᒻߔࠆ᧚ᢱ߇᦭ߔࠆ
․ᕈߢ޽ࠅ‫ޔ‬ᄢᄌᒻߦ઻߁ᒻ⁁ᄌൻߣౝㇱᔕജᄌൻ߽ᔕജ́߭ߕߺ㑐ଥࠍ㕖✢ᒻൻߐߖࠆⷐ࿃ߢ޽ࠆ‫ޕ‬ធ⸅ߦ߅ߌࠆ㕖✢ᒻߣߪធ⸅ߔࠆ‛૕ߦኻߔࠆႺ⇇᧦ઙߦ㑐ߔࠆ߽ߩߢ‫᧚ޔ‬ᢱ߇‛૕ߦធ⸅ߒᄌൻߔࠆ
ߣ߈ធ⸅ߔࠆ‛૕ߦ᜔᧤ߐࠇߡ޿ࠆ⁁ᘒߢ޽ࠆ‫ޕ‬ኻ⽎ߣߔࠆ᭴ㅧ‛㧟ߟߩ㕖✢ᒻ․ᕈߩ޿ߕࠇ߆৻ߟߦߢ߽⹥ᒰߔࠆ႐ว‫ޔ‬㕖✢ᒻ⸃ᨆߩኻ⽎ߣߥࠅ‫ᧄޔ‬࠮ࡦࠨߦ↪޿ߚᨵエធ⸅ㇱ߿ੱ㑆ߩ⊹⤏ߥߤߪߎࠇࠄ㧟ߟߩ㕖✢ᒻ․ᕈࠍ߽ߟ‫⎇ᧄޕ‬ⓥߢߪ ANSYS 7.0
ߦࠃࠅ㕖✢ᒻ FEM ⸃ᨆࠍⴕߞߚ‫ޕ‬㕖✢ᒻ FEM ⸃ᨆߩᚻ㗅ߣߒߡߪ৻⥸⊛ߦ㕖✢ᒻ․ᕈࠍ᦭ߔࠆ᧚ᢱ
ߩ᭴ㅧ⸃ᨆࠍⴕ߁႐ว‫᧚ߩߘޔ‬ᢱ․ᕈࠍᓧࠆߚ߼ߩ⹜㛎ࠍⴕߞߚᓟ‫ޔ‬ᓧࠄࠇߚ․ᕈࠍ㕖✢ᒻࡕ࠺࡞ߦㆡ
ᔕߔࠆ‫ޕ‬
ߪߓ߼ߦ᧚ᢱ․ᕈࠍᓧࠆߚ߼ߦᔕജ㧙߭ߕߺߩ㑐ଥߪᜰవ࠮ࡦࠨߩᨵエߥធ⸅ㇱࠍᒻᚑߔࠆ߽ߩߣห
ߓ᧚ᢱߦࠃߞߡ࿑㧡㧚㧞ߦ␜ߔࠃ߁ߥඨᓘ r‫ޔ‬㜞ߐ l ߩ౞ᩇࠍ૞ᚑߒ‫ࠅࠃߦ࡯࠲ࠬ࠹ࡠࠢࠗࡑࠍࠇߎޔ‬࿶❗ߒ‫ޔ‬Ǎl ᄌ૏ߒߚߣ߈ߩജ F ࠍ㓐ᤨ⸘᷹ߒߚ‫ޕ‬Ǎl ᄌ૏ߒߚᓟߩ౞ᩇߩඨᓘࠍ r’‫ޔ‬㜞ߐ l’ߣߔࠆߣ‫ޔ‬ᄌ૏ᓟߩ㕙Ⓧ S’ߪᑼ㧔㧡㧚㧝㧕ߩࠃ߁ߦ⴫ߐࠇࠆ‫ޕ‬S ' Sr c 2§ lc ·©l ¹

2

S ¨ r ¸                           㧔㧡㧚㧝㧕ࠃߞߡ‫' ߺߕ߭ޔ‬l / l(l 'l ) / l ߩߣ߈‫ޔ‬౞ᩇ߇ฃߌࠆᔕജ P ߪᑼ㧔㧡㧚㧞㧕ߩࠃ߁ߦ⴫ߐࠇࠆ‫ޕ‬

θ㧙36

P

F
Sc

2

F §l·
¨ ¸                           㧔㧡㧚㧞㧕
Sr 2 © l ' ¹࿑㧡㧚㧞 ☼ᒢᕈࠧࡓߩ࿶❗
ᧄ⹜㛎ߢߪඨᓘ 1.5㨙㨙‫ޔ‬㜞ߐ 4cm ߩ⹜㛎ࠍ↪޿⹜㛎ࠍⴕ޿‫᧚ޔ‬ᢱߩ߭ߕߺ㧙ᔕജ․ᕈࠍ᳞߼ߚ‫ޕ‬⚿ᨐࠍ࿑㧡㧚㧟ߦ␜ߔ‫ޕ‬

6WUHVV 03D



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



















6WUDLQ࿑㧡㧚㧟 ߭ߕߺߣᔕജߩ㑐ଥ਄⸥ߩ࿶❗⹜㛎ߦࠃߞߡ᳞߼ߚᔕജ́߭ߕߺ࠺࡯࠲㈩೉ࠍ⿥ᒢᕈ૕⸃ᨆߦᦨㆡߥㄭૃᦛ✢ߦㆡᔕߔࠆߎߣߢߎࠇࠍ᧚ᢱቯᢙߣߒ‫⸃ޔ‬ᨆࠍⴕ߁‫ޕ‬ㄭૃᦛ✢ߦߪ Mooney-Rivlin ߩㄭૃℂ⺰ࠍ↪޿ߚߎࠇߪኈ
ᤃߦᄢᄌᒻࠍ⿠ߎߔ㧔ᒁߞᒛࠅߢ 100%‫ޔ‬࿶❗ߢ 30%⒟ᐲᄌൻߔࠆ㧕‛૕ߦኻߒ‫ᦨޔ‬ㆡߥㄭૃᦛ✢ࠍㆡᔕߔࠆ߽ߩߢ޽ࠆ‫⸃ޕ‬ᨆࡕ࠺࡞ߪ࿑㧡㧚㧠㧔a㧕ߦ␜ߔࠃ߁ߦ Si ࠍ᭴ㅧ᧚ᢱߣߒߚ࠮ࡦࠪࡦࠣ࠴࠶ࡊ෸
߮࠻࡜ࡦࠬࡒ࠶࡚ࠪࡦࡇ࡜࡯ߣ‫ޔ‬࿶❗⹜㛎ߢ᳞߼ߚ㕖✢ᒻ᧚ᢱ․ᕈࠍ߽ߟᒢᕈ૕ߩඨ⃿૕ធ⸅ㇱߦࠃߞߡ᭴ᚑߐࠇߡ޿ࠆ‫ޕ‬ඨ⃿૕ធ⸅ㇱߩඨᓘ‫ߩ࡯࡜ࡇࡦ࡚ࠪ࠶ࡒࠬࡦ࡜࠻ޔ‬㜞ߐߪߘࠇߙࠇ a=2mm ߣ2h=1.6mm ߢ޽ࠅ‫࡯࡜ࡇࡦ࡚ࠪ࠶ࡒࠬࡦ࡜࠻ޔ‬นേ▸࿐㧔0. 50. 5 mm 㧕ࠍ㒰ߊඨ⃿૕ធ⸅ㇱߩᐩ㕙ߪႺ⇇᧦ઙߦࠃࠅ᜔᧤ߐࠇࠆ㧔࿑㧡㧚㧠(b)㧕‫ޕ‬ߎߩࡕ࠺࡞ߦ࿑㧡㧚㧡ߦ␜ߔࠃ߁ߥ೰૕ߩ᧼ࠍඨ⃿૕ߩࠞࡃ࡯਄ㇱߦ⸳⟎ߒ‫ޔ‬ធ⸅㕙ߦኻߒု⋥ߥജFz’෸߮ធ⸅㕙ౝߩജ Ft’ࠍශടߔࠆ‫ޕ‬Ft’ߪ╙㧞┨ߢ␜ߒߚࠃ߁ߦȀ=Ǹ/2 ߩߣ߈ Ft’=Fy’‫ ޔ‬Ȁ=0 ߩߣ߈
Ft’=Fx’‫߈ߣߩߎޕࠆߥߣޔ‬ᒢᕈ૕ߩࠞࡃ࡯ߪኈᤃߦᄌᒻߔࠆߎߣ߆ࠄ೰૕ߩ᧼ߣ㕙ߢធ⸅ߔࠆߎߣߦߥ
ࠆ‫ޔ߈ߣߩߎޕ‬೰૕ߩ᧼ߣඨ⃿૕ߩࠞࡃ࡯ߩ㑆ߦߔߴࠅߪߥ޿߽ߩߣߔࠆ‫ߚ߹ޕ‬ធ⸅ߩ㕖✢ᒻᕈࠍ⠨ᘦߔࠆߣ‫ߩ࡯ࡃࠞޔ‬ᄌᒻߦࠃࠅ೰૕ߩ᧼ߪ᜔᧤ߐࠇࠆߎߣ߆ࠄ‫ޔ‬ANSYS7.0 ߢߪ㧟ᰴరߩធ⸅‫ޔ‬TARGE
θ㧙37

170,CONTA173 ࠍቯ⟵ߔࠆ‫ޕ‬ඨ⃿૕ធ⸅ㇱ
㧔㕖✢ᒻ᧚ᢱ․ᕈ㧕 ࠮ࡦࠪࡦࠣ࠴࠶ࡊ
㧔✢ᒻ᧚ᢱ․ᕈ㧕(a)     (b)࿑㧡㧚㧠 (a)㧲㧱㧹⸃ᨆࡕ࠺࡞‫(ޔ‬b)ඨ⃿૕ᐩ㕙ߩ᜔᧤࿑㧡㧚㧡 ജߩශടᣇᴺ㧔ធ⸅㕙ߦኻߒု⋥ߥജ Fz’෸߮ធ⸅㕙ౝߩജ Ft’㧕θ㧙38Ԝ ⸃ᨆ⚿ᨐ⸃ᨆ⚿ᨐߦࠃࠅ FMS1㨪㧟ࠍ៞タߒߚᜰవ࠮ࡦࠨߩᗵᐲࠍ᳞߼ࠆ‫ޕ‬Fz’‫ޔ‬Fx’(Fy’)ࠍ೰૕ߩ਄ㇱߦශടߒߚߣ߈ߩฦ࠮ࡦࠪࡦࠣ࠴࠶ࡊߩࡆ࡯ࡓߦ߆߆ࠆᔕജ୯ߦࠃࠅ㧠┨ߣห᭽ߦᗵᐲࠍ⸘▚ߒߚ‫౉ޕ‬ജ㔚࿶ߪ 5V ߢ޽ࠆ‫ޕ‬⴫㧡㧚㧝 ⸃ᨆ⚿ᨐ߆ࠄ⸘᷹ߒߚᗵᐲ a=2mm h=1.6mm‫ ޔ‬Vin

5(V )SF’(mV/mN)

Fingertip-sensor

SFz’

SFx’, SFy’

FMS-1P

0.21㩷

1.02㩷

FMS-2P

0.24㩷

1.18㩷

FMS-3P

0.04㩷

0.21㩷


ԝ ᜰవ࠮ࡦࠨߩታⵝߣ⹏ଔ
ԝ ᜰవ࠮ࡦࠨߩታⵝࡊࡠ࠮ࠬ
࿑㧢㧚㧝ߦᜰవ࠮ࡦࠨߩߩ᭴ㅧ࿑ߣኸᴺࠍ␜ߔ‫ޕ‬࿑㧢㧚㧞ߣ⴫㧢㧚㧝ߦታⵝࡊࡠ࠮ࠬߩᎿ⒟ߣ૞ᬺᣇᴺࠍ␜ߔ‫ޕ‬(1)FR4 ᧚⾰ 㧠ጀၮ᧼(࿑ਛ Printed circuit board)ߦ࠮ࡦࠪࡦࠣ࠴࠶ࡊࠍធ⌕ߔࠆ‫ޕ‬ធ⌕ߪࠛࡐࠠࠪ᮸
⢽ࠍ↪޿ߚ‫ޕ‬(2)࠮ࡦࠪࡦࠣ࠴࠶ࡊߩࡏࡦ࠺ࠖࡦࠣࡄ࠶࠼ߣၮ᧼ߩ㈩✢ࠍ㊄✢(Au wire)ߢࡏࡦ࠺ࠖࡦࠣߔࠆ‫ߣߩߎޕ‬߈ FMS-1P ߪ FMS-1 ߩ Mx‫ޔ‬My‫ޔ‬Fz‫ޔ‬Mz ⸘᷹↪ࡉ࡝࠶ࠫߩߺၮ⋚਄ߩ㔚ᭂߦធ⛯ߔࠆ㧔⸘㧠ゲ㧕‫ޕ‬FMS-2P‫ޔ‬3P ߪ FMS-2‫ޔ‬3 ߩ Mx‫ޔ‬My‫ޔ‬Fz‫⸘ޔ‬᷹↪ࡉ࡝࠶ࠫࠍၮ⋚ߦធ⛯ߔࠆ㧔⸘㧟ゲ㧕‫ޕ‬(3)ࡊ࡜ࠬ࠴࠶ࠢ⵾ࠤ࡯ࠬ(Case)ࠍࠛࡐࠠࠪ᮸⢽ߦࠃࠅធ⌕ߔࠆ‫ߩࠬ࡯ࠤޕ‬ਛᄩㇱߩⓣ߆ࠄ࠻࡜ࡦࠬࡒ࠶
࡚ࠪࡦࡇ࡜࡯(Transmission pillar)ࠍ࠮ࡦࠪࡦࠣ࠴࠶ࡊߩਛᄩㇱ࠮ࡦ࠲࡯ࡊ࡟࡯࠻ߦࠛࡐࠠࠪ᮸⢽ߦࠃࠅធ⌕ߔࠆ‫ޕ‬(4)Alignment spacer ࠍធ⌕ߔࠆ‫ ߩߎޕ‬spacer ࠍ࠻࡜ࡦࠬࡒ࠶࡚ࠪࡦࡇ࡜࡯๟ࠅߦ⸳⟎ߒ‫ߩߘޔ‬਄߆ࠄ
Soft hemisphere ߩធ⸅ㇱࠍធ⌕ߔࠆ‫ޕ‬ធ⌕ߪធ⸅ㇱߣห᧚ᢱߩࡐ࡝࠙࡟࠲ࡦߢⴕ߁‫ޕ‬(5)ၮ᧼ߦࠦࡀࠢ࠲ࠍធ⌕ߒ‫ࠍ࡞ࡉ࡯ࠤ࡞ࡉࠪࠠ࡟ࡈߦ࠲ࠢࡀࠦޔ‬ធ⛯ߔࠆࡈ࡟ࠠࠪࡉ࡞ࠤ࡯ࡉ࡞ߪ⸘㧝㧟࠴ࡖࡀ࡞ߩ⁛┙ߒߚ㈩✢ߢ޽ࠆ‫ޕ‬એਅ‫ ࡊ࠶࠴ࠣࡦࠪࡦ࠮ޔ‬FMS-1‫ޔ‬FMS-㧞‫ޔ‬FMS-3 ࠍታⵝߒߚᜰవ
࠮ࡦࠨࠍߘࠇߙࠇ FMS-1P‫ޔ‬FMS-2P‫ޔ‬FMS-3P ߣߔࠆ‫ޕ‬θ㧙39࿑㧢㧚㧝 ᜰవ࠮ࡦࠨߩ᭴ㅧ࿑ߣኸᴺ
Soft hemisphere

Alignment spacer

Transmission pillar

Cover
Connector
Sensin chip
Flexible cable
Au wirePrinted circuit board࿑㧢㧚㧞 ᜰవ࠮ࡦࠨߩታⵝࡈࡠ࡯࿑

⴫㧢㧚㧝 ᜰవ࠮ࡦࠨߩታⵝߩᎿ⒟ߣ૞ᬺᣇᴺ

θ㧙40

ࠦࡀࠢ࠲
ធ⸅ㇱ

ၮ᧼
ࠤ࡯ࠬ
࿑㧢㧚㧟 ⵾૞ߒߚᜰవ࠮ࡦࠨߩో૕౮⌀ࡇ࡜࡯࠮ࡦࠨ࠴࠶ࡊ
㊄✢ࠟ࡜ࠬࡌ࡯ࠬ

࿑㧢㧚㧠 ⵾૞ߒߚᜰవ࠮ࡦࠨߩᢿ㕙౮⌀θ㧙41ԝ Fz’ߩ⸘᷹ԝ ࡑࠗࠢࡠ࠹ࠬ࠲࡯ࠍ↪޿ߚ⸘᷹ࠪࠬ࠹ࡓ
࿑㧢㧚㧡ߪ⵾૞ߒߚᜰవ࠮ࡦࠨߩ⹏ଔߦ↪޿ߚ⸘᷹ࠪࠬ࠹ࡓߩ᭴ᚑ࿑ࠍ࿑㧢㧚㧢ߪߘߩ౮⌀ߢ޽ࠆ‫ޕ‬࠮ࡦࠨ࠴࠶ࡊ(࿑ਛ Sensor)ߦᚲᦸߩജࠍශടߐߖࠆߚ߼ߦ‫࡯࠲ࠬ࠹ࡠࠢࠗࡑ⵾ࡦࡠ࠻ࠬࡦࠗޔ‬㧔࿑ਛ
Micro Tester㧕ߢജࠍශടߒߘࠇࠍࡕ࠾࠲࡝ࡦࠣߒߚ‫⋥ုߪ࡯࠲ࠬ࠹ࡠࠢࠗࡑޕ‬㒠ਅߔࠆࡠ࠶࠼ㇱ‫⹜ޔ‬㛎ߦടࠊߞߚജࠍᗵ⍮ߔࠆࡠ࡯࠼࠮࡞ㇱ‫⹜߇࠼࠶ࡠޔ‬㛎ߦട߃ࠆജ߿⒖േㅦᐲߥߤࠍ೙ᓮߔࠆࠦࡦ

࠻ࡠ࡯࡞ㇱ߆ࠄ᭴ᚑߐࠇߡ޿ࠆ‫࡞࠮࠼࡯ࡠޕ‬ㇱߦߪᦨᄢශടน⢻ߥᔕജ߇ 10N‫ޔ‬ಽ⸃⢻߇ 0.01N ߩࡠ࡯࠼࠮࡞ࠍ↪޿ߚ‫ޕ‬੹࿁⹜㛎ߦ૶↪ߒߚ⸘᷹↪ᴦౕߪ࠮ࡦࠨߦട߃ࠆශടࡠ࠶࠼㧔ᜰవ࠮ࡦࠨߩඨ⃿૕ធ⸅ㇱߦኻߒචಽ
ᄢ߈ߥធ⸅㕙ࠍᜬߟ೰૕ߢ޽ࠆ㧕‫ޔ‬෸߮ Fz ⸘᷹↪ࠬ࠹࡯ࠫ‫ޔ‬Fx(Fy)⸘᷹↪ࠬ࠹࡯ࠫߢ޽ࠆ‫ޕ‬Fz ⸘᷹↪
ࠬ࠹࡯ࠫߪ࠮ࡦࠨࠍߘߩਛᄩㇱߦ࿕ቯߔࠆߎߣߢ࠮ࡦࠨߩ਄ㇱߦ᳓ᐔ㕙ߦኻߒု⋥ߥജࠍශടߔࠆߎ
ߣ߇ߢ߈ࠆ‫⸘ޕ‬᷹↪ᴦౕߪࠕ࡞ࡒ࠾࠙ࡓ᧚ࠍ᧚ᢱߣߒ‫ޔ‬10N એਅߩ⸘᷹ߦ߅޿ߡචಽߥᒝᐲࠍᜬߟࠃ߁
⸳⸘ߐࠇߡ޿ࠆ(࿑㧢㧚㧢)‫ޕ‬࠮ࡦࠨ಴ജ㔚࿶ࠍ⸘᷹ߒߚ‫ᧄޔߚ߹ޕ‬ታ㛎ߢߪ㕒⊛࿶❗⹜㛎ࠍⴕ߁ߚ߼ࡠ࠶࠼ߩㅦᐲࠍ 0.1mm/secߒ‫⋡ޔ‬ᮡශടജߦ㆐ߒߚᓟ 5sec ஗ᱛᓟ࡝࠲࡯ࡦߔࠆ߽ߩߣߔࠆ‫ޕ‬(

Micro Tester
Fingertip sensor

Fingertip sensor
Power supply

AD converter࿑㧢㧚㧡 ⸘᷹ࠪࠬ࠹ࡓߩ᭎ⷐ࿑

θ㧙42ශടࡠ࠶࠼

ࡑࠗࠢࡠ࠹ࠬ࠲࡯

⸘᷹↪ࠬ࠹࡯ࠫ

PC

A/D C
㔚Ḯ

࿑㧢㧚㧢 ⸘᷹ࠪࠬ࠹ࡓߩ౮⌀ԝ ⸘᷹⚿ᨐ࿑㧢㧚㧣㨪࿑㧢㧚㧥ߪߘࠇߙࠇ FMS1㨪3 ߩ࠮ࡦࠪࡦࠣ࠴࠶ࡊࠍ៞タߒߚᜰవ࠮ࡦࠨߦജ 100㨪500mN

OutputVoltage(m V)߹ߢ 100mN ࠬ࠹࠶ࡊߕߟශടߒߚߣ߈ߩ಴ജ㔚࿶ࠍ⴫ߒߡ޿ࠆ‫ޕ‬
40

VFz'

30

VMx'

20

VMy'

10
0
0

100

200

300

400

500

Load(mN)

Output Voltage(mV)࿑㧢㧚㧣 FMS-1P ߩශടജߣ಴ജ㔚࿶ߩ㑐ଥ Vin

2(V )

50
40

VFz'

30

VMx'
VMy'

20
10
0
0

100

200

300

400

500

Load(mN)࿑㧢㧚㧤 FMS-2P ߩශടജߣ಴ജ㔚࿶ߩ㑐ଥ Vin

θ㧙43

2(V )

Output Voltage(mV)

8
7
6
5
4
3
2
1
0

Fz'
Mx'
My'

0

100

200

300

400

Load(mN)࿑㧢㧚㧥 FMS-3P ߩශടജߣ಴ജ㔚࿶ߩ㑐ଥ Vin

2(V )FMS-1P㨪3P ߩ Fz’ߩᗵᐲ SFz’‫ޔ‬෸߮ࠢࡠࠬ࠻࡯ࠢߩᦨᄢ୯ [ Fz max ࠍ߹ߣ߼ߚ߽ߩࠍ⴫㧢㧚㧞ߦ␜ߔ‫ޕ‬⴫㧢㧚㧞 FMS-1P㨪3P ߩ Fz’ߩᗵᐲ㧔 Vin

2(V ) 㧕䈫ࠢࡠࠬ࠻࡯ࠢߩᦨᄢ୯

㩷㩷

SF㫑㵭㩿㪭㪆㪥㪀㩷[ Fz max 㩿㩼㪀㩷㪝㪤㪪㪄㪈㪧㩷

㪇㪅㪇㪏㪌㩷 㩷㪌㪅㪐㩷 㩷

㪝㪤㪪㪄㪉㪧㩷

㪇㪅㪇㪐㪌㩷 㩷㪍㪅㪍㩷 㩷

㪝㪤㪪㪄㪊㪧㩷

㪇㪅㪇㪈㪊㩷 㩷㪎㪅㪊㩷 㩷

θ㧙44ԝ-3 Fx’(Fy’)ߩ⸘᷹
ԝ-3-1 ࡠࡏ࠶࠻ࡂࡦ࠼ࠍ↪޿ߚ⸘᷹ࠪࠬ࠹ࡓ
࿑㧢㧚㧝㧜ߦ␜ߔࠃ߁ߦ㧞ߟߩᜰవ࠮ࡦࠨࠍߘࠇߙࠇะ߈ว߁ࠃ߁ߦࡠࡏ࠶࠻ࡂࡦ࠼(TAKANOBEARING.Co ⵾ Mu-Gripper RH707)ߩ㧞ᜰߦⵝ⌕ߒ‫⾰ޔ‬㊂ M ߩ‛૕ߩ㊀ᔃࠍᛠᜬߔࠆ‫࠮߈ߣߩߎޕ‬ࡦࠨߦߪᛠᜬജߦኻߔࠆ෻૞↪ߩജ Fz’㧔ធ⸅㕙ߦኻߒߡု⋥ߥജ㧕෸߮‫‛ޔ‬૕ߩ⥄㊀ߦࠃࠆജ Mg㧔g
ߪ㊀ജടㅦᐲ㧕ߦࠃࠆജ Ft’߇ᜰవ࠮ࡦࠨߣ‛૕ߩធ⸅㕙ౝߦ૞↪ߔࠆ㧔╙ੑ┨ࠍෳᾖߔࠆߣ‫ޔ‬Ȁ=Ǹ/2
ߩߣ߈ Ft’=Fy’‫ ޔ‬Ȁ=0 ߩߣ߈ Ft’=Fx’‫ࠆߥߣޔ‬㧕‫ޕ‬ᜰవ࠮ࡦࠨߪ㧞ኻ↪޿ࠄࠇߡ޿ࠆߚ߼৻ߟߩᜰవ࠮
ࡦࠨߦ૞↪ߔࠆജߪ Ft’=Mg/2 ߢ޽ࠆ‫ޕ‬ᛠᜬ‛૕ߦߪဋ৻ߥኒᐲߩ⾰㊂ 35.7g ߩࠕ࡞ࡒ࠾࠙ࡓߩ⋥ᣇ૕(14147mm)ࠍ↪޿ߚ‫ޕ‬㊀ജടㅦᐲࠍ
9.8m/s2 ߣߔࠆߣ‫⋥ߩࡓ࠙࠾ࡒ࡞ࠕޔ‬ᣇ૕߇㧞ኻߩᜰవ࠮ࡦࠨߦ૞↪ߔࠆജߪ 35.79.8ѳ350(mN)ߢ޽
ࠆ‫ߩߟ৻ߡߞࠃޕ‬ᜰవ࠮ࡦࠨߦ૞↪ߔࠆജߪ Ft’=350/2=175(mN)ߢ޽ࠆ‫⹜ᧄޕ‬㛎ߢߪࠕ࡞ࡒ࠾࠙ࡓߩ⋥ᣇ૕ࠍ⸘㧠ߟߦߥࠆ߹ߢ৻ߟߕߟჇ߿ߒߡ޿ߞߚ‫ޕ‬n ୘ߩߣ߈‫ޔ‬Ft’=175n(N)ߣߥࠆ‫⹜ߥ߁ࠃߩߎޕ‬㛎ࠍȀ=Ǹ/2 ‫ޔ‬Ȁ=0 ߔߥࠊߜ Ft’=Fy’‫ ޔ‬Ft’=Fx’ߩੑㅢࠅߦߟ޿ߡ‫ޔ‬FMS1㨪3P ߩ಴ജ㔚࿶ࠍߘࠇߙࠇ
⹏ଔߔࠆ‫ޕ‬6HQVRU
2EMHFW
*ULSSHU

࿑㧢㧚㧝㧜 ࡠࡏ࠶࠻ࡂࡦ࠼ࠍ↪޿ߚ⸘᷹ࠪࠬ࠹ࡓ  ࿑㧢㧚㧝㧝 ࡠࡏ࠶࠻ࡂࡦ࠼ߦⵝ⌕ߩ౮⌀θ㧙45

ԝ-3-2 ⸘᷹⚿ᨐ
ԝ-3-2-1 FMS-1P ߩ⸘᷹⚿ᨐ

Output Voltage(mV)࿑㧢㧚㧝㧞‫ޔ‬࿑㧢㧚㧝㧟ߦߘࠇߙࠇȀ=0‫ޔ‬Ǹ/2 ߩߣ߈ߩ FMS-1P ߩ⸘᷹⚿ᨐߩࠣ࡜ࡈࠍ␜ߔ‫ޕ‬
30
25
20
15
10
5
0

VMx'
VMy'
VMz'

0

175

350

525

700

Half of the weight of gripped object(mN)

Output Voltage(mV)࿑㧢㧚㧝㧞 FMS-1P ߩ⸘᷹⚿ᨐȀ=0‫ ޔ‬Vin

30
25
20
15
10
5
0

2(V )

VFx'
VMy'

0

175

350

525

700

Load(mN)࿑㧢㧚㧝㧟 FMS-1P ߩ⸘᷹⚿ᨐȀ=Ǹ/2‫ ޔ‬Vin2(V )ԝ-3-2-2 FMS-2P ߩ⸘᷹⚿ᨐ

Output Voltage(mV)࿑㧢㧚㧝㧠‫ޔ‬࿑㧢㧚㧝㧡ߦߘࠇߙࠇȀ=0‫ޔ‬Ǹ/2 ߩߣ߈ߩ FMS-2P ߩ⸘᷹⚿ᨐߩࠣ࡜ࡈࠍ␜ߔ‫ޕ‬
60
50
40
30
20
10
0

VMx'
VMy'

0

200

400

600

800

Load(mN)

Output Voltage(mV)࿑㧢㧚㧝㧠 FMS-2P ߩ⸘᷹⚿ᨐȀ=0‫ ޔ‬Vin
50
40
30
20
10
0

2(V )

VMx'
VMy'

0

175

350

525

700

Load(mN)࿑㧢㧚㧝㧡 FMS-2P ߩ⸘᷹⚿ᨐȀ=Ǹ/2‫ ޔ‬Vin

θ㧙46

2(V )

ԝ-3-2-3 FMS-3P ߩ⸘᷹⚿ᨐ

Output Voltage(mV)࿑㧢㧚㧝㧢‫ޔ‬࿑㧢㧚㧝㧣ߦߘࠇߙࠇȀ=0‫ޔ‬Ǹ/2 ߩߣ߈ߩ FMS-3P ߩ⸘᷹⚿ᨐߩࠣ࡜ࡈࠍ␜ߔ‫ޕ‬
5
4

Mx'

3

My'

2
1
0
0

175

350

525

700

Half of the Weight of Gripping Objects(mN)O u tp u t V o lta g e (m V )࿑㧢㧚㧝㧢 FMS-3P ߩ⸘᷹⚿ᨐȀ=0‫ ޔ‬Vin
5
4
3
2
1
0

2(V )

VMx'
VMy'

0

175

350

525

700

Half of the Weight of Gripping Objects(mN)࿑㧢㧚㧝㧣 FMS-3P ߩ⸘᷹⚿ᨐȀ=Ǹ/2‫ ޔ‬Vin

2(V )ԝ-4 ࡠࡏ࠶࠻ࡂࡦ࠼ࠍ↪޿ߚ Mz ߩ⸘᷹(FMS-1P ߩߺ)
ԝ-4-1 ⸘᷹ᣇᴺᰴߦ࿑㧢㧚㧝㧤ߦ␜ߔࠃ߁ߦ FMS-1P ߦࠃࠅࠕ࡞ࡒ࠾࠙ࡓߩ㊀ᔃ G ߆ࠄ l ߩ〒㔌ߩ C ὐࠍᛠᜬߔࠆߣ
߈‫ޔ‬Fz’‫ ޔ‬Ft’ߦട߃ C ߩ๟ࠅߩࡕ࡯ࡔࡦ࠻ Mz’߇ FMS-1P ߦ૞↪ߔࠆ‫⋥ߩࡓ࠙࠾ࡒ࡞ࠕޕ‬ᣇ૕㨚୘ࠍᛠᜬߔࠆߣ߈ Mz’=175㨚l ߢ޽ࠆ‫ ߢߎߎޕ‬l=12mm ߣߔࠆ‫ޕ‬࿑㧢㧚㧝㧤 ࡠࡏ࠶࠻ࡂࡦ࠼ࠍ↪޿ߚ Mz ߩ⸘᷹(FMS-1P ߩߺ)θ㧙47ԝ-4-2 ⸘᷹⚿ᨐ

Output Voltage(mV)࿑㧢㧚㧝㧥ߦ㨚㧩1㨪㧠ߩߣ߈ߩ FMS-1P ߩ⸘᷹⚿ᨐࠍ␜ߔ‫ޕ‬
30
25
20
15
10
5
0

VMz'
VMy'
VMx'

0

175

350

525

700

Half of the weight of gripped object(mN)࿑㧢㧚㧝㧥 FMS-1P ߩ⸘᷹⚿ᨐȀ=Ǹ/2ԝ-5 ߹ߣ߼
ᜰవ࠮ࡦࠨ FMS-1㨪3P ߩ⸘᷹ߦࠃߞߡᓧࠄࠇߚᗵᐲࠍ⴫㧢㧚㧟ߦ␜ߔ‫ޔߚ߹ޕ‬FMS-1㨪3P ߩฦゲߩࠢࡠࠬ࠻࡯ࠢߩᦨᄢ୯ࠍ⴫㧢㧚㧠ߦ␜ߔ‫ޕ‬⴫㧢㧚㧟 FMS-1㨪3P ߩᗵᐲ Vin

2(V )SF'(mV/mN)

Fingertip-sensor

SM'(mV/NǍm)

SFz'

SFx'

SFy'

SMz'

FMS-1P

0.085

0.039

0.039

0.004

FMS-2P

0.095

0.031

0.030

FMS-3P

0.013

0.015

0.016

⴫㧢㧚㧠 FMS-1㨪3P ߩࠢࡠࠬ࠻࡯ࠢߩᦨᄢ୯ Vin
Fingertip-sensor2(V )[ Fz max (%)[ Fz max (%)[ Fz max (%)[ Fz max (%)㩷FMS-1P㪌㪅㪐㩷 㩷

㪍㪅㪍

㪎㪅㪊

3.2

FMS-2P

6.8㩷

2.4

2.4

FMS-3P

5.6㩷

9.7

3.8

ԝ-6 ⠨ኤ㧔ℂ⺰୯ߣߩᲧセ㧕ᜰవ࠮ࡦࠨߩ⸃ᨆߢ▚಴ߒߚ⸃ᨆ୯ߩᗵᐲ㧔⴫㧡㧚㧝㧕ࠍ Vin

2(V ) ߣߒߡ⴫㧢㧚㧠ߣᲧセߒߚ‫ޕ‬FMS-1

㨪3 ߩฦゲߩ⸃ᨆ୯ߣ⸘᷹୯ߩᏅ⇣ߩഀว 4 ߪ⴫㧢㧚㧡ߩࠃ߁ߦߥࠆ‫ޕ‬⴫㧢㧚㧡 ⸃ᨆ୯ߣ⸘᷹୯ߩᏅ⇣ߩഀว 4
Fingertip-sensor

㩷 4 (1  S Measure / S Analysis ) u 100 (%)
Fz'

Fx'

Fy'

FMS-1P

9.57㩷

9.67㩷

9.49㩷

FMS-2P

10.57㩷

6.64㩷

6.33㩷

FMS-3P

8.33㩷

17.84㩷

18.28㩷

θ㧙48

⴫㧢㧚㧡ߢ␜ߒߚ FMS-1P㨪3P ߩ⸃ᨆ୯ߣ⸘᷹୯ߩᏅ⇣ߩഀว 4 ߩᐔဋ୯ߪ 10.7%ߢ޽ߞߚ‫ ߚ߹ޕ‬4ߩᮡḰ஍Ꮕߪ 4.1%ߢ޽ߞߚ‫ߪࠇߎޕ‬㧠㧚㧠ߢ␜ߒߚ࠮ࡦࠪࡦࠣ࠴࠶ࡊߩ 4 ߩᮡḰ஍Ꮕߩ⚂㧞୚ߩ୯ࠍ␜ߒߡ޿ࠆ‫ޕ‬ߎࠇߪታⵝࡊࡠ࠮ࠬߦࠃࠅ୘૕Ꮕ߇↢ߓ‫⚿ߩߘޔ‬ᨐࡃ࡜ߟ߈߇↢ߓߚ߽ߩߣ⠨߃ࠆ‫ޕ‬߹ߚ‫⴫ޔ‬㧢㧚㧟ߦ␜ߒߚᜰవ࠮ࡦࠨߩᗵᐲ S Fx ' ‫ ޔ‬S Fy ' ‫ ޔ‬S Fz ' ‫ ޔ‬S Mz ' ࠍᑼ㧔㧞㧚㧥㧕㨪㧔㧞㧚㧝㧝㧕ߦઍ౉ߔࠆߎߣߢᛠᜬ‛૕ߩ⾰㊂ M‫ߩ࠼ࡦࡂ࠻࠶ࡏࡠޔ‬ᛠᜬജ Fgrip ‫ޔ‬ᛠᜬὐߣ‛૕ߩ㊀ᔃ߹ߢߩ〒㔌 l㧔FMS-1P ߩߺ㧕ߣᜰవ࠮ࡦࠨ಴ജ㔚࿶ߩ㑐ଥ߇᣿ࠄ߆ߦߥߞߚ‫ޕ‬߹ߚ‫ޔ‬ᜰవ࠮ࡦࠨߩᗵᐲ S Fx ' ‫ ޔ‬S Fy ' ‫ ޔ‬S Fz ' ‫ ޔ‬S Mz ' ࠍᑼ㧔㧞㧚㧞㧞㧕㨪㧔㧞㧚㧞㧢㧕ߦઍ౉ߔࠆߎߣߢ‫ޔ‬ࡠࡏ࠶࠻ࡂࡦ࠼ߦ௑߈ࠍਈ߃ߚߣ߈ߩ‫ޔ‬x ゲ߹ࠊࠅ‫ޔ‬y ゲ߹ࠊࠅߩ௑ᢳⷺȀ‫ޔ‬ǰ‫ޔ‬ᛠᜬ‛૕ߩ⾰㊂ M‫ޔ‬ࡠࡏ࠶࠻ࡂࡦ࠼ߩᛠᜬജ Fgrip ‫ޔ‬ᛠᜬὐߣ‛૕ߩ㊀ᔃ߹ߢߩ〒㔌 l㧔l ߪ FMS-1P ߩߺ㧕ࠍ㧞ߟߩᜰవ࠮
ࡦࠨ಴ജ㔚࿶߆ࠄዉ಴ߔࠆߎߣ߇ߢ߈ࠆ‫ޕ‬Ԟ ߹ߣ߼
ᧄ⎇ⓥߢߪන⚿᥏ࠪ࡝ࠦࡦࠍ᭴ㅧ᧚ᢱߣߒߚዊဳ㧢ゲࡈࠜ࡯ࠬ࠮ࡦࠨ࠴࠶ࡊࠍ㐿⊒ߒ‫߇⌕ⵝޔ‬ኈᤃߢ⸘᷹቟ቯߥࡄ࠶ࠤ࡯ࠫ᭴ㅧࠍណ↪ߒࡠࡏ࠶࠻ࡂࡦ࠼↪ᨵエᜰవ⸅ⷡ࠮ࡦࠨߩታ↪ൻ⹜૞ࠍⴕߞߚ‫ޔߚ߹ޕ‬㐿⊒ߒߚ࠮ࡦࠨࠍࡠࡏ࠶࠻ࡂࡦ࠼ߦⵝ⌕ߒ‫‛ޔ‬૕ߩᛠᜬࠍⴕߞߚ‫ߢ࠻ࠢࠚࠫࡠࡊᧄޕ‬ᓧࠄࠇߚ⚿ᨐࠍએਅߦⷐ⚂ߔࠆ‫ޕ‬Ԙ㧟⒳㘃ߩዊဳ㧢ゲ࠮ࡦࠨ࠴࠶ࡊࠍ⠨᩺࡮⸳⸘ࠍⴕߞߚ‫ߩࡓ࡯ࡆޕ‬ᡰᜬὐᢙ߇ߘࠇߙࠇ⇣ߥࠆ࠮ࡦࠪࡦ
ࠣ࠴࠶ࡊ FMS-1㨪3 ߦߟ޿ߡ㧲㧱㧹⸃ᨆࠍⴕ޿ߘࠇߙࠇᦨᄢශടജ‫ᦨޔ‬ᄢශടࡕ࡯ࡔࡦ࠻‫ޔ‬ฦゲߩᗵᐲࠍᲧセߒߚ‫⚿ߩߘޕ‬ᨐ‫ߩࡈࠝ࠼࡯࡟࠻ߪࠄࠇߎޔ‬㑐ଥߦ޽ࠆߎߣࠍ⏕⹺ߒߚ‫ޕ‬ԙMEMS ࡈࠔࡦ࠼࡝࡯ࠨ࡯ࡆࠬࠍᵴ↪ߒ‫⵾ࡂࠛ࠙ޔ‬૞‫ ࡊ࠶࠴ޔ‬FMS-1㨪3 ߩ⵾૞ࠍⴕߞߚ‫ޕ‬  ࠮ࡦࠨ࠴࠶ࡊ⹜૞ᢙว⸘ 1000 ୘Ԛ࠮ࡦࠨ࠴࠶ࡊ FMS-1㨪3 ߩ⹏ଔࠍⴕߞߚ‫ޕ‬ฦ࠮ࡦࠪࡦࠣ࠴࠶ࡊߣ߽✢ᒻߥ⚿ᨐ߇ᓧࠄࠇߚ‫ޕ‬᷹ቯᗵᐲߦߟ޿ߡℂ⺰ߣߩᲧセࠍⴕߥߞߚ‫⸘ޕ‬᷹୯ߪ⸃ᨆ୯ࠃࠅᐔဋ 5.0%ዊߐ޿⚿ᨐ߇ᓧࠄࠇߚ‫ޕ‬ԛᨵエᜰ࠮ࡦࠨ FMS-1㨪3P ߩࡄ࠶ࠤ࡯ࠫ᭴ㅧࠍ⸳⸘‫⵾ޔ‬૞‫⹏ޔ‬ଔࠍⴕߞߚ‫ࠫ࡯ࠤ࠶ࡄޕ‬ታⵝ୘ᢙว⸘
250 ୘‫ޕ‬ฦ࠮ࡦࠨߣ߽✢ᒻߥ⚿ᨐ߇ᓧࠄࠇߚ‫ޕ‬᷹ቯᗵᐲߦߟ޿ߡ‫ޔ‬ℂ⺰୯ߣߩᲧセࠍⴕߥߞߚ‫⸘ޕ‬᷹୯ߪ⸃ᨆ୯ࠃࠅᐔဋ 5.0%ዊߐ޿⚿ᨐ߇ᓧࠄࠇߚ‫ޕ‬Ԝᜰవ࠮ࡦࠨࠍࡠࡏ࠶࠻ࡂࡦ࠼ߦⵝ⌕ߒ‫‛ޔ‬૕ߩᛠᜬࠍⴕ߁ߎߣߢࡠࡏ࠶࠻ࡂࡦ࠼↪ᜰవ࠮ࡦࠨߣߒߡ
ߩ᦭↪ᕈࠍᬌ⸽ߒߚ‫⚿ޕ‬ᨐ‫ޔ‬㧞ߟߩะ߆޿ว߁ᜰవ࠮ࡦࠨߦࠃࠅ‛૕ࠍᛠᜬߔࠆߣ߈‫ޔ‬ᜰవ࠮ࡦࠨ
ߩ಴ജ㔚࿶ߦࠃࠅᛠᜬ‛૕ߩᖱႎ㧔‛૕ᛠᜬ‛૕ࠍᛠᜬߔࠆജ‫⾰ޔ‬㊂‫ޔ‬ᜰవ࠮ࡦࠨߩ௑߈ⷺ‫ޔ‬ᛠᜬὐ߆ࠄᛠᜬ‛૕ߩ㊀ᔃ߹ߢߩ〒㔌㧕ࠍᓧࠆߎߣ߇ߢ߈ࠆߎߣࠍ⏕⹺ߒߚ‫ޕ‬੹ᓟ‫⎇ᧄޔ‬ⓥ⹜૞࠮ࡦࠨࠍࡠࡏ࠶࠻‫ޔ‬FA ⎇ⓥࠣ࡞࡯ࡊ߳ឭଏߒ‫ޔ‬㐿⊒࠮ࡦࠨߩ᦭↪ᕈ‫ࡂ࠻࠶ࡏࡠޔ‬ࡦ࠼ߦ߅ߌࠆ⸅ⷡ࠮ࡦࠨ⎇ⓥ‫‛ޔ‬૕ᛠᜬߩ⎇ⓥߩㅴዷߦ⾗ߔࠆ੍ቯߢ޽ࠆ‫ޕ‬↢‛ࠍᮨ୮ߒߚੱᎿ⸅ⷡ࠮ࡦࠨߩᕈ⢻ߪ✚ว⊛ߦߪ߹ߛ೔ᐩ↢‛ߩᗵᕈߦߪ߶ߤ㆙޿ߣ޿ߞߡࠃ޿‫ޕ‬ߒ߆ߒߥ߇ࠄ‫ੱޔ‬Ꮏ‛⸅ⷡ࠮ࡦࠨߪ↢‛ࠃࠅ߽৻⥸⊛ߦ⸃௝ᐲ߇㜞ߊ‫ߚ߹ޔ‬ቯ㊂⊛ߥᖱႎࠍᓧࠆߎߣ߇
น⢻ߢ޽ࠆ‫ߥ߁ࠃߩߎޕ‬ᕈ⾰ߪක≮ߦ߅ߌࠆᚻⴚ‫↥ޔ‬ᬺ↪㧔․ߦ⚻㛎߿ࠬࠠ࡞ࠍᔅⷐߣߔࠆ✺ኒߥ૞ᬺ㧕ߥߤ‫ੱޔ‬㑆߇࿎㔍ߣߒߡ޿ࠆ࠲ࠬࠢ߳ዷ㐿น⢻ߣ⠨߃ࠄࠇࠆ‫ޔ␩⑔ޔߚ߹ޕ‬ኅᐸ‫ߥ࠻ࡦࡔ࠭࡯ࡘࡒࠕޔ‬θ㧙49

ߤੱ㑆ⷫ๺ᕈ߇ⷐ᳞ߐࠇࠆࡠࡏ࠶࠻ߦ߅޿ߡ߽ᨵエធ⸅ㇱࠍ᦭ߔࠆ⸅ⷡ࠮ࡦࠨߪዷ㐿น⢻ߢ޽ࠆߣ⠨߃ࠆ‫੹ޕ‬ᓟㅴ߻ߴ߈ᣇะߣߒߡࠕ࡟ࠗൻ‫࠻࡯ࡑࠬޔ‬ൻ‫ߩ߳ࡦ࡚ࠫ࡯ࡘࡈࠨࡦ࠮ޔ‬ᔕ↪߇ᦼᓙߐࠇߡ޿ࠆ‫ޕ‬ߎࠇࠄߩᦼᓙߦᔕ߃ࠆߚ߼ߦߪ࠮ࡦࠨߣᖱႎಣℂᛛⴚ߇Ⲣวߔࠆߎߣ߇ਇนᰳߢ޽ࠅ‫ߔ߹ߔ߹ޔ‬ඨዉ૕ᛛⴚߣㆡวᕈߩ⦟޿ MEMS ⵾ㅧᛛⴚߩᵴ↪‫ޔ‬ㅴዷ߇㊀ⷐߥߢ޽ࠆߣ⠨߃ࠆ‫ޕ‬䋨䋳䋩ᚑᨐ䈱ᗧ⟵㩷ࡅࡘ࡯ࡑࡁࠗ࠼࠲ࠗࡊࡠࡏ࠶࠻ߥߤ‫ޔ‬Ყセ⊛ዊဳߩࡠࡏ࠶࠻ߩⶄ㔀ߥㆇേࠍᬌ಴ߔࠆߚ߼ߦߪ‫ޔ‬ᬌ಴ኻ⽎߳ߩᓇ㗀ࠍน⢻ߥ㒢ࠅዋߥߊߔࠆዊဳߩ࠮ࡦࠨ߇ᔅⷐߣߥࠆ‫ߩ࠻࠶ࡏࡠޕ‬േ૞ⅣႺ╬ߦࠃߞߡߪ‫ޔ‬ಽᏓ⊛ߦ㈩⟎ߒ⸘᷹ߔࠆᔅⷐ߇޽ࠆߚ߼‫ޔ‬ᓥ᧪ߩᄢ߈ߐߦᲧߴᩰᲑߦዊߐ޿ 6 ゲࡈࠜ࡯ࠬ࠮
ࡦࠨࠍ㐿⊒ߒ‫࠻࠶ࡏࡠޔ‬೙ᓮ⎇ⓥߦଏߒ‫᦭ߩߘޔ‬ലᕈࠍ⹏ଔߔࠆߎߣߦ㊀ὐࠍ⟎߈ㅴ߼ߡ߈ߚ‫ޕ‬ᧄ⎇ⓥߪ‫ޔ‬࿖ౝߩ MEMS ࡈࠔ࠙ࡦ࠼࡝࡯⹜૞ࠨ࡯ࡆࠬࠍᵴ↪ߒ‫ߩߢ߹ࠇߎޔ‬ᢙ୘㨪ᢙච୘න૏ߩ⎇ⓥ⹜૞߆ࠄᢙ⊖୘㨪ජ୘ߩࠝ࡯࠳࡯ߩታ↪⹜૞ࠍታᣉߔࠆߎߣ߽⋡⊛ߦߒߚ‫⵾ߩ߼ߚߩߘޕ‬૞ࡊࡠ࠮ࠬ
਄ߩ⺖㗴ߩ᛽಴ߣߘߩ⸃᳿ߦ㑐ߔࠆᬌ⸛߽ⴕߞߚ‫ߢߎߎޕ‬ᓧࠄࠇߚ⚿ᨐߪ‫ޔ‬࿖ౝ MEMS ࡈࠔ࠙ࡦ࠼࡝
࡯ߩᛛⴚജߩะ਄ߩߺߢߥߊ‫⹜ޔ‬૞୘ᢙߩᢙჇߒߦࠃߞߡ‫࠻࠶ࡏࡠޔ‬ᔕ↪⎇ⓥߩ▸࿐᜛ᄢߣଦㅴߦߟߥ
߇ࠆ߽ߩߢ޽ࠆ‫ޕ‬ᧄ⎇ⓥߢߪ‫ޔ‬MEMS ࡈࠔ࠙ࡦ࠼࡝࡯⹜૞ࠨ࡯ࡆࠬࠍᵴ↪ߒ‫⎇ᧄߢ߹ࠇߎޔ‬ⓥࠣ࡞࡯ࡊ߇㐿⊒ߒߡ߈ߚ  ゲࡈࠜ࡯ࠬ࠮ࡦࠨߩ࠴࠶ࡊኸᴺࠍ 3mm ⷺ߆ࠄ 2mm ⷺߦߐࠄߦ❗ዊߒߚ࠴࠶ࡊߩ㐿⊒ࠍⴕߞߚ‫ޕ‬߹ߚⵝ⌕߇ኈᤃߢ⸘᷹߇቟ቯߥࡄ࠶ࠤ࡯ࠫ᭴ㅧࠍណ↪ߔࠆߎߣߦࠃߞߡ‫ޔ‬᳢↪ᕈߩᭂ߼ߡ㜞޿ࡠࡏ࠶࠻
ࡂࡦ࠼↪ᨵエᜰవ⸅ⷡ࠮ࡦࠨߩታ↪ൻ㐿⊒ࠍⴕߞߚ‫⎇ᧄޕ‬ⓥ㐿⊒ߦࠃߞߡ‫ޔ‬ᛩ౉䈘䉏䈢੍▚䈮⷗ว䈦䈢චಽߥᚑᨐ߇ᓧࠄࠇߚߣ⠨߃ࠆ‫੹ޕ‬ᓟ‫↥࠻࠶ࡏࡠޔ‬ᬺߩߺߥࠄߕࡀ࠶࠻ࡢ࡯ࠢ࠮ࡦࠪࡦࠣ߿࡙ࡆࠠ࠲ࠬ
࠮ࡦࠪࡦࠣߥߤ߳ߩᔕ↪ዷ㐿߽฽߼ᐢߊ↥ᬺߦ⽸₂ߔࠆ߽ߩߣ⠨߃ࠆ‫ޕ‬
䋨䋴䋩․⸵䈱ขᓧ㩷ᧄ⎇ⓥ㐿⊒ߪ⎇ⓥታᣉᜂᒰ⠪ࠄ߇ᣢߦ಴㗿ߒߚ․⸵㧔㧢ゲജⷡ࠮ࡦࠨ㧦․㗿2002-199037㧕ߩታ⸽߅ࠃ
߮ߘߩታ↪ൻࠍ࿑ߞߚ߽ߩߢ޽ࠅ‫ޔ‬MEMSࡈࠔ࠙ࡦ࠼࡝࡯⹜૞ࠨ࡯ࡆࠬࠍᵴ↪ߒߚᧄ⎇ⓥᚑᨐߦࠃߞߡ
ߘߩ⋡⊛ࠍචಽߦᨐߚߔߎߣ߇ߢ߈ߚ‫ޔߚ߹ޕ‬㑐ㅪ․⸵ߣߒߡ1ઙߩ․⸵಴㗿ࠍⴕ߁ߎߣ߇ߢ߈ߚ‫ޕ‬䋨䋵䋩ᚑᨐ䈱᥉෸㩷ᧄ⎇ⓥᚑᨐࠍએਅߩቇળ߅ࠃ߮ዷ␜ળߢ⊒⴫ 10 ઙ߅ࠃ߮ዷ␜ 7 ઙࠍⴕ޿ᐢߊ৻⥸ߦᖱႎ⊒ାࠍⴕߞߚ‫ޕ‬䋼ቇળฬ䋾㩷
[1](Transducers'03)The 12th International Conference on Solid-State Sensors, Actuators and Microsystems, IEEE,
Boston, June 8-12, 2003
[2]The 20th Symposium on Sensors, Micromachines, and Applied Systems, IEEJ, Tokyo, July 23-24, 2003
[3](APCOT MNT 2004) Asia-Pacific Conf. of Transducers and Micro-Nano Technology 2004, Sapporo, Japan,
July 4-8, 2004
[4](ICMT2004) The 8th International Conference on Mechatronics Technology, Hanoi, Vietnam, Nov. 8-12, 2004
[5]The 22nd Symposium on Sensors, Micromachines and Applied Systems, IEEJ, Tokyo, Japan, Oct. 20-21, 2005
[6](APCOT2006) Asia-Pacific Conference of Transducers and Micro-Nano Technology, IEEE, Singapore, Jun.
25-28, 2006

θ㧙50

[7](ISFA2006) 2006 Int'l Symposium on Flexible Automation, ISCIE/ASME-DSC, Osaka, Japan,
July,10-12,2006[8]The 23rd Symposium on Sensors, Micromachines and Applied Systems, IEEJ, Takamatsu, Japan, Oct.5-6,2006[9](IEEE Sensors 2006) The 5th IEEE Conference on Sensors, Daegu, Korea, Oct.22-25, 2006[10](IEEE MHS 2006) The 2003 International Symposium on Micromechatronics and Human Science, Nagoya,Japan, Nov.6-8, 2006
䋼ዷ␜ળฬ䋾
[1] 2005.11.09-11, ╙ 16 ࿁䊙䉟䉪䊨䊙䉲䊮ዷ, ᧲੩, ਥ௅䋺䊙䉟䉪䊨䊙䉲䊮䉶䊮䉺䊷[2] 2005.12.07-09, 䌓䌅䌍䌉䌃䌏䌎㩷 Japan 2005, ᐀ᒛ䊜䉾䉶, ਥ௅䋺䌓䌅䌍䌉䉳䊞䊌䊮[3] 2006.06.10-11, ╙ 5 ࿁↥ቇቭㅪ៤ផㅴળ⼏, ࿖┙੩ㇺ࿖㓙ળ㙚, ਥ௅䋺ౝ㑑ᐭ, ✚ോ⋭, ᢥㇱ⑼ቇ⋭,⚻ᷣ↥ᬺ⋭, ᣣᧄ⚻ᷣ࿅૕ㅪวળ, ᣣᧄቇⴚળ⼏[4] 2006.08.29-09.01, ╙ 67 ࿁ᔕ↪‛ℂቇળቇⴚ⻠Ṷળ䌍䌅䌍䌓․೎ዷ␜, ┙๮㙚ᄢቇ䈶䉒䈖⨲ᵤ䉨䊞䊮䊌䉴,ਥ௅䋺䋨␠䋩㩷 ᔕ↪‛ℂቇળ
[5] 2006.09.13-15, 䉟䊉䊔䊷䉲䊢䊮䊶䉳䊞䊌䊮 2006, ᧲੩࿖㓙䊐䉤䊷䊤䊛, ਥ௅䋺䋨⁛䋩⑼ቇᛛⴚᝄ⥝ᯏ᭴, 䋨⁛䋩ᣂ䉣䊈䊦䉩䊷↥ᬺᛛⴚ✚ว㐿⊒ᯏ᭴
[6] 2006.11.07-09, ╙ 17 ࿁䊙䉟䉪䊨䊙䉲䊮ዷ, ᧲੩࿖㓙䊐䉤䊷䊤䊛, ਥ௅䋺䊙䉟䉪䊨䊙䉲䊮䉶䊮䉺䊷[7] 2006.12.06-08, 䌓䌅䌍䌉䌃䌏䌎㩷 Japan 2006, ᐀ᒛ䊜䉾䉶, ਥ௅䋺䌓䌅䌍䌉䉳䊞䊌䊮θ㧙51