GS3-4-4
LIFE2012 2012 ೥ 11 ݄ 2 ೔–4 ೔ Ѫ஌ (໊‫ݹ‬԰େֶ)ӡಈ‫ػ‬ೳো֐Λ໛ٖ͢Δ૷ண‫ܕ‬μϛʔɿؔઅ঱ʹΑΔෆ࿈ଓͳຎࡲ఍߅ͷϞσϧͱͦͷධՁ

Wearable dummy to simulate disordered motor function:Development and evaluation of a modelof discontinuous frictional resistance caused by osteoarthritis˓ੴ઒ढ़ʢ໊‫ݹ‬԰େֶʣ Ԭຊਖ਼‫ޗ‬ʢ໊‫ݹ‬԰େֶʣ ळࢁ༃തʢ໊‫ݹ‬԰େֶʣ∗ү֋߳ʢ඿দେֶɾ໊‫ݹ‬԰େֶʣ ࢁాཅ࣎ʢ໊‫ݹ‬԰େֶʣ ‫ ݪ‬ਐʢ໊‫ݹ‬԰େֶʣ
Shun ISHIKAWA, Shogo OKAMOTO, Yasuhiro AKIYAMA, Nagoya University,
Kaoru ISOGAI, Hamamatsu University and Nagoya University,
Yoji YAMADA, and Susumu HARA, Nagoya University
Abstract: Physical therapists master manual examination techniques for testing impaired motor functions and thedegree of recovery. We developed a wearable robotic dummy joint to simulate disordered joint resistances for supporting
physical therapists to learn such techniques. A model to simulate discontinuous joint friction resistances due to diseases
such as osteoarthritis was developed. Because such resistance originates from abnormal frictions of bones and cartilages,
we used a stick-slip model to simulate the resistances. The model was validated based on the introspection of physicaltherapists. This study concludes that a discontinuous friction model presents forces that are perceptually similar to
those typically caused by damaged or roughened joint cartilages.
Key Words: Rehabilitation, Robot Dummy, Wearable Device1.

ॹ‫ݴ‬ཧֶྍ๏࢜͸ϦϋϏϦςʔγϣϯΛߦ͏ͨΊʹɼెख‫ݕ‬ࠪͱ‫ݺ‬͹ΕΔٕज़Λ਎ʹ෇͚Δඞཁ͕͋Δɽెख‫ࠪݕ‬ͷҰྫͱͯ͠ɼ‫ऀױ‬ͷؔઅΛ۶‫ۂ‬ɾ৳లͤ͞ɼखʹՃΘΔ൓ྗ΍ؔઅͷՄಈൣғɼ௧ΈͳͲͷ‫ऀױ‬ͷૌ͑Λ‫ʹج‬ɼӡಈೳྗͷ௿Լͷఔ౓΍ճ෮ঢ়ଶΛ஌Δٕज़͕͋Δɽӡಈ‫ػ‬ೳো֐Λ༗͢Δؔઅ͕ੜ੒͢Δ൓ྗύλʔϯ͸঱ྫ͝ͱʹಛ௃
తͰ͋ΔͨΊɼ͜ͷٕज़ͷशख़ͷͨΊʹ͸‫܇‬࿅ऀ͸͞·͟·ͳ঱ྫΛମ‫͢ݧ‬Δඞཁ͕͋Δɽ͔͠͠ɼཧֶྍ๏࢜ͷཆ੒‫Ͱؔػ‬͸͞·͟·ͳ঱ྫΛମ‫͢ݧ‬Δ‫ػ‬ձ͕গͳ͍ɽ͞Βʹɼ࣮शʹ͓͍ͯ΋ࢿ֨Λ࣋ͨͳֶ͍शऀ͕‫ʹऀױ‬৮ΕΔ͜ͱ͸ྙཧతʹ໰୊ࢹ͞Ε͍ͯΔɽͦ͜Ͱɼཧֶྍ๏࢜ͷཆ੒Λࢧԉ͢ΔͨΊɼ͞·͟·ͳ঱ྫͷମ‫ݧ‬Λิॿ͢Δμϛʔ͕ඞཁͰ͋Δɽؔ࿈‫ʹͰ·ࡏݱ ڀݚ‬ཧֶྍ๏࢜ͷཆ੒Λࢧԉ͢ΔͨΊͷ‫܇‬࿅༻ϩϘοτμϛʔͷ։ൃ͕ߦΘΕ͖ͯͨɽKikuchi Β͸ؔઅՄಈҬ੍‫ݶ‬Λ໛ٖ͢ΔࡍʹඞཁͱͳΔେ͖͍఍߅ྗΛग़ྗͰ͖ΔΑ͏ MR ྲྀମΫϥονͱϞʔλΛ༻͍ͯϩϘοτͷකؔઅΛ੍‫( ͨ͠ޚ‬1) ɽGrow Β͸ɼගؔઅͷᙲੑΛ໛ٖͨ͠ೋछͷϞσϧΛൺֱɼ‫( ͨ͠ূݕ‬2) ɽ·ͨɼ൴Β͸͜ΕΒͷϞσϧΛ࢖ͬͨϩϘοτ͕঱ঢ়Λ෼ྨ͢Δ‫܇‬࿅ʹ༗ޮͰ͋Δ͜ͱΛࣔͨ͠ɽҎ্ͷ‫Ͱڀݚ‬͸ؔઅΛҰ࣠ੑؔઅͱͯࣗ͠༝౓Λ‫ݮ‬Β͠୯७Խͨ͠ɽ͔͠͠ɼਓؒͷؔઅΛ໛ٖ͢ΔͨΊʹ͸ؔઅͷෳࡶͳࣗ༝౓Λߟྀ͢Δඞཁ
͕͋ΔɽTakahashi Β͸ؔઅ෦ʹପԁ‫ܗ‬ͷΧϜΛ༻͍Δ͜ͱʹΑΓ্ࢶͷ৳లɼ۶‫ʹۂ‬൐͏લ࿹ͷ৳ுɼ୹ॖΛ໛ٖͨ͠ (3) ɽϩϘοτμϛʔͷ໰୊఺ ؔ࿈‫ڀݚ‬Λਫ਼ࠪ͢Δͱ͍͔ͭ͘ͷٕज़తͳ໰୊ʹয఺͕͋ͯΒΕ͍ͯΔ͜ͱ͕෼͔Δɽͻͱͭ͸঱ঢ়ͷ࠶‫ݱ‬ੑͷ໰୊Ͱ͋Δɽ঱ྫ͝ͱͷෳࡶͳ൓ྗύλʔϯ΍߆ॖ౳ʹ൐͏େ͖ͳ఍߅ྗΛఄࣔͰ͖Δඞཁ͕͋Δɽ·ͨɼϩϘοτμϛʔ͸ਓؒͷؔઅͷෳࡶͳӡಈ‫੻ي‬Λ༗͢Δඞཁ͕͋Δɽྫ͑͹ɼਓମͷؔઅ͸۶‫ۂ‬ɾ৳ల͞∗ This study was in part supported the Naito Research Grant.

−1−ͤͨͱ͖ɼճટ΍৳ுɾ୹ॖͱ͍ͬͨӡಈΛߦ͏ɽ͞Βʹɼؔઅͷಈ࡞Ҏ֎ͷਓؒΒ͠͞ɼྫ͑͹֎‫ݟ‬΍ൽෘɼ‫ͱऀױ‬ͷձ࿩ͳͲͱ͍࣮ͬͨࡍͷ‫͍ͯ͠઀ʹऀױ‬Δ͔ͷΑ͏ͳԋग़ΛϩϘοτμϛʔ͸ߦ͏ඞཁ͕͋ΔɽՃ͑ͯɼ‫ڭ‬ҭ‫ݱ‬৔ʹී‫ͤ͞ٴ‬ΔͨΊʹ૷ஔΛ؆ུԽͯ͠ίετΛ࡟‫͢ݮ‬Δ͜ͱ΋ඞཁͰ͋Δɽ͜ΕΒͷ໰୊Λ͢΂ͯղܾ͢Δ͜ͱ͸೉͘͠ɼ͏·͘ղܾ͍ͯ͠Δྫ͸ͳ͍ɽ͜ΕΒͷ໰୊ΛόϥϯεΑ͘ղܾ͢Δμϛʔͷ։ൃ͕ඞཁͰ͋Δɽ

2.

ఏҊɿ૷ண‫ܕ‬μϛʔδϣΠϯτΘΕΘΕ͸μϛʔϩϘοτΛ݈ৗऀʹ૷ண͢Δɼ૷ண‫ܕ‬μϛʔδϣΠϯτΛఏҊ͍ͯ͠Δ (4) ɽFig. 1 ͸݈߁ͳֶੜ͕୤ྗͨ͠ঢ়ଶͰකؔઅʹ૷ணͨ͠μϛʔδϣΠϯτͷ֓೦ਤΛ͍ࣔͯ͠Δɽ͜ͷμϛʔδϣΠϯτ͸Ϟʔλͱ 2ϦϯΫͱ͍ͬͨ୯७ͳ‫͕ͳߏػ‬Β΋ਓମͷෳࡶͳӡಈ‫੻ي‬Λ࣮‫͢ݱ‬Δ͜ͱ͕Ͱ͖ΔɽμϛʔδϣΠϯτ͸ਓؒͷකؔઅ͕༗͢Δճટ΍৳ுɼ୹ॖͱ͍ͬͨ‫ߏػ‬Λ༗͍ͯ͠ͳ͍͕ɼ͜ΕΒͷ‫ֶߏػ‬తͳࠩ͸ΧϑΛ௨ͯ͠ɼൽෘ΍ҥ෰ͷͣΕʹ‫ٵ‬ऩ͞ΕΔɽ·ͨɼਓؒͷ଍ͷॏ͞ɼஆ͔͞ɼഽͷ‫֮ײ‬Λମ‫͖Ͱݧ‬Δͱ͍͏఺Ͱɼ࣮ࡍͷ‫͍ͯ͠઀ʹऀױ‬Δ͔ͷΑ͏ͳԋग़Λߦ͏͜ͱ͕Ͱ͖Δɽཧֶྍ๏࢜ͷཆ੒‫ݱ‬৔Ͱ͸ɼೋਓҰ૊ͱͳͬͯɼҰਓ͕‫ऀױ‬໾ͱͳͬͯ঱ྫͷ‫ڍ‬ಈΛ໛ٖ͠ɼҰਓ͕ྍ๏࢜໾ͱͳֶͬͯशΛߦ͍ͬͯΔɽμϛʔδϣΠϯτ͸ͦͷΑ͏ͳཆ੒‫ݱ‬৔ͱͷ਌࿨ੑ΋ߴ͍ɽֶशऀ͸͜ͷμϛʔδϣΠϯτΛ༻͍ɼ͞·͟·ͳମ੎ʹ͓͚Δెख‫ࠪݕ‬Λ࿅शͰ͖Δɽྫ͑͹ɼFig. 1 ͷΑ͏ʹ෬թҐɼFig. 2 ͷΑ͏ʹண੮ͨ͠ঢ়ଶͰ࿅शͰ͖Δɽֶशऀ͸‫ऀױ‬໾ͷԼ଼Λ௫ΈɼකΛ۶‫ۂ‬ɼ৳లͤ͞Δɽ͜ͷͱ͖ɼ‫ऀױ‬໾͸࣮ࡍͷెख‫ͱࠪݕ‬ಉ༷ʹ୤ྗ͓ͯ͠ΓࣗൃతͳӡಈΛߦΘͳ͍ɽϞʔλ͸໛ٖ͞Εͨ঱ঢ়ͱμϛʔδϣΠϯτͷಈ͖ʹԠͯ͡Լ଼΁ͷ఍߅ྗΛੜ੒͠ɼකؔઅͷ‫ۓے‬ுҟৗ΍ই֐Λ໛ٖ͢Δɽ։ൃͨ͠μϛʔδϣΠϯτͷࢼ࡞‫ػ‬Λ Fig. 2 ʹࣔ͢ɽ

Learner
CuffFlexion
and Extension
Fig. 3 Stick-slip model of rotary motion

Link

Healthy person

Motor and Encoder

໛ٖ͢Δɽ͞Βʹɼ໛ٖͨ͠ crepitus Λཧֶྍ๏͕࢜ମ‫ݧ‬ɾධՁ͠ɼϞσϧͷଥ౰ੑΛ‫͢ূݕ‬Δɽ

Fig. 1 Conceptual diagram of wearable dummy joint

Stick-slip ‫ݱ‬৅Λ‫ ͨ͠ʹج‬crepitus Ϟσϧ

4-1Crepitus Ϟσϧͷղੳࣜ

Crepitus ͸ೈࠎͳͲͷೈ෦૊৫͕ഁյ͞ΕΔ͜ͱʹΑΔࠎಉ࢜ͷ઀৮͕‫ݪ‬ҼͰ͋Δ (5) ɽCrepitus ͸ؔઅͷෆ࿈ଓͳຎࡲͰ͋ΔͨΊɼΘΕΘΕ͸ stick-slip ӡಈͷྗֶϞσϧΛ༻͍ͯ crepitus Λ໛ٖ͢Δ͜ͱΛఏҊ͍ͯ͠Δ (4) ɽ͜ͷϞσϧ͸த໺Βͷฏ໘্Ͱͷ̎෺ମͷ stick-slip ͷϞUpper thigh sideσϧ (7) Λճసମʹద༻͞ΕΔΑ͏ʹվมͨ͠΋ͷͰ͋Δɽճస࣠ͱԾ૝෺ମͷຎࡲʹΑͬͯൃੜ͢Δ stick-slip ‫ݱ‬৅ͷϞσϧΛ Fig. 3 ʹࣔ͢ɽ͜ͷϞσϧ͸֯଎౓ Ω (t) Ͱճస͢Δ࣠ͱ֯଎౓ θ̇ (t) Ͱճస͢ΔԾ૝෺ମ͔Β੒ΔɽԾ
૝෺ମʹ͸ճస͹Ͷ͕औΓ෇͚ͯ͋ΓɼԾ૝෺ମͷճస֯౓ʹԠͯ͡෮‫ݩ‬τϧΫ͕ੜ͡Δɽ·ͨɼ͜ͷ̎෺ମʹ͸઀৮໘ͰຎࡲτϧΫ͕ൃੜ͓ͯ͠Γɼͦͷ஋Λ T (t) ͱ͢Δɽ͜ͷ T (t) ͕ཧֶྍ๏࢜ͷֶशऀʹఄࣔ͞ΕΔɽຎࡲಛੑͱͯ͠ΫʔϩϯຎࡲΛԾఆ͢Δɽຊख๏Ͱ༻͍Δม਺͸

Motor

Encoder
Lower thigh side
Fig. 2 Wearable dummy joint simulating motor disorder3.

4.

໛ٖఄࣔ͢Δ঱ঢ়: Crepitus͜Ε·ͰʹϩϘοτμϛʔʹΑΓ໛ٖ͞Ε͖ͯͨ঱ঢ়͸ຑᙺ‫ऀױ‬ಛ༗ͷᙲॖɼ‫ݻ‬ॖɼؔઅՄಈҬ੍‫ݶ‬ɼΫϩʔψε͕த৺Ͱ͋ΔɽҰํɼΘΕΘΕ͸໛ٖର৅ͱ͢Δ঱ঢ়ʹ
crepitus ΛબΜͩɽCrepitus ͱ͸ม‫ܗ‬ੑؔઅ঱ (OA) ͳͲʹ‫ݦ‬ஶʹ‫ݟ‬ड͚ΒΕΔɼؔઅͷෆ࿈ଓͳຎࡲ఍߅ͷ͜ͱͰ͋ΔɽOA ͱ͸ɼؔઅೈࠎͷഁյͱ‫ݮ‬গʹΑͬͯಛ௃͚ͮ
ΒΕΔશͯͷؔઅͷຫੑؔઅো֐Ͱ͋ΔɽOA ͸உੑΑΓ΋ঁੑͷํ͕ൃ঱͠΍͘͢ɼੈքதͰ 60 ࡀҎ্ͷஉੑͷ
໿ 9.6%ɼঁੑͷ໿ 18.0% ͕ OA ͷ঱ঢ়Λ͍ࣔͯ͠Δ (5) ɽOA ͷධՁʹ͸ X ઢɼྟচ‫ࠪݕ‬ɼMRIɼؔઅ‫͍༻͕ڸ‬ΒΕΔɽ͜ΕΒͷதͰɼؔઅ‫ڸ‬͸ద֬ͳ৘ใΛ΋ͨΒ͕͢ɼॳ‫ͨ·ظ‬͸ܰ঱‫ऀױ‬ͷධՁʹ͓͍ͯ͸ྟচ‫ࠪݕ‬ͷ༗༻ੑ͕ߴ͍ (6) ɽྟচ‫͍͓ͯʹࠪݕ‬ɼཧֶྍ๏͕࢜ OA ΛධՁ͢Δ߲໨ͷҰ ͭͱͯ͠ crepitus ͷ൑ఆ͕͋ΔɽCrepitus ͸ɼؔઅͷՔಈʹΑͬͯੜ͡Δฉ͖औΕΔఔ౓ͷຎࡲԻ΍৮஌Մೳͳৼಈͱͯ͠ఆٛ͞ΕΔ͜ͱ͕ଟ͍ (5) ɽCrepitus Λཧֶྍ๏࢜ͷ‫ڭ‬ҭऀ͕໛ٖͯ͠ɼֶशऀʹମ‫ͤ͞ݧ‬Δ͜ͱ͸ࠔ೉Ͱ͋ΓɼϩϘοτσόΠεʹΑΔ໛ٖ͸঱ঢ়ͷֶशʹ͓͍ͯ༗༻Ͱ͋Δɽ͜Ε·Ͱʹ crepitus ʹ൐͏ຎࡲ఍߅ΛޮՌతʹ໛ٖ͢Δํ๏͸஌ΒΕ͍ͯͳ͍ɽ
Crepitus ͸Ԝತͱͳͬͨؔઅೈࠎ·ͨ͸ᡲ͕‫ݪ‬ҼͰ͋Γ͏Δ͕ɼਓؒͷෳࡶͳؔઅߏ଄ʹՃ͑ͯɼcrepitus ͷൃੜϝΧχζϜΛਫ਼֬ʹγϛϡϨʔτ͢Δ͜ͱ͸೉͍͠ɽͦ͜ͰΘΕΘΕ͸͜ͷ crepitus Λෆ࿈ଓຎࡲϞσϧΛ༻͍ͯ−2−J: Ծ૝෺ମͷ‫׳‬ੑϞʔϝϯτ [kg · m2 ]θ (t) : Ծ૝෺ମͷมҐ [rad]θ̇ (t) : Ծ૝෺ମͷ֯଎౓ [rad/s]: ճస͹Ͷఆ਺ [N]krΩ (t) : ࣠ͷճస֯଎౓ [rad/s]
T (t) : ຎࡲτϧΫ [Nm]: ಈຎࡲτϧΫ [Nm]
TkTsmax : ࠷େ੩ຎࡲτϧΫ [Nm]Ͱ͋Δɽ͜ͷϞσϧʹ͸ stick ঢ়ଶͱ slip ঢ়ଶͷ̎ঢ়ଶ͕ଘࡏ͢
Δͱߟ͑Δɽstick-slip ӡಈͷ༷ࢠΛ໛ࣜతʹදͨ͠΋ͷΛ Fig. 4 ʹࣔ͢ɽ
stick ঢ়ଶͰ͸Ծ૝෺ମͱ࣠ͷ଎౓͸౳͘͠ (Ω (t) −θ̇ (t) = 0)ɼԾ૝෺ମͱ࣠ؒͰ੩ຎࡲτϧΫ͕ൃੜ͢Δɽ

T (t) = kr θ (t)(1)−Tsmax ≤ Th (t) ≤ Tsmax(2)

͕੒ཱ͢Δɽstick ঢ়ଶͰ͸͜ͷ T (t) ͕μϛʔδϣΠϯτʹΑֶͬͯशऀͷखʹ఻ΘΔɽkr ͸ stick ঢ়ଶͷप‫ʹظ‬Ө‫͢ڹ‬Δɽ·ͨɼTsmax ֶ͕शऀʹఄࣔ͞ΕΔྗͷ࠷େ஋Ͱ͋Δɽ
slip ঢ়ଶͰ͸Ծ૝෺ମͱ࣠ͷ֯଎౓͸ҟͳΔ (Ω (t) −θ̇ (t) ̸= 0)ɽԾ૝෺ମͷ֯଎౓͸࣠ͷ֯଎౓ΑΓখ͘͞ɼԾ

Ω(t0 )
0−ATktSticking
phase

Slipping
phase

Sticking
phase

Slip

StickStickSlip

26250.424230.35220.3

Angular velocity of lower thigh [deg/s]

A

0.45 Stick

Presented torque [Nm]Friction torque

Tsmax

Angular velocity of imaginary object

θ&(t )T (t )

21
00.05

0.1

0.15

Time [s]Fig. 4 Schematic diagram of stick-slip motion

Fig. 5 Angular velocity and presented torque during simulation of crepitus૝෺ମͱ࣠ؒͰಈຎࡲτϧΫ͕ൃੜ͠ɼ

()T (t) = sign Ω (t) − θ̇ (t) · Tk(3)Ͱࣔ͞ΕΔɽslip ঢ়ଶͰ͸ɼ͜ͷຎࡲτϧΫ͕μϛʔδϣΠϯτʹΑֶͬͯशऀʹఄࣔ͞ΕΔɽ࠷େ੩ຎࡲτϧΫͱಈຎࡲτϧΫͷେ͖͕͞ҧ͏ͨΊɼ͜ΕΒ̎ঢ়ଶ͕‫܁‬Γฦ͠ભҠ͠ɼstick-slip ӡಈ͕‫ܧ‬ଓతʹੜ͡Δɽ࣍ʹͦΕͧΕͷঢ়ଶ΁ͷભҠ৚݅ʹ͍ͭͯઆ໌͢Δɽstick-to-slip ભҠ͕ൃੜ͢Δ৚݅͸ճస͹Ͷͷ෮‫ݩ‬τϧΫͷେ͖͕͞࠷େ੩ຎࡲͷେ͖͞Λ௒͑Δ͜ͱͰ͋Δɽ͜Ε͸J θ̈ (t) + kr θ (t) ≥ Tsmax(4)ͱࣔ͞ΕΔɽslip Λ։࢝͢Δ࣌ࠁΛ t0 ͱ͢Δͱɼͦͷ࣌ͷ࣠ͷ֯଎౓͸

θ̇ (t0 ) = Ω (t0 ) ,(5)࣌ࠁ t0 ͷͱ͖ͷԾ૝෺ମͷҐஔ͸θ (t0 ) = (Tsmax − J θ̈ (t0 ))/kr(6)ͱͳΔɽ͔͠͠ɼJ ͱ θ̈ (t0 ) ͷ஋͸খ͍ͨ͞Ίɼθ (t0 ) ∼ Tsmax /kr(7)ͱۙࣅͰ͖Δɽslip-to-stick ભҠ͕ൃੜ͢Δ৚݅͸ slip ঢ়ଶʹ͓͚ΔԾ૝෺ମͷ֯଎౓͕࣠ͷճస֯଎౓ʹୡ͢Δ͜ͱͰ͋Γθ̇ (t) = Ω (t)(8)ͱࣔ͞ΕΔɽslip ӡಈதʹ͸ಈຎࡲτϧΫ͕࣠ͷճసํ޲ͱಉ͡ํ޲ʹಇͨ͘Ίӡಈํఔࣜ͸J θ̈ (t) + kr θ (t) = Tk(9)ͱͳΔɽઌ΄Ͳͷ slip ͕։࢝ͨ࣌͠ͷॳ‫ظ‬৚݅ (5) ͱ (6)Λ༻͍ͯ͜ΕΛղ͘ͱԾ૝෺ମͷ֯଎౓͸√√
Tsmax − Tkkrkr√
t + Ω (t0 ) cos
tsinJJJkr(√)Ω (t0 )kr
= A cost + arccos
,(10)
JA
√
2(Tsmax − Tk )2
A=+ Ω (t0 ) .
(11)
Jkr

θ̇ (t) = −−3−ͱͳΔɽθ̇ (t) ͕ Ω (t0 ) ͱ౳͘͠ͳͬͨͱ͖ slip-to-stickભҠ͕ൃੜ͢Δɽ(10) ʹΑΔͱɼJ ʹର͢Δ kr ͷൺ཰͸
slip ঢ়ଶͷप‫ʹظ‬Ө‫͢ڹ‬Δɽ͜ͷൺ཰͕૿Ճ͢ΔʹͭΕͯslip ঢ়ଶͷप‫ݮ͕ظ‬গ͢Δɽ
4-2 Crepitus Ϟσϧͷ࣮૷্‫Ͱه‬આ໌ͨ͠ crepitus ͷϞσϧΛ։ൃͨ͠μϛʔδϣΠϯτʹ࣮૷ͨ͠ɽϞσϧͷม਺͸ J = 0.01 kg · m2 ɼ
kr = 400 N/radɼTk = 0.2 NmɼTsmax = 0.4 Nm Ͱ͋Δɽ͜ΕΒͷม਺͸ཧֶྍ๏࢜ͷ‫ݴॿͱ֮ײ‬Λ΋ͱʹܾఆͨ͠ɽ࣮ࡍʹଌఆͨ͠ɼԼ଼෦ͷ֯଎౓ͱఄࣔ͞ΕͨτϧΫͷάϥϑΛ Fig. 5 ʹࣔ͢ɽఄࣔ͞ΕͨτϧΫ͸Լ଼෦ʹऔΓ෇͚ͨྗηϯαʹΑͬͯ‫ܭ‬ଌ͞Εͨɽstick ঢ়ଶͰ͸ఄࣔτϧΫ͕૿Ճ͠ɼಉ࣌ʹ֯଎౓͕‫ݮ‬গ͢Δɽ൓ରʹɼslip ঢ়ଶͰ͸ఄࣔτϧΫ͕‫ݮ‬গ͠ɼ֯଎౓͕૿Ճ͢Δɽ
stick ঢ়ଶͱ slip ঢ়ଶؒͷભҠʹΑΓৼಈຎࡲ఍߅Λੜ੒
͢Δɽ͔͠͠ͳ͕ΒɼFig. 4 ʹࣔ͢ຎࡲτϧΫͱঢ়ଶભҠͷུ֓ਤͱ Fig. 5 Ͱ‫͞࡯؍‬ΕΔάϥϑʹ͸͍͔ͭ͘ͷ૬ҧ͕͋Δɽ·ͨɼFig. 4 ͷ֯଎౓͸Ծ૝෺ମͷ֯଎౓Ͱ͋Δͷʹର͠ɼFig. 5 ͷ֯଎౓͸μϛʔͷԼ଼ͷ֯଎౓Ͱ͋
ΔͨΊɼ૒ํͷਤͷ֯଎౓͸ൺֱ͢ΔྔͰͳ͍͜ͱʹ஫ҙ͢Δඞཁ͕͋Δɽ·ͣɼFig. 4 Ͱ͸ɼslip ঢ়ଶͰ͸ɼఄࣔτϧΫ͕ಈຎࡲτϧΫ Tk ͷ஋ͰҰఆͰ͋Δ͕ɼFig. 5 Ͱ͸ɼఄࣔτϧΫͷ஋͕ҰఆͰ͸ͳ͍ɽ͜Ε͸ stick ঢ়ଶ͔Β slip ঢ়ଶ΁ͷભҠͷࡍʹϞʔλ͕‫ͳܹٸ‬τϧΫࢦྩมԽʹԠ౴Ͱ͖ͳ͍͜ͱ͕ཧ༝Ͱ͋Δɽ͞ΒʹɼFig. 5 Ͱ͸ɼstick ঢ়ଶؒͷִ͕ؒখ͘͞ɼൃੜྗ͕ಈຎࡲτϧΫʹୡ͢Δલʹ stick ঢ়ଶ͕࢝·ͬͨɽ࣍ʹɼঢ়ଶભҠͱൃੜྗͷҐ૬͕‫ͱ࡯؍‬ϞσϧͰ͸Θ͔ͣʹҟͳ͍ͬͯΔɽFig. 4Λ‫ݟ‬ΔͱɼϞσϧͰ͸ભҠͷॠؒ͸ຎࡲτϧΫͷϐʔΫ࣌Ͱ͋Δɽ͔͠͠ͳ͕ΒɼFig. 5 Ͱ͸ɼຎࡲτϧΫͷϐʔΫ͕ঢ়ଶભҠ‫ൃʹޙ‬ੜ͢Δɽ͜ͷࠩҟ΋ɼϞʔλͷԠ౴଎౓ͷ੍໿ʹͳΔɽ͔͠͠ɼֶशऀ͸ঢ়ଶભҠͷִؒͰ͸ͳ͘ຎࡲτϧΫͷมԽͷΈΛ஌֮͢ΔͨΊʹɼ͜ͷΑ͏ͳঢ়ଶભҠͱຎࡲτϧΫͷҐ૬ͷͣΕ͸ɼ໛ٖ͞Εͨ crepitus ͷ࣭ΛѱԽͤ͞Δ͜ͱʹͳΒͳ͍ɽ
5.

ཧֶྍ๏࢜ʹΑΔධՁμϛʔδϣΠϯτ͸ཧֶྍ๏࢜ͷ‫ڭ‬ҭΛ໨తͱ͍ͯ͠
ΔɽΏ͑ʹμϛʔδϣΠϯτ͸‫܇‬࿅ऀ͕య‫ܕ‬తͱΈͳ͢঱ঢ়Λ໛ٖ͢Δ͜ͱ͕޷·͍͠ɽ͜ͷߟ͑Λ‫ʹج‬ɼೋਓͷΔϩϘοτμϛʔ΋໌Β͔ʹਓؒͱ͸ҟͳΔप೾਺Ԡ౴ಛੑΛ͓࣋ͬͯΓɼਓؒͱϩϘοτͷप೾਺Ԡ౴ಛੑͷҧ͍͸ɼμϛʔϩϘοτʹ‫ڞ‬௨ͨ͠໰୊Ͱ͋Δɽ
6.

Fig. 6 Joint motion of severe knee osteoarthritisཧֶྍ๏͕࢜μϛʔδϣΠϯτ͓Αͼ໛ٖ͞Εͨ crepitusΛධՁͨ͠ɽ࣮ࡍͷ‫ऀױ‬ͷσʔλͱຊϞσϧͷ఍߅ྗΛൺֱ͢Δͱ͍͏ํ๏΋͋Δ͕ɼ‫ऀױ‬͸େ఍ɼcrepitus ʹՃ͑ͯ͞·͟·ͳ঱ঢ়Λซൃ͢ΔͨΊɼ͜ͷධՁํ๏Ͱ͸crepitus ͷΈΛຊ࣭తʹൺֱ͢Δ͜ͱ͸Ͱ͖ͳ͍ɽ·ͨɼ࣮ࡍͷ‫͔ऀױ‬Βͷσʔλʹ͸‫ݸ‬ਓ͕ࠩ͋Δɽెख‫ࠪݕ‬ͷ‫܇‬࿅ͷͨΊͷμϛʔδϣΠϯτ͸ɼ‫ݸ‬ʑͷ‫ऀױ‬ͷಛ௃Λ໛ٖ͢Δ͜ͱΑΓ΋ɼΉ͠Ζ‫ڞʹऀױ‬௨͢Δయ‫ܕ‬తͳ঱ঢ়ͷಛ௃ΛͱΒ͑ͳ͚Ε͹ͳΒͳ͍ɽྟচ‫͕ݧܦ‬๛෋ͳཧֶྍ๏࢜͸ɼ͜ͷΑ͏ͳయ‫ܕ‬తͳ঱ঢ়Λཧղ͍ͯ͠ΔͨΊɼཧֶྍ๏࢜ͷධՁͱ͍͏ํ๏ΛબΜͩɽཧֶྍ๏࢜͸ 50 ୅Ͱྟচ‫͕ݧܦ‬๛෋Ͱ͋ͬͨɽ൴Β͸μϛʔδϣΠϯτͰ໛ٖ͞Εͨ఍߅ྗΛମ‫ޙͨ͠ݧ‬ɼͦͷ఍߅ͷେ͖͞΍प‫ظ‬తมԽ͕య‫ܕ‬తͳ crepitus ʹྨࣅͯ͠
͍ΔͱධՁͨ͠ɽ·ͨɼҰਓͷཧֶྍ๏࢜͸ͦͷΑ͏ͳ‫ײ‬֮ʹՃ͑ͯɼਓؒͷ‫٭‬ͷॏ͞ɼଠ͞ɼஆ͔͞ͷΑ͏ͳ‫ײ‬৮͕ॏཁͰ͋Δͱड़΂ͨɽ൴͸ͦͷ఺Ͱ͜ͷμϛʔδϣΠϯτ͕༗༻Ͱ͋ΔͱධՁͨ͠ɽ͔͠͠ɼ࣍ͷ 2 ͭͷ໰୊͕ࢦఠ͞ΕͨɽҰͭ໨ͷ໰୊͸૷ண‫ܕ‬μϛʔδϣΠϯτ͕Լ଼෦ͷ௕खํ޲ʹԊͬͯมҐ͠ͳ͍͜ͱͰ͋ΔɽFig. 6 ʹࣔ͢Α͏ʹɼॏ౓ͷม‫ܗ‬ੑකؔઅ঱‫ऀױ‬ͷࠎ͸ૈ͘ͳ͓ͬͯΓɼཧֶྍ๏͕࢜කؔઅΛडಈతʹ۶‫ۂ‬ɼ৳లͤͨ͞ͱ͖ɼͦͷ௕खํ޲ʹԊͬͯԼ଼͕มҐ͢Δɽ‫ࡏݱ‬ͷμϛʔδϣΠϯτͷࢼ࡞‫Ͱػ‬͸ͦͷΑ͏ͳํ޲ʹมҐ͢Δ‫ߏػ‬͸ઃ͚͍ͯͳ͍ͨΊɼ͜ͷ໰୊ΛղܾͰ͖ͳ͍ɽ͞Βʹɼ͜ͷμϛʔδϣΠϯτΛ݈ৗऀ͕૷ண͢Δ‫ݶ‬Γɼ݈ৗͳؔઅ͕‫ڍ‬ಈ͠ͳ͍Α͏ͳҟৗͳ঱ঢ়͸໛ٖͰ͖ͳ͍ɽྫ͑͹ɼଆ෭ਟଳ͕ଛইͨ͠කؔઅͷ৔߹ɼԼ଼͕಺ɾ֎൓ํ޲΁ෆ҆ఆʹಈ͕͘ɼ݈߁ͳਓؒͷԼ଼͸ͦͷΑ͏ʹಈ͔ͳ͍ɽ͕ͨͬͯ͠ɼҟৗͳؔઅӡಈΛ൐͏ಛఆͷ঱ঢ়Λ໛ٖ͢Δ৔߹ɼ૷ண‫ܕ‬μϛʔδϣΠϯτʹ͸੍‫͕͋ݶ‬Δ͜ͱ͕෼͔Δɽ͔͠͠ɼͦͷΑ͏ͳҟৗͳؔઅӡಈΛ൐Θͳ͍঱ঢ়ͷ໛ٖʹ͓͍ͯͷ༗ޮੑ͸ࣔ͞Εͨɽೋͭ໨ͷ໰୊͸ৼಈ৮‫֮ײ‬ͷߴप೾੒෼͕‫ݮ‬ਰ͢Δ͜ͱ
Ͱ͋Δɽཧֶྍ๏࢜͸ม‫ܗ‬ੑකؔઅ঱ͷ‫ऀױ‬Λ‫ࠪ͢ݕ‬Δͱ͖ɼ௨ৗɼ‫ऀױ‬ͷᡧࠎ෦෼Λอ࣋͢Δɽᡧࠎ෦෼ͷൽෘ͸ബ͘ɼཧֶྍ๏࢜͸ࠎΛհͯ͠఻ΘΔߴप೾੒෼Λ৮஌͢
Δ͜ͱ͕Ͱ͖Δɽ૷ண‫ܕ‬μϛʔδϣΠϯτ͸ΧϑΛհֶͯ͠शऀʹ఍߅ྗΛఄࣔ͢ΔͨΊɼ͜ͷΧϑʹΑΓߴप೾੒෼͕‫ݮ‬ਰ͢Δɽ͜ͷΑ͏ͳप೾਺ಛੑͷҧ͍ʹΑΔ໰୊͸૷ண‫ܕ‬μϛʔδϣΠϯτʹҰҙͰ͸ͳ͍ɽؔ࿈‫͚͓ʹڀݚ‬−4−݁‫ݴ‬ΘΕΘΕ͸ཧֶྍ๏࢜ཆ੒ͷͨΊʹɼ݈ৗऀ͕μϛʔϩϘοτΛ૷ண͢Δɼ૷ண‫ܕ‬μϛʔδϣΠϯτΛఏҊͨ͠ɽ͜ͷμϛʔδϣΠϯτ͸঱ঢ়ʹಛ༗ͳ఍߅ྗΛ໛ٖ͢Δ͜
ͱ͕Ͱ͖ΔɽμϛʔδϣΠϯτ͸ਓؒͷؔઅͷෳࡶͳӡಈ‫੻ي‬Λҡ࣋͠ͳ͕Βɼैདྷ͔ΒϞσϦϯά͞Ε͖ͯͨ঱ঢ়
Λ໛ٖͰ͖Δɽ·ͨɼମͷ෦Ґͷॏ͞ɼஆ͔͞ɼൽෘͳͲਓؒΒ͕͠͞ද‫͖Ͱݱ‬Δ͜ͱ͸ཧֶྍ๏͔࢜Βߴ͍ධՁ͕ಘΒΕͨɽΘΕΘΕ͸ೈࠎͳͲͷೈ෦૊৫͕ഁյ͞ΕΔ͜
ͱʹΑΔࠎಉ࢜ͷ઀৮͕‫ݪ‬ҼͰ͋Δ crepitus Λ໛ٖͨ͠ɽ
Crepitus ͸ؔઅͷճసʹ͓͚ΔৼಈຎࡲΛ༗͢Δ઀৮ʹΑͬͯൃੜ͢Δ‫ݱ‬৅Ͱ͋ΔͨΊɼΘΕΘΕ͸ stick-slip ‫ݱ‬৅Λ‫ ʹج‬crepitus ΛϞσϧԽͨ͠ɽμϛʔδϣΠϯτʹ࣮૷ͨ͠ crepitus ϞσϧΛମ‫ͨ͠ݧ‬ೋ໊ͷཧֶྍ๏࢜ͷ಺‫؍‬ใࠂ͔ΒɼΘΕΘΕ͸͜ͷϞσϧ͕య‫ܕ‬తͳ crepitus ʹ஌֮తʹྨࣅ͍ͯ͠Δؔઅ఍߅Λఄࣔ͢Δ͜ͱ͕ՄೳͰ͋Δͱ݁࿦෇͚Δɽࢀߟจ‫ݙ‬(1) T. Kikuchi, K. Oda, S. Yamaguchi, and J. Furusho,“Leg-robot with MR clutch to realize virtual spasticmovements,” Journal of intelligent material systems
and structures, vol. 21, pp. 1523–1529, 2010.
(2) D. I. Grow, M. Wu, M. J. Locastro, S. K. Arora,
A. J. Bastian, and A. M. Okamura, “Haptic simulation of elbow joint spasticity,” IEEE symposiumon haptic interfaces for virtual environments andteleoperator systems, pp. 475–476, 2008.
(3) Y. Takahashi, T. Komeda, H. Koyama, S. Yamamoto, T. Arimatsu, Y. Kawakami, K. Inoue, andY. Ito, “Development of an upper limb patient simulator for physical therapy exercise,” Proceedingsof the 2011 IEEE international conference on rehabilitation robotics, pp. 1–4, 2011.
(4) ੴ઒ढ़, Ԭຊਖ਼‫ޗ‬, ळࢁ༃ത, ү֋߳, ࢁాཅ࣎, “ؔઅ‫ػ‬ೳো֐Λ໛ٖ͢Δ૷ண‫ܕ‬μϛʔδϣΠϯτ: ม‫ܗ‬ੑؔઅ঱ʹΑΔෆ࿈ଓͳຎࡲ఍߅Ϟσϧ,” ೔ຊϩϘοτֶձֶज़ߨԋձ, 2K3-5, 2012.
(5) D. Schiphof, “Identifying knee osteoarthritis –Classiﬁcation, early recognition and imaging,” Erasmus University Rotterdam, p. 94, Ph.D. thesis,
2012.
(6) C. W. Wu, M. R. Morrell, E. Heinze, A. L. Concoﬀ, S. J. Wollaston, E. L. Arnold, R. Singh, C.
Charles, M. Louise Skovrun, J. D. FitzGerald, L. W.
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for knee oateoarthritis using arthroscopically deﬁned cartilage damage scores,” Seminars in arthritis
and rheumatism, pp. 197–201, 2005.
(7) த ໺ ݈, ٠ ஑ ߁ ਓ, “Ϋ ʔ ϩ ϯ ຎ ࡲ Ϟ σ ϧ ʹ ‫͘ ͮ ج‬
Stick-Slip ӡಈͷൃੜ৚݅ࣜ (ୈ 1 ใ) –ൃੜ৚݅ࣜͷఆࣜԽͱۙࣅ–,” τϥΠϘϩδετ, ୈ 51 ‫ר‬, ୈ 2߸, pp. 131–139, 2006.