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1 NAIST-IS-MT

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3 ,,,,,,, NAIST-IS- MT1518, i

4 Arm motion analysis based on agonist and antagonist muscle activity Takahiro Ito Abstract Human has much more muscles than joints and control joint stiffness using agonist and antagonist muscles. In this case, joint stiffness means spring coefficient of flexion or extension of joint, many motion analysis research based on the joint stiffness are reported. From the other viewpoint, we can say that an arm posture is depended on a balance of agonist and antagonist muscles. The balanced arm posture is called equilibrium point. The equilibrium point control hypothesis which arm movement is achieved by gradually shifting equilibrium point is proposed. In this thesis, I produce an estimation method of stiffness and equilibrium point using surface electromyography (SEMG) and arm posture during arm motion. Muscle force is calculated from the SEMG and the arm posture using an arm musculoskeletal model. Then the stiffness and the equilibrium point are estimated from the muscle force using the arm model. Drawing circle motion on a horizontal plane is employed for an experiment of the stiffness and the equilibrium point estimation. I discuss about an effect of agonist and antagonist muscles based on the experimental results. Keywords: Musculoskeleton, Surface Electromyography, Internal Force, Stiffness, Equilibrium Position, Reaching Movement Master s Thesis, Department of Information Systems, Graduate School of Information Science, Nara Institute of Science and Technology, NAIST-IS-MT1518, March 16, 212. ii

5 iii

6 A. 51 B. 52 iv

7 1 [13] [23] [24] [32] [32] : 1( ) : 1( ) : 2( ) : 3( ) : 4( ) : 5( ) [sec] : : : 1( ) : 2( ) : 3( ) : 4( ) v

8 29 : 5( ) [sec] : : vi

9 [1] 1 [2][3] [4][5][6][7] 1

10 [8][9][1] 1 Flash [11] 1 [12] Mussa-Ivaldi Gribble 1(a) [13][14] 1[m] [N] 1(b) 2

11 Mussa-Ivaldi [15] 2 [16] Flash 2 [17] Miler [18][19] Flash [17] [2] [21][22] 3

12 (a) (b) 1 [13] [23] 2 [24] 3 4

13 図 2 右上肢の筋骨格 [23] 図 3 水平面内における右上肢の筋群モデル [24] 5

14

15 (a) (b) 4 7

16 [24] Hill [25] Hill Hatze 7 [26] F(t) = T max {τ (t) k (x(t)) h (ẋ(t)) + f p (x(t))} (1) [27] t[sec] F(t) τ (t)( α 1) T max (Physiological Cross Sectional Area: PCSA) (62[N/cm 2 ]) Wood Ikai [28][29][3] 8

17 5 9

18 x(t) l(t) r(θ 1 (t), θ 2 (t))=( 45[deg], 9[deg] ) ẋ(t) l(t) x(t) l(t) = l m A x(t) = l(t) r θ 1(t) θ 2 (t) (2) l m =( [deg], [deg] ) A 6 r Wood (3) 1

19 3 2 [28][29] A = a 11 a 12 a 15 a 16 a 23 a 24 a 25 a 26 (4) k(x(t)) x(t) h(ẋ(t)) ẋ(t) f p (x(t)) x(t) 8(a) 8(b) 9(a) 9(b) k(x(t)) = exp { 1.112(x(t) 1)} sin {3.722(x(t).656)} (5) h(ẋ(t)) = 1.5 {1 + tanh(3ẋ(t))} (6) f p (x(t)) =.1exp {7.2 (x(t) 1)} (7) 11

20 (a) α = 1. (b) α =.5 8 (a) α = 1. (b) α =

21 2.3 Hogan [1] R(t) R(t) = R jk (t) = i R 11 R 12 R 21 R 22 (8) (a ji F i (t)) θ k (9) R jk (t) R(t) a j,i F i (t) i {1,..., 6} j {1, 2},k {1, 2} 6 (8) [31] i {1, 3, 5}, θ 1 (t) > θ 2 (t) > R jk (t) = (a ji F i (t)) i {1, 4, 5, 6}, θ 1 (t) > θ 2 (t) <, (1) i θ k i {2, 3, 5, 6}, θ 1 (t) < θ 2 (t) > i {2, 4, 6}, θ 1 (t) < θ 2 (t) < θ(t) = θ(t) θ( t) (11) 1.2 [13] 13

22 1 K(t) = (J T ) 1 R(t) J 1 (12) 2.4 Gomi [16] τ (t) = (τ 1 (t), τ 2 (t)) R(t) θ eq (t) = (θ eq1 (t), θ eq2 (t)) τ (t) = R(t) (θ eq (t) θ(t)) (13) θ eq (t) = R(t) 1 (τ (t) R(t) θ(t)) (14) τ (t) τ (θ(t), θ(t), τ (t)) + G(θ(t)) = H(θ(t)) θ(t) + B(θ(t), θ(t)) (15) H(θ(t)) = B(θ(t), θ(t)) = H 11 H 12 (16) H 21 H 22 B 1 B 2 (17) G(θ(t)) H(θ(t)) B(θ(t), θ(t)) 14

23 (a) (b) (c) (d) 1 15

24 I 1,I 2 M 1,M 2 S 1,S 2 b 1,b 2 H(θ(t)) B(θ(t), θ(t)) 4 H 11 = { I 1 + I 2 + M 2 L L 1 S 2 cos(θ 2 (t)) } (18) H 12 = I 2 + M 2 L 1 S 2 cos(θ 2 (t)) (19) H 21 = I 2 + M 2 L 1 S 2 cos(θ 2 (t)) (2) H 22 = I 2 (21) B 1 = M 2 L 1 S 2 sin(θ 2 (t)) { 2 θ 1 (t) θ 2 (t) + θ 2(t) } 2 + b 1 θ1 (t) (22) B 2 = M 2 L 1 S 2 sin(θ 2 (t)) θ 1(t) 2 + b 2 θ2 (t) (23) 16

25 Vicon Motion Systems VICON 2[Hz] 13 EMG [Hz] %MVC B 17

26 11 1 6, 2 1Hz 1Hz( 3dB) 1 (4dB) 18

27 [mm] 7.5[mm] 5[sec] [sec] %MVC %MVC

28 図 12 計測する筋肉 [32] 図 13 マーカの配置 [32] 2

29 4. 無負荷での円軌道到達運動 本章ではそのうちの１つの実験について説明する 3 章で述べた実験環境と実 験条件下で 手先に負荷のない状態での円軌道を描く運動を被験者に行なっても らった 実験結果と考察を次節に示す 図 14 無負荷の円軌道運動実験の概観 21

30 (a) 15(b) 15(c) (a), 17(a), 18(a), 19(a), 2(a) x (. 2.[sec] ) x ( 2. 4.[sec] ) y ( 2.[sec] ) y ( 3. 4.[sec] ) 5 4 x y ( 3. 4.[sec] ) 16(a) 1 y ( 3.[sec] ) 4 15(b) 1 22

31 16(b), 17(b), 18(b), 19(b), 2(b) 16(c), 17(c), 18(c), 19(c), 2(c) x y y 23

32 F[N] t[sec] (a) [N/m].5.5 (b) (c) 15 : 1( ) 24

33 F[N] t[sec] (a) [N/m].5.5 (b) (c) 16 : 1( ) 25

34 F[N] t[sec] (a) [N/m].5.5 (b) (c) 17 : 2( ) 26

35 F[N] t[sec] (a) [N/m].5.5 (b) (c) 18 : 3( ) 27

36 F[N] t[sec] (a) [N/m].5.5 (b) (c) 19 : 4( ) 28

37 F[N] t[sec] (a) [N/m].5.5 (b) (c) 2 : 5( ) 29

38 (a) 15(a) 3.2[sec] (a) 21(b) 21(c) 15(c), 16(c)

39 [N/m] 12.5[N/m] (a) (b) Ky[N/m] Kx[N/m] (c) [sec] 31

40 [N/m] (a) : [N/m].5.5 (b) :4 22 : 3 32

41 (a) : (b) :4 23 : 3 33

42 5. 手先に負荷のある円軌道到達運動 本章では 3 章で述べた実験環境と実験条件下で 手先にゴムバンドによる負 荷を与えながら円軌道を描く運動による実験について述べる 手先に負荷を掛け ることで 手先に負荷の無い場合と比べて異なる筋活動となることが予想される ため その点を提案手法による剛性と平衡位置推定を用いて評価することが可能 であるかを検証する 図 24 負荷のある円軌道運動実験の概観 34

43 (a), 26(a), 27(a), 28(a), 29(a) x (. 2.[sec] ) x ( 2. 4.[sec] ) y (. 2.[sec] ) ( 5.[sec] ) 25(a) 1 y ( 3. 4.[sec] ) 4 26(a) 2 y ( 3. 4.[sec] ) 4 25(b), 26(b), 27(b), 28(b), 29(b) 25(c), 26(c), 27(c), 28(c), 29(c) x 35

44 y y y y 36

45 F[N] t[sec] (a) [N/m].5.5 (b) (c) 25 : 1( ) 37

46 F[N] t[sec] (a) [N/m].5.5 (b) (c) 26 : 2( ) 38

47 F[N] t[sec] (a) [N/m].5.5 (b) (c) 27 : 3( ) 39

48 F[N] t[sec] (a) [N/m].5.5 (b) (c) 28 : 4( ) 4

49 F[N] t[sec] (a) [N/m].5.5 (b) (c) 29 : 5( ) 41

50 (a) 3(b) 3(c)

51 [N/m] 12.5[N/m] (a) (b) Ky[N/m] Kx[N/m] (c) 3 2.6[sec] : 1 43

52 [N/m] (a) : [N/m].5.5 (b) :4 31 : 3 44

53 6. 2 MRI 45

54 46

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59 A. 2 T max [N] P CSA[cm 2 ] r[m] a 11 a 12 a 23 a 24 a 15 a 16 a 25 a 26 a ji [m] M[kg] L[m] S[m] I[kg m 2 ].65.1 b[kg m 2 /s]

60 B. ISEK [33] [Hz] [Hz] %MVC 1%MVC [34] 25[N] %MVC [N]

61 図 32 手先の発揮力計測の実験環境 53