**2. Modeling assumptions and theoretical framework**

Walking is a complex dynamic activity. A good human model for gait analysis should be simple, but extensive enough to capture the dynamics of most walkers.

Human Walking Analysis, Evaluation and Classification Based on Motion Capture System 365

[ ( ), , ( ), ( ), ( ), ( ), ( ), ( ), ( )]

*Vt t t A ttt* 

 

 1 2 3 19 *<sup>T</sup> P(t) p ,p ,p , ,p*

 1 2 3 14 *<sup>T</sup> Φ(t) , , , ,* 

 1 2 3 12 *<sup>T</sup> Θ(t) θ ,θ ,θ , , θ*

 1 2 3 19 *<sup>T</sup> V(t) v ,v ,v , ,v*

 1 2 3 19 *<sup>T</sup> A(t) a ,a ,a , ,a*

*ΛΦ(t) α ,α ,α , ,α* 

Segment angle, as shown in Equation (2), is the angle of the projections of segment with the coordinate axes. It consists of the angles between projections in transverse plane, frontal

Note that it is an absolute measure, meaning that it changes according to the orientation of

Joint angle is the angle between the two segments on either side of the joint. It is defined as

where *θs* is the joint angle in space, and *θxoy, θyoz, θzox* are the projections of joint angle in transverse plane, frontal plane and sagittal plane respectively. Since joint angle *θs* is relative

Velocity may be linear (change in displacement) or angular (change in angle). Normally, velocity is derived from displacement or angle data by the process of differentiation. Acceleration is change in velocity. Again, it may be linear (change in linear velocity) or angular (change in angular velocity). Acceleration, too, is usually calculated from the displacement

data by differentiating twice. It can also be measured directly by an accelerometer.

*ΩΦ(t) ω*

plane and sagittal plane with axis X, Y and Z respectively, see Fig. 2.

to the segment angles, it doesn't change with the body orientation.

 

1 2 3 14

*,<sup>ω</sup> ,<sup>ω</sup> , ,<sup>ω</sup>*

 1 2 3 12 *<sup>T</sup> ΩΘ θθθ θ (t) <sup>ω</sup> ,<sup>ω</sup> ,<sup>ω</sup> , , <sup>ω</sup>*

1 2 3 14

 1 2 3 12 *<sup>T</sup> ΛΘ θθθ θ (t) <sup>α</sup> ,<sup>α</sup> ,<sup>α</sup> , , <sup>α</sup>* *T*

*T*

*φ* = (*φx*, *φy*, *φz*) (2)

*θ* = (*θxoy*, *θyoz*, *θzox*, *θs*) (3)

   

(1)

*M P t Φ(t) t*

where

the body.

Equation (3).

Almost existing models, which have from 2 segments to more than 15 segments, have two pitfalls. Firstly, they paid more attention to the sagittal plane, and overlook the other two planes, transverse plane and frontal plane. Secondly, it is not enough to describe the particularity of the feet. Most of them regarded the foot as a point. Thus, it is difficult to decide the gait cycle, such as initial heel contact, heel rise, and toe off. So a new walking model, so called Fourteen-Linkage (FL) model, is proposed.

#### **2.1 Fourteen-linkage model**

DEFINITION 1. (Fourteen-Linkage Model) We suggest a walking model, which is a collection of 19 points, 14 segments and 12 joints, used to specify the position and the configuration of a human body, as shown in Fig. 1.

Position describes the location of a body segment or joint in space, measured in meters. In FL model, the 19 points can be decided by the 30 markers we measured from motion capture system. The relationships between the model and markers are also shown in Fig. 1(a).

Fig. 1. Fourteen-linkage (FL) Model

Body segments are considered to be rigid bodies for the purposes of describing the motion of the body. 14 segments are composed of these points, such as head (*S1*), shoulder (*S2*), left and right upper-arms (*S3, S4*), left and right forearms (*S5, S6*), trunk (*S7*), pelvis (*S8*), left and right thighs (*S9, S10*), left and right shanks (*S11, S12*), and left and right feet (*S13, S14*).

12 joints between adjacent segments are composed of these segments, such as head-trunk (*θ1*), head-shoulder (*θ2*), shoulder (*θ3, θ4*), elbows (*θ5, θ6*), hips (*θ7, θ8*), knees (*θ9, θ10*), ankles (*θ11, θ12*), see Fig. 1(b).

#### **2.2 Definitions of walking stability**

In human movement, kinematics is the study of the positions, angles, velocities, and accelerations of body segments and joints during motion.

FL model M consists of displacement P, segment angle Φ, joint angle Θ, and their velocity V and acceleration A, angular velocity Ω and angular acceleration Λ at time t, represented as 9-tuple as Equation (1).

$$\begin{aligned} M &= [P(t), \Phi(t), \Theta(t), \\ V(t), \Omega\_{\Phi}(t), \Omega\_{\Theta}(t), \\ A(t), \Lambda\_{\Phi}(t), \Lambda\_{\Theta}(t)] \end{aligned} \tag{1}$$

where

364 Health Management – Different Approaches and Solutions

Almost existing models, which have from 2 segments to more than 15 segments, have two pitfalls. Firstly, they paid more attention to the sagittal plane, and overlook the other two planes, transverse plane and frontal plane. Secondly, it is not enough to describe the particularity of the feet. Most of them regarded the foot as a point. Thus, it is difficult to decide the gait cycle, such as initial heel contact, heel rise, and toe off. So a new walking

DEFINITION 1. (Fourteen-Linkage Model) We suggest a walking model, which is a collection of 19 points, 14 segments and 12 joints, used to specify the position and the

Position describes the location of a body segment or joint in space, measured in meters. In FL model, the 19 points can be decided by the 30 markers we measured from motion capture

> *θ*1 *θ*2

*θ*<sup>7</sup> *θ*<sup>8</sup>

*θ*<sup>11</sup> *θ*<sup>12</sup>

*θ*4

*θ*6

*θ*9

*θ*3

*θ*5

*θ*<sup>10</sup>

system. The relationships between the model and markers are also shown in Fig. 1(a).

*p*<sup>17</sup>

right thighs (*S9, S10*), left and right shanks (*S11, S12*), and left and right feet (*S13, S14*).

(a) (b)

Body segments are considered to be rigid bodies for the purposes of describing the motion of the body. 14 segments are composed of these points, such as head (*S1*), shoulder (*S2*), left and right upper-arms (*S3, S4*), left and right forearms (*S5, S6*), trunk (*S7*), pelvis (*S8*), left and

12 joints between adjacent segments are composed of these segments, such as head-trunk (*θ1*), head-shoulder (*θ2*), shoulder (*θ3, θ4*), elbows (*θ5, θ6*), hips (*θ7, θ8*), knees (*θ9, θ10*), ankles

In human movement, kinematics is the study of the positions, angles, velocities, and

FL model M consists of displacement P, segment angle Φ, joint angle Θ, and their velocity V and acceleration A, angular velocity Ω and angular acceleration Λ at time t, represented as

model, so called Fourteen-Linkage (FL) model, is proposed.

configuration of a human body, as shown in Fig. 1.

*<sup>p</sup>*<sup>1</sup> *<sup>p</sup>*<sup>3</sup>

accelerations of body segments and joints during motion.

*p*7

*p*5

*p*8

*p*9

*p*<sup>12</sup>

*p*<sup>14</sup>

*p*<sup>13</sup>

*p*<sup>19</sup>

*p*<sup>16</sup>

*p*<sup>15</sup>

*p*<sup>18</sup>

*p*<sup>4</sup> *p*<sup>2</sup>

*p*6

Fig. 1. Fourteen-linkage (FL) Model

**2.2 Definitions of walking stability** 

(*θ11, θ12*), see Fig. 1(b).

9-tuple as Equation (1).

*p*<sup>10</sup> *p*<sup>11</sup>

**2.1 Fourteen-linkage model** 

 1 2 3 19 *<sup>T</sup> P(t) p ,p ,p , ,p* 1 2 3 14 *<sup>T</sup> Φ(t) , , , ,* 1 2 3 12 *<sup>T</sup> Θ(t) θ ,θ ,θ , , θ* 1 2 3 19 *<sup>T</sup> V(t) v ,v ,v , ,v* 1 2 3 14 *T ΩΦ(t) ω ,<sup>ω</sup> ,<sup>ω</sup> , ,<sup>ω</sup>* 1 2 3 12 *<sup>T</sup> ΩΘ θθθ θ (t) <sup>ω</sup> ,<sup>ω</sup> ,<sup>ω</sup> , , <sup>ω</sup>* 1 2 3 19 *<sup>T</sup> A(t) a ,a ,a , ,a* 1 2 3 14 *T ΛΦ(t) α ,α ,α , ,α* 1 2 3 12 *<sup>T</sup> ΛΘ θθθ θ (t) <sup>α</sup> ,<sup>α</sup> ,<sup>α</sup> , , <sup>α</sup>*

Segment angle, as shown in Equation (2), is the angle of the projections of segment with the coordinate axes. It consists of the angles between projections in transverse plane, frontal plane and sagittal plane with axis X, Y and Z respectively, see Fig. 2.

$$
\!\!\!\!\!\!\!\!\!\!\/) = \begin{pmatrix} \!\!\!\!\!\!\!\!\/) \!\!\!\!\!\!\!\!\/) \!\!\!\!\!\!\!\!\!\/) \tag{2}
$$

Note that it is an absolute measure, meaning that it changes according to the orientation of the body.

Joint angle is the angle between the two segments on either side of the joint. It is defined as Equation (3).

$$\theta = \begin{pmatrix} \theta\_{x \lor \nu} \,\, \theta\_{y \lor z} \,\, \theta\_{z \lor x} \,\, \theta\_s \end{pmatrix} \tag{3}$$

where *θs* is the joint angle in space, and *θxoy, θyoz, θzox* are the projections of joint angle in transverse plane, frontal plane and sagittal plane respectively. Since joint angle *θs* is relative to the segment angles, it doesn't change with the body orientation.

Velocity may be linear (change in displacement) or angular (change in angle). Normally, velocity is derived from displacement or angle data by the process of differentiation. Acceleration is change in velocity. Again, it may be linear (change in linear velocity) or angular (change in angular velocity). Acceleration, too, is usually calculated from the displacement data by differentiating twice. It can also be measured directly by an accelerometer.

Human Walking Analysis, Evaluation and Classification Based on Motion Capture System 367

10 11

14 15

*x*

*y* 

*y*

*x*

*z* 

The motion capture system can detect the three dimensions displacement data at tree directions: anterior-posterior, left-right, and superior-inferior. The sampling rate of motion data is 120Hz. At the same time, a tri-axial accelerometer unit is mounted with CASI, the same point as marker 18, see Fig. 3. The accelerometer is connected with a mobile phone to save the acceleration data. After that the data can be transferred to computer. Acceleration data are also collected in three dimensions as same as motion data, including the gravity acceleration. But the directions are not same. The sampling rate of acceleration data is 90Hz. To calibrate the accelerometer, before each testing session, it was placed with each of the

By the way, a movie is taken by a video camera while he/she is walking. 44 normal persons from 20 to 69 year old are measured. These subjects are classified into 5 groups (20+, 30+,

*z* 

1

2

7

13

21

24 25

16

17 18

22 23

30

orthogonal axes vertically, to estimate the ±1g values.

Fig. 4. A snapshot of data acquisition using a motion capture system

26

9

3 4 5

12

19

27 28

Fig. 3. Markers attached to the body

40+, 50+, and 60+) by the age.

8

6

20

 1: LFHD, left front head 2: RFHD, right front head 3: LBHD, left back head 4: RBHD, right back head 5: C7, under of medulla oblongata 6: T10, about center of spondylus 7: CLSV, center of clavicle 8: LSHO, left shoulder 9: LELB, left elbow

12: RSHO, right shoulder 13: RELB, right elbow

16: LASI, left front waist 17: RASI, right front waist 18: CASI, center front waist 19: LPSI, left back waist 20: RPSI, right back waist 21: LKNE, left knee 22: LANK, left ankle 23: LHEE, left heel 24: LMT5, left small toe 25: LTOE, left toe 26: RKNE, right knee 27: RANK, right ankle 28: RHEE, right heel 29: RMT5, right small toe 30: RTOE, right toe

10: LWRA, left inside wrist (thumb side) 11: LWRB, left outside wrist (little finger side)

14: RWRA, right inside wrist (thumb side) 15: RWRB, right outside wrist (little finger side)

Fig. 2. Segment angle

#### **2.3 Definitions of walking symmetry**

For walking symmetry, only consider the bilateral of positions, segments and joints on both sides of human body. In FL-Model, there are 8 points, 5 segments and 5 joint angles unilateral met this condition. These attributes are all three-dimensional data. They are motion data and its velocity and acceleration of {Knee, Ankle, Heel, Toe, Shoulder, Elbow, Wrist, Hip}, Segment Angle and its velocity and acceleration of {Thigh, Shank, Foot, Upper-arm, Forearm}, Joint Angle and its velocity and acceleration of {Hip, Knee, Ankle, Shoulder, Elbow}. These attributes can also be expressed with p1~10, p13~18, φ3~6, φ9~14, θ3~12, as shown in Fig. 1.
