calculated and normalized by the maximum manipulability value among all the points at a givenα andβ. The normalized manipulability measureM is shown in Fig. 2-12, using a three-color coding scheme. The points0.0< M ≤0.1,0.1< M ≤0.9, and0.9< M ≤1.0are coded in red, green, and blue, respectively. The red dots indicate areas which are more likely to have singularities.
The singularity position was shifted by changing the tilting angles. The red zone, which rep- resents the area close to singularity positions, appeared atα = 0◦, β =0◦ in the straight-forward posture. The red zone was shifted asαand β are changed as shown in Fig. 2-12b and Fig. 2-12c.
Finally, the red zone disappeared atα=27.5◦,β=50◦, which were chosen as the final tilting angles;
i.e., the singularities did not occur in the workspace for the tilting angles.
Vertically translating shoulder joint
Tilted shoulder joint Six-axis force sensor
Hand knob
(a) Side view of the exoskeleton prototype
Fy Fx
Fz
(b) Tilted shoulder joint of the exoskeleton prototype
Figure 2-13: Manufactured exoskeleton prototype.
(a) Straight forward position of the exoskeleton prototype
(b) Singularity position of the exoskeleton prototype
Figure 2-14: Shifted singularity position of the exoskeleton prototype.
0 1 2 3 4 5 6 7 0
50 100 150
Time (sec)
Net shoulder elevation (deg)
(a) Net shoulder elevation (θ) during arm elevation
0 1 2 3 4 5 6 7
-10 0 10 20 30
Time (sec)
Measured force (N) F
F
F
(b) Measured force during arm elevation
Figure 2-15: Net shoulder elevation and the measured force with the fixed shoulder joint.
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8
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Figure 2-16: Measured forces during arm elevation with the vertically movable shoulder joint.
0 2 4 6 8 10 12 14 16 18
Fz Fy Fx
Force (N)
Fx
Fy
Fz
Fixed joint Movable joint
001 . 0
<
t-test
p p<0.001 p =0.19Figure 2-17: Statistical analysis of the measured forces during arm elevation.
installed force sensor. The weight of the force sensor and the exoskeleton itself were compensated by subtracting the weight of itself from the measured force in the z-direction. Each participant performed the experiment ten times.
Figure 2-15 shows one representative result of the calculated net shoulder elevation angle and measured force changes. The directions are specified in Fig. 2-13b. Thez direction force force increases as the net shoulder elevation angle increases, which means the arm cannot be moved nat- urally by the fixed shoulder joint(Fig. 2-15b). Figure 2-16 shows a typical measured forced during arm elevation with the vertically movable joint. The vertical force (Fz) decreased significantly, compared with that of the fixed joint case.
Figure 2-17 shows the statistical analysis of the upper-limb exoskeletons with a fixed or verti- cally movable shoulder joint. The thick bars show mean values and the thin lines represent standard deviations of the data. The p-values from t-test were written below each graph. Note that the aver- age of the maximum force in the vertical direction (Fz) of the fixed joint case was 12.09 N, which restricted the natural motion of the upper limb seriously. For the vertically movable joint case, the average of the maximum force in the vertical direction was much smaller. Also, it was shown that the difference of vertical forces was statistically significant indicated as the p-values in the figure.
The vertical force of the vertically movable joint may be caused by friction of the guide rail, but it could be reduced in an actuated version of the exoskeleton.
The forces in the forward direction (Fy) were statistically different as shown in Fig. 2-17. Since
the vertically movable shoulder joint allowed free motion of the shoulder joint, the force might be less exerted than that of the fixed joint case even in the forward direction. The forces in the side direction (Fx) were not much different as shown in the figure.
These results imply that the proposed exoskeleton structure with the vertically movable shoulder joint can allow more natural upper-limb motion than the conventional exoskeleton structure with the fixed shoulder joint by reducing the compression force applied to the user’s shoulder.
2.5.2 Motion Analysis
A camera-based motion capture system [68] was used to analyze the upper-limb movement with the proposed exoskeleton structure. The experimental setup and the analyzed tasks are shown in Fig. 2- 18. The same participants of the force analysis experiments were asked to perform three tasks;
forward flexion/extension, abduction/adduction and cross-body adduction/abduction, 1) wearing the exoskeleton with the fixed shoulder joint, and 2) wearing the exoskeleton with the vertically movable shoulder joint. Markers for the motion capture system were attached to the user’s shoulder, elbow and wrist. The positions of these markers were captured while the participants were performing the tasks. To allow comparison of the three cases, each test was performed during the same time. The participants repeated the task for five times, and the position changes were normalized by the height of each participant. The normalized data of the fixed and vertically movable shoulder joints were compared using t-test. One of the representative results is shown in Fig. 2-19. As shown in the figure, the height changes of each joint using the exoskeleton with the vertically movable shoulder joint is larger than those of the vertically fixed shoulder joint case. The statistical analysis results for both cases are shown in Fig. 2-20. The mean values of height changes for all joints using the exoskeleton with the vertically movable shoulder joint were greater than those of the vertically fixed shoulder joint case. Also, the t-test demonstrated that these differences were statistically significant.
These results imply that the proposed exoskeleton structure with the vertically movable shoulder joint allowed more natural upper-limb motion than the conventional exoskeleton structure with the fixed shoulder joint.