Nagasawa, Kaneko and Adachi, Journal of Advanced Mechanical Design, Systems, and Manufacturing, Vol.13, No.1 (2019)
and arranged in Fig. 14.
T ,1 (0)= E 1 ln( Z / 0.2) + E 0 , (9) Seeing Figure 13 and Fig.14, the gradient E 1 was changed from the negative (decrease) to the positive (increase) in a short time holding: 1s< t 1ep <2s. It was asymptotically and slightly increased for t 1ep >5s. This tendency seems to be caused by the relaxation of folding posture against the pre-stage accumulation of elastic bending energy. If the hold time is sufficiently long for reducing the residual bending stress, the effect of folding (first half) rotational velocity Z seems to be isolated and then only the unfolding (second half as the returning back) velocity Z ’ appears to affect the initial release angle. E 0 = T 2,1 (0)| Z =0.2rps
40 45 50 55 60 65
t 1ep = 20s
4
60
t 1ep = 10s
t 1ep = 1s t 1ep = 2s t 1ep = 3s t 1ep = 5s
Gradient E 1 E 0 = T 2,1 (0) | Z =0.2 rps
2
40
0
20
4 =90°, J =0.6, Z = Z ’
t 1ep = 0s
4 =90°, J =0.6
-2
0
0
5 20 Holding time for relaxation t 1ep /s 10 15
0.01
0.1
1
Rotational velocity Z (= Z ’) /rps
Figure 13 Relationship between initial released angle and synchronized rotational velocity by varying
Figure 14 Gradient and intercept of initial released angle with respect to rotational velocity when varying
hold time. hold time. In order to verify this isolation effect, an additional experiment was carried out. Namely, when the unfolding velocity was kept in Z ’= 0.2 rps (1.26 rad ή s ), the folding velocity Z was chosen as 0.02, 0.2 and 0.4 rps (0.13, 1.26, 2.51 rad ή s ). This is the asynchronous condition. Figure 15 shows a ratio of the coefficients of Eq.(9): E 1 / E 0 with respect to the hold time t 1ep =0~20s. Here, the synchronized condition ( Z = Z ’) was derived from Fig.14. It is found that the coefficient ratio of asynchronous condition is sufficiently small-positive for t 1ep >10s. The effect of first half rotational velocity Z is fairly isolated by the hold time of 10~20s, but its effect is observed in a small extent.
-0.04 -0.02 0 0.02 0.04
Z = Z ’= 0.02~0.4 rps
Z =0.02~0.4, Z ’=0.2 rps
4 =90°, J =0.6
0
5 20 Holding time for relaxation t 1ep /s 10 15
Figure 15 Comparison of ratio of coefficients E 1 / E 0 between synchronized and asynchronous condition
3.4 Dissipation of accumulated bending moment and variation of initial released angle As mentioned in the section 9.1, in the synchronized condition, the time-dependent response of the bending moment at the tracking position ( 4 =90°) was revealed as shown in Fig.11. When the hold time is kept in a certain duration, e.g. t 1ep >1s, the energy dissipation of accumulated bending moment seems to be characterized with the pre-stage folding velocity Z . As the result, when the release (returning back) process starts, the bending moment has a decreased level with respect to the pre-stage folding velocity Z . Seeing Fig.13 and Fig.14, the initial release angle T 2,1 (0) increased with the velocity Z (in the synchronized condition) when t 1ep >2s. This is the same as that the spring back energy of folded posture decreases with Z when the hold time is
© 2019 The Japan Society of Mechanical Engineers
[DOI: 10.1299/jamdsm.2019jamdsm0004]
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