以簡化的模式探討蛇及軟性機器蛇的游動特性

Abstract

本論文的研究主要分成兩大部分。第一部分旨在提出線性放大、非等振幅的行進波形，以改進Sir Taylor的正弦波形，使之能更適切描繪蛇在水中的游動現象。研究發現，非等振幅行進波形較之於正弦波形不僅具有較佳的游動效率，在能量消耗上也更有效率，同時和實際觀察的量測值也更為接近。 論文的第二部分則主要在於以第一部分的研究為基礎，探討不同波形對游動現象的影響，俾能對日後軟性機器蛇的設計有所助益。除正弦波形外，分析的波形主要分成兩大類；一類稱之為凸形波(convex wave)，一類稱之為凹形波(concave wave)。凸形波的特徵在於波形的前緣相較於正弦波形具有較大的斜率，波形較為陡峭，凹形波則在波形的前緣具有較小的斜率，波形較為緩和。研究發現若以游動速度為考量，凸形波會是設計上較佳的選擇；而若以所需耗費的彎曲能量為考量，則正弦波會是較佳的選擇。

Two main subjects are theoretically investigated by the present study. In the first part of this study, the traveling waves with linearity increasing amplitudes, instead of the traveling sine waves analyzed by Sir Taylor, are proposed to simulate the swimming motion of snakes. The result indicates that, by generating traveling waves with linearily increasing amplitudes, the snake will swim more efficiently, the predictions by the new mathematical model are closer to the observational data than those by Sir Taylor. The second part of the present study is aimed at investigating the shape effect on the swimming characteristics of a snake-like soft robot. Using sine wave as the reference, two types of wave forms are studied. One, called convex wave, has a larger slope and shape changes more rapidly than the sine wave in the leading portion of the body. The other, called concave wave, possesses a smaller slope and the shape changes mildly in the leading portion of the body. It is found from the analysis that the traveling convex waves will be the best choice for generating a lager swimming velocity of the snake-like soft robot. However, The traveling sine waves are preferred when energy saving is the main consideration.