MECHANICAL ADVANTAGE AND EFFICIENCY FOR DIFFERENT CROSS-SECTION GEOMETRIES

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Chapter 2 Biologically Inspired Whole Skin Locomotion

Single celled organisms have three primary ways of locomotion; using flagella, cilia, or pseudopods [16]. A flagellum is a single tail that drives itself like that of a tadpole, and cilia are small hair-like strands that are used for swimming or crawling. A pseudopod is part of a cell that extends itself, similar to a leg (Figures 1 and 2). Pseudopods form by a process called cytoplasmic streaming, a process in which endoplasm flows forward inside the ectoplasmic tube to protrude the pseudopod tip outward of the body [16, 17] as shown in Figure 2.
The name “Whole Skin Locomotion” comes from the fact that the entire outer surface of a robot using this locomotion mechanism is used as a surface for traction and that the entire skin is used for the actuation by cycling through contractions and expansions to generate an everting motion [6]. This is fundamentally different from the undulatory motion of snakes [7, 18, 19] or inchworms [20, 21], as WSL works more like a three-dimensional tank tread. Since the entire skin is used for locomotion, the robot can move as long as any surface of the robot is in contact with the environment, be it the ground, walls or obstacles on the side, or the ceiling. With an elastic membrane or a mesh of links acting as its outer skin, the robot can easily squeeze between obstacles or under a collapsed ceiling and move forward using all its contact surfaces for traction (Figure 3(a)), or even squeeze itself through holes with diameters smaller than its nominal width (Figure 3(b)). This makes WSL the ideal locomotion method for search-and-rescue robots, medical robots [22, 23, 24], or robots for inspecting gas pipes for corrosion and leakage [25].
Especially for robotic endoscope applications, since the very delicate gastrointestinal tract has sharp turns and changes in diameter [9], WSL could be used to minimize the possibility of damage to a person as it distributes the force required for movement over the largest possible area and morphs its shape to match that of the gastrointestinal tract.
Some examples of robots that use the idea of distributed contact locomotion include the rolling stent endoscope [26] and a cylindrical robot with feet distributed over the surface [27, 28]. The rolling stent endoscope uses a “rolling donut” constructed from three stents positioned around the endoscope tip for intestinal locomotion, and the cylindrical robot with distributed feet performs a coordinated shoveling motion of the feet that provides forward propulsion wherever a foot is in contact with any feature in the environment. Another example is a mono-tread robot that uses a steerable single continuous belt. In a sense, all of these robots share some similar characteristics with WSL; however, their topology and method of actuation are completely different.

Theories of Amoeboid Motility Mechanisms

Among the many theories of amoeboid motility mechanisms proposed by biologists [16, 17, 30], we will be applying two theories we consider the most useful to adapt and implement for the WSL actuation models. These are the tail contraction model and the frontal-zone contraction model.
In both models, the motion of the body is caused by the process of cytoplasmic streaming (Figure 2). Cytoplasm is made up of gel-like ectoplasm and liquid endoplasm. The endoplasm flows forward inside the ectoplasmic tube, which acts as the outer skin. When the endoplasm reaches the front, it turns into the gel-like ectoplasm forming the pseudopodial tip in a region called the hyaline cap. The pseudopodial tip in turn forms an extension of the ectoplasmic tube, moving the organism forward. As the amoeba advances, the ectoplasmic tube turns into the liquid endoplasm at the rear, or uroid of the cell, and the process continues [16, 17]. The net effect of this ectoplasm-endoplasm transformation is the forward motion of the amoeba.
Most researchers in the field agree that the motor for the motion of the amoeba is actomyosin based. Actomyosin is a protein complex in muscle fibers composed of myosin and actin. It shortens when stimulated and causes muscle contractions in biological systems [16, 17, 31]. Exactly how the actomyosin based cytoplasmic streaming happens is still debated, and many theories exist; however, the tail contraction model and the frontal-zone contraction model are the two theories we apply to the WSL mechanism model.

Tail Contraction

The tail contraction model, first put forward by Ecker [32, 33], is based on the observable contraction of the rear of the cell. While the amoeba is moving, the membrane around the uroid, or tail, folds up because the ectoplasm immediately under it is turning into endoplasm. The idea is that as the tail contracts, it causes a small positive pressure within the cytoplasm which would force more fluid endoplasm forward along the line of least resistance. This theory was supported by basic observations of a moving amoeba, and in experiments where particles implanted in the cytoplasm come closer together in the uroid, indicating contraction of the cytoplasm [34]. The pressure gradient caused by the contraction can be measured by having an amoeba crawl through a hole between two chambers and measuring the pressure difference [16].

Frontal-Zone Contraction

The frontal-zone contraction model proposes to explain the mechanism by the assembly process of endoplasm into gel-like ectoplasm at the advancing tip of the pseudopod, accompanied by contraction, pulling the endoplasm forward and pushing the pseudopod tip outward. This theory was proposed after an experiment in 1960 which could not be explained by the tail contraction model [30]. In this experiment, the membrane of an amoeba is broken by taking an amoeba in a glass capillary, and then breaking the glass capillary. The cytoplasm was able to flow in multiple directions even without the contracting uroid suggesting that the tail contraction model is not the only mechanism for cytoplasmic streaming [31, 35]. Other experiments followed further showing that the pressure gradient was not the sole driving force behind amoeboid locomotion [30, 36, 37]. However, there is still no direct evidence showing either theory to be correct or incorrect, and thus the debate on the amoeboid motility mechanism continues.

ABSTRACT.
Acknowledgments 
Chapter 1: Introduction
Chapter 2: Biologically Inspired Whole Skin Locomotion .
Chapter 3: Theories of Amoeboid Motility Mechanisms
3.1 TAIL CONTRACTION
3.2 FRONTAL-ZONE CONTRACTION
Chapter 4: Models for the Whole Skin Locomotion Mechanism
4.1 REAR CONTRACTILE RINGS WITH CST
4.2 FRONTAL EXPANSILE RINGS WITH CST
4.3 WAVE CONTRACTILE/EXPANSILE RINGS WITH CST
4.4 REAR SKIN CONTRACTION WITH FFT
4.5 ACTUATION METHODS AND PACKAGING
Chapter 5 Feasibility Experiments
5.1 FEASIBILITY EXPERIMENT WITH PRE-TENSIONED ELASTIC SKIN
5.2 REAR SKIN CONTRACTION EXPERIMENT USING TENSION CORDS
Chapter 6: Analysis of the CST Model .
NOMENCLATURE
6.1 MECHANICS OF A SINGLE ACTUATION RING OVER A CST
6.1.1 Region
6.1.2 Region II
6.1.3 Region III
6.1.4 Region IV
6.2 MECHANICAL ADVANTAGE AND EFFICIENCY FOR DIFFERENT CROSS-SECTION GEOMETRIES
6.2.1 Round Cross-section, Region
6.2.2 Straight Line Cross-section, Region
6.2.3 Composite Cross-section, Region
6.2.4 Region II
6.2.5 Region III and
6.3 ANALYSIS AND SIMULATION FOR THE CST MODEL SYSTEM
6.3.1 Displacement Constraints of the Actuation Rings for the CST Model System
6.3.2 Input Tension Required for the Actuation Rings for the CST Model System
Chapter 7: Conclusions and Future Work
References
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Whole Skin Locomotion Inspired by Amoeboid Motility Mechanisms: Mechanics of the Concentric Solid Tube Model