Mechanics of the Whole Skin Locomotion Mechanism Concentric Solid Tube Model: the Effects of Geometry and Friction on the Efficiency and Force Transmission Characteristics

In this paper, the effects of cross-sectional geometry and friction on the mechanical advantage and efficiency of the whole skin locomotion (WSL) mechanism concentric solid tube (CST) model are presented. WSL is a novel locomotion mechanism for mobile robots, which is inspired by the motility mechanisms of single celled organisms that use cytoplasmic streaming to generate pseudopods for locomotion. It works by way of an elongated toroid which turns itself inside out in a single continuous motion, effectively generating the overall motion of the cytoplasmic streaming ectoplasmic tube in amoebae. WSL can be considered as a new class of mechanism that converts the expanding and contracting motion of rings to an everting motion of the body. A brief description of the WSL mechanism is presented first, followed by the mechanics of a single and multiple actuator rings over a CST showing the relationship between the input ring tension force and the output propulsion force for a quasi-static case. Then a study of the force transmission characteristics is presented by studying the effects of crosssection geometry and friction on the efficiency and mechanical advantage of a single actuator ring over a semicircular and composite cross section CST. INTRODUCTION Whole Skin Locomotion (WSL) [1] is a biologically inspired alternative fundamental locomotion mechanism for mobile robots inspired by the motility mechanisms of single celled organisms that use cytoplasmic streaming to generate pseudopods for locomotion. The name comes from the fact that the entire outer surface of the robot, which has a body of a ll correspondence to this author. 1 http://proceedings.asmedigitalcollection.asme.org/ on 05/02/2015 Ter shape of an elongated torus, is used as a surface for traction and that the skin is used for the actuation by cycling through contraction and expansion. The inspiration for this novel locomotion strategy comes from the way certain single celled organisms, such as the Amoeba proteus (giant amoeba) or Chaos chaos, move. The motion of these organisms is caused by the process of cytoplasmic streaming where the liquid form endoplasm that flows inside the ectoplasmic tube transforms into the gel-like ectoplasm outer skin at the front, and the ectoplasm outer skin at the end transforms back into the liquid form endoplasm at the rear. The net effect of this continuous ectoplasm-endoplasm transformation is the forward motion of the amoeba [1-3]. Directly imitating this cytoplasmic streaming process with a robot is very difficult to do if not possible since it would be very challenging to implement something similar to the endoplasm-ectoplasm transformation in macro scale. Thus, instead of using the process of liquid to gel transformation of cytoplasm, the WSL is implemented by a flexible membrane skin (or a mesh of links) in the shape of a long torus. The skin of this elongated torus can then rotate in a fashion of turning itself inside out in a single continuous motion, effectively generating the overall motion of the cytoplasmic streaming ectoplasmic tube in amoebae (Figure 1). A robot that uses WSL 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, since the entire skin is used for locomotion. 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 of its contact surfaces for traction, or Copyright © 2006 by ASME ms of Use: http://asme.org/terms Downl even squeeze itself through holes with diameters smaller than its nominal width as demonstrated in [4]. Figure 1. EVERTING MOTION GENERATED BY THE CONTRACTING (1a, 2a, 3a) AND EXPANDING (1b, 2b, 3b) ACTUATOR RINGS FOR THE CONCENTRIC SOLID TUBE WSL MODEL. Some examples of robots that use the idea of distributed contact locomotion include the rolling stents endoscope [5], and a cylindrical robot with feet distributed over the surface [6,7]. 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 perform 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 monotread robot [8] that uses a steerable single continuous belt. All of these robots share some similar characteristics with WSL in a sense; however their topology and method of actuation are completely different. In this paper, we present the effects of cross-sectional geometry and friction on the mechanical advantage and efficiency of the WSL mechanism concentric solid tube (CST) model. First, a brief description of the WSL mechanism is presented, followed by the mechanics of a single and multiple actuator rings over a CST showing the relationship between the input ring tension force and the output propulsion force for a quasi-static case. Then a study of the force transmission characteristics is presented by studying the effects of crosssection geometry and friction on the efficiency and mechanical advantage of a single actuator ring over a semicircular and composite cross section CST. WHOLE SKIN LOCOMOTION MECHANISM The body of the WSL mechanism is consisted of a toroid shaped skin that either has a solid tube inside (concentric solid tube model, or CST), or is filled with liquid (fluid filled toroid oaded From: http://proceedings.asmedigitalcollection.asme.org/ on 05/02/2015 Ter model, or FFT) like that of a common child's toy that is often referred to as a “water worm.” The motion of the torus shaped skin is generated by the contraction and expansion of the actuation rings embedded in the skin using several different mechanisms as proposed in [1]. Among these actuation mechanisms, in this paper the analysis of the “rear contractile rings with concentric solid tube” actuation strategy is presented. As the contractile ring near the edge (1a) begins to contract it pulls itself over the rounded edge of the concentric solid tube, pulling the currently inactive rings behind them, as shown in Figure 1(a). When the following contractile ring (2a) approaches the rounded edge it begins to contract, adding to the force of the first ring, as shown in Figure (b). This process continues as the first rings begin to pass completely inside the tube, as shown in Figures 1(c) and 1(d). The active rings will continue to pull the inactive rings allowing for a continuous motion of the membrane skin. The WSL mechanism is considered as a new class of mechanism that converts contracting and expanding motion of a ring to a toroidal everting motion. Thus, it does not require conventional actuators such as electric motors or linear actuators. To actuate the contracting and expanding rings to generate the desired motion for the WSL mechanism, two different methods were proposed [1], one method for the larger scale implementation, the other for the smaller scale implementation. The larger scale method consists of rings of accordion type hoses that are expanded and contracted using pressurized fluid, such as compressed air. The benefit of this strategy is that a large displacement (strain) can be obtained easily and the actuation force can be made large since it simply depends on the pressure of the fluid in the expanding hoses. These expanding rings can be embedded into the skin of the robot as channels, making it a robust approach of generating the everting motion. The smaller scale method being considered uses rings of electroactive polymer (EAP) strips around the toroid to drive the motion. Active materials maybe the ideal actuators for WSL, since the strain they are able to produce is the type of displacement needed for WSL. Though promising, the general problem of this approach is the lack of force generated by these active materials. Thus, EAPs are only considered for small-scale implementations. MECHANICS OF THE CONCENTRIC SOLID TUBE MODEL A simplified analysis of the mechanics for the concentric solid tube (CST) type body with rear contractile rings was performed to gain insight into the mechanics of the simplest WSL mechanism actuation model. In this analysis, the effects of the elastic membrane skin are not considered, which can have a significant effect on the overall mechanics of the WSL CST model. Nomenclature η Efficiency of a single actuating ring over a CST μ The coefficient of Coulomb friction between the contracting ring and the CST surface 2 Copyright © 2006 by ASME ms of Use: http://asme.org/terms Dow φ The slope angle of the CST surface in the longitudinal direction f Distributed force along the inside of a contracting ring in the radial direction (the “squeezing” force of an actuator ring on the CST surface) [force/length] fN Distributed normal force on the surface of a CST in the radial direction due to a contracting ring actuator [force/length] fR Distributed output “propulsion” force in the longitudinal direction of a single contracting ring actuator [force/length] ff Distributed friction force in the longitudinal direction between the contracting ring and the CST surface [force/length] F The total “propulsion” output force generated by a contracting actuation ring(s) [force] R The current radius of a contracting ring actuator [length] s Position of an actuation ring represented as the distance from a fixed reference on the CST, along its travel path on the CST surface in the longitudinal direction [length] TR Tension in a contracting ring actuator [force] n The nominal number of actuating rings per unit length in the longitudinal direction assuming equal distribution N The number of active contracting actuator rings Single Contracting Ring Actuator Over a CST Figure 2 shows the free body diagram of a single contracting ring at the instant when its radius is R and when it is squeezing the membrane over the CST with a distributed force in the radial direction of f (unit: [force]/[length]). Figure 2. FREE BODY DIAGRAM OF A CONTRACTING RING ACTUATOR The relationship between the tangential direction tension in the contracting actuator TR and the distributed “squeezing” force f in the radial direction can be found by ! Fx1 = 0 " # f cos$ % R %d$