Design, Modeling and Fabrication of Micro-Robotic Actuators With Ionic Polymeric Gel and SMA Micro-Muscles
Authors: Shahinpoor Mohsen , Burmeister Martin W. J. , Hoffman Wesley 
Published: March 2021

Abstract
Presented are the details for design and fabrication of a novel micro-robotic actuator in a few micron-size range. The model is in the form of contractile fiber bundles embedded in or around micron size helical compression springs. The fiber bundle is assumed to consist of a parallel array of contractile fibers made form either electrically or chemically (pH muscles) contractile ionic polymeric muscles such as polyacrylic acid plus sodium acrylate cross-linked with bisacrylamide (PAAM) or polyacrylonitrile (PAN) fibers or electrically contractile shape-memory alloy (SMA) fiber bundles. The proposed model considers the electrically or pH-induced contraction of the ionic polymeric fibers as well as resistive heating of the SMA fiber bundles in case of shape-memory alloys. A theoretical model is also presented for the dynamic modeling of such micron size robotic actuators. These robotic micro-actuators will open a new frontier to the micro-universes of biological, scientific, medical and engineering systems.
On the fabrication side, helical compression springs and bellows in a few microns size range have been manufactured in our laboratories to serve as the main resilient structure for the micro-robotic actuator. In principle, any size micro-robotic linear actuator can be fabricated and tested in our laboratory.
For the case of ionic polymeric gel fibers the model consists of an encapsulated hermetically sealed, helical compression spring-loaded cylindrical linear actuators containing a counterionic solution or electrolyte such as water+acetone, a cylindrical helical compression micro-spring and a collection of polymeric gel fibers (polyelectrolytes) such as polyvinyl alcohol (PVA) polyacrylic acid (PAA) or polyacrylamide. Furthermore, the helical micro-spring not only acts as a compression spring between the two hermetically sealed circular end-caps but contains snugly the polymeric gel fiber bundle and also acts as the cathode (anode) electrode -while the two actuator end-caps act as the other cathode (anode) electrodes. In this fashion, a DC electric field of a few volts per centimeter per gram of polymer gel can cause the polymer gel fiber bundle to contract (expand). This causes the compression spring to contract and pull the two end-caps closer to each other against the elastic resistance of the helical spring. By reversing the action by means of reversing the electric field polarities the gel is allowed to expand while the compression spring is also expanding and helping the linear expansion of the actuator since the polymeric gel muscle expands due to the induced alkalinity along the helical spring body. Thus, electrical control of the expansion and the contraction of the micro-robotic linear actuator is possible. A mathematical model is presented based on the proposed composite structure that takes into account all pertinent variables such as the pH of the gel fiber bundle, the pH of the surrounding medium, the hyperelastic parameters of the fiber bundle, the electrical variables of the gel, the electric field strength, the pH field strength and all pertinent dimensions followed by some numerical and experimental simulations and data.
For the second model, we consider the fiber bundle of SMA to be either circumscribed inside a micron size helical compression spring with flat heads or in parallel with a number helical compression springs, end-capped by two parallel circular plates with embedded electrodes to which the ends of the SMA fibers are secured. Thus, the fibers can be electrically heated and subsequently contracted to compress the helical compression spring back and forth. Design details are first described. In essence the dynamic behavior of the actuator depends on the interaction between the current supplied to the wires and the heat transfer from the wires. Further, a mathematical model is presented to simulate the electro-thermo-mechanics of motion of such actuators. The proposed model takes into account all pertinent variables such as the strain ϵ, the temperature of the fibers T(t) as a function of time t, the ambient temperature T0, the martensite fraction ξ, the helical compression spring constant k and the overall heat transfer coefficient h. Numerical simulations are then carried out and the results are compared with experimental observations of a number of fabricated systems in a size range of a few mcrons.