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318   Control theory in biomedical engineering


          instruments should be flexible when traversing long and narrow paths, but
          able to become rigid upon reaching the surgical site for force application.
             Structures that allow for variable stiffness result in many desirable prop-
          erties, such as curvilinear navigation, dynamic force feedback, and shape
          deformation capabilities (Chen et al., 2016; Li et al., 2014, 2015a; Tan
          and Ren, 2017). Having a module with tunable stiffness is imperative for
          our robotic device as it allows for load-bearing capability, which is essential
          for isolating, cutting, and extracting tumors in a safe manner without con-
          taminating the surrounding healthy tissues. Currently explored variable stiff-
          ness mechanisms often involve at least one of the following: expensive and
          lengthy fabrication processes, bulky setups, and unsuitability for fast-
          changing applications. More details with regards to these limitations can
          be found in the literature review below.
             We focus on creating a novel, tunable stiffness module using auxetic
          materials to allow us to vary the rigidity of the surgical instruments and
          the backbone as required. We created a method that integrates actuation
          and stiffness modulation that allows for easy implementation and low com-
          plexity. Additionally, we use simple 3D printing, paper cutting, and folding
          methods to ensure that our approach is economically feasible and easy to fab-
          ricate compared to other variable stiffness methods.
             In the following section, we evaluate different existing methods and ana-
          lyze their suitability for surgical robots.


          2 Literature review/concept evaluation

          Currently, there are a few different methods that have been explored as
          potential mechanisms for achieving tunable stiffness. The theories behind
          these methods and their limitations are highlighted.

          2.1 Electro/magneto-rheological fluids
          Electro/magneto-rheological (ER/MR) fluids can be used to achieve tun-
          able stiffness.
             In this method, the fluid is usually composed of a primary liquid, which is
          mostly silicone oil suspended particles of a polymer. This fluid undergoes a
          change in its rheological properties, such as viscosity, when subjected to an
          electric or magnetic field (Fig. 1A). As such, the fluid transforms from a liq-
          uid phase to a solid gel phase as the field density is increased. On a micro-
          scopic level, the particles in the fluid align with the electric or the magnetic
          field lines, resulting in a change in its yield stress, viscosity, and other fluid
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