Building a macroscopic three-link swimmer at low Reynolds number

Purcell theorized that one of the simplest robots that can move at low Reynolds number is a three-link swimmer, which consists of three hinged links in a chain. The work of Hatton and Choset (IEEE Trans. Robot, 2013) provides a theoretical framework to predict the displacement and rotation of such a swimmer, but assumes the robot links are slender. They use a phase space of the two joint angles and a 3-D map known as a height function derived from the Navier-Stokes equations to determine the motion of the swimmer. However, no one has tested this theory experimentally using a macroscopic three-link robot. Our robot will swim in highly viscous silicone oil so the Reynolds number is small, and we track the motion in videos to compare the displacement and rotation to that predicted by theory. We will also determine the height function for our robot empirically (Hatton et al., PRL 2013) to understand the error introduced by our robot not being a slender body. We use a 3-D printed body and vary its shape to see how the how the performance of the swimmer changes.