Purcell's Three Link Swimmer in a Macroscopic Lab

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. We use a 3-D printed body and vary its shape to see how the how the performance of the swimmer changes in a sand test bed before placing the robot into a tank of highly viscous silicone oil so the Reynolds number is small. Once the robot design is complete we wil lthen track the motion in videos to compare the displacement and rotation to that predicted by theory. We plat to 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.