Measuring Three-dimensional Deformations of Elastic Ribbons
Experimental techniques to measure and visualize kinematics in structural and solid mechanics range from humble strain gage rosettes to sophisticated digital image correlation methods. This thesis develops a stereo visionbased optical measurement technique and evaluates its efficacy for measuring three-dimensional elastic deformations of slender structures. Our motivation to develop the technique stems from the need to quantify/digitize the kinematics of slender elastic structures undergoing large displacements and rotations within the small strain regime. As devices composed of highly flexible elements become ubiquitous in engineering applications, especially at small length scales, it is imperative to examine the mechanics underlying their functioning through a combination of modeling and experimental studies. The technique proposed here is a step towards addressing challenges in the context of the latter. We adopt elastic ribbons as prototypical examples in our study. Owing to the disparities in their dimensions (length ≫ width ≫ thickness), ribbons naturally contort into complex three-dimensional energy-minimizing configurations in response to simple loading scenarios. For this reason, elastic ribbons furnish excellent test cases to investigate the capabilities of the proposed technique. Besides, such measurements complement on-going efforts within the research group to understand the mechanics and envision novel applications of elastic ribbons. The proposed technique relies on familiar principles of stereo vision— a pair of calibrated digital cameras, an ansatz for pixel correspondences, and triangulation of corresponding pixel pairs to reconstruct points of interest in the scene. Hence, we will photograph a ribbon sample from multiple vantage points using a pair of digital cameras and reconstruct the locations of markers labeling its surface. The novel aspects of the technique include: the choice of fiducial markers to paint flexible surfaces, an algorithm to encode/decode 5-letter marker dictionaries that helps limit the number of distinct markers required to label surfaces, and an optimization-based algorithm to determine full-field approximations of deformations mappings by unifying independent Lagrangian marker and Eulerian shape measurements. The set of markers labeling ribbon surfaces serve multiple purposes. They define Lagrangian coordinates that can be tracked during deformation, establish pixel correspondences between cameras in a stereo arrangement, and aid in registering partial reconstructions to a common coordinate system. Throughout our study, we adopt the ArUco marker system that is commonly used for positioning and alignment of coordinate systems in virtual reality and robotics applications. This choice is mainly based on convenience; alternate marker systems (e.g., AprilTags, color-based markers, shape-based markers) along with reliable detection algorithm can be employed as well. Through a detailed set of measurements of shapes and displacements of straight and annular ribbons, we quantify the accuracy of the proposed technique at a desktop-scale. When available, we also compare the measurements with idealized finite element simulations available in the literature. We conclude the thesis by listing possible strategies to improve the technique.