| dc.description.abstract | 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. | en_US |
