arXiv subjects

Lucas R. Meza

Publications and source records attributed to Lucas R. Meza.

3 recordsLinked to original sources

arXiv2026

Robots That Generate Planarity Through Geometry

Constraining motion to a flat surface is a fundamental requirement for equipment across science and engineering. Modern precision robotic motion systems, such as gantries, rely on the flatness of components, including guide rails and granite surface plates. However, translating this static flatness into motion requires precise internal alignment and tight-tolerance components that create long, error-sensitive reference chains. Here, we show that by using the geometric inversion of a sphere into a plane, we can produce robotic motion systems that derive planarity entirely from link lengths and connectivity. This allows planar motion to emerge from self-referencing geometric constraints, and without external metrology. We demonstrate these Flat-Plane Mechanisms (FPMs) from micron to meter scales and show that fabrication errors can be attenuated by an order of magnitude in the resulting flatness. Finally, we present a robotic FPM-based 3-axis positioning system that can be used for metrology surface scans ($\pm 12$-mm) and 3D printing inside narrow containers. This work establishes an alternative geometric foundation for planar motion that can be realized across size scales and opens new possibilities in metrology, fabrication, and micro-positioning.

cs.RO↗

arXiv2023

Rethinking Ductility -- A Study Into the Size-Affected Fracture of Polymers

Ductility quantifies a material's capacity for plastic deformation, and it is a key property for preventing fracture driven failure in engineering parts. While some brittle materials exhibit improved ductility at small scales, the processes underlying this phenomenon are not well understood. This work establishes a mechanism for the origin of ductility via an investigation of size-affected fracture processes and polymer degree of conversion (DC) in two-photon lithography (TPL) fabricated materials. Microscale single edge notch bend ($μ$SENB) specimens were written with widths from 8 to 26 $μ$m and with different laser powers and post-write thermal annealing to control the DC between 17\% and 80\%. We find that shifting from low to high DC predictably causes a $\sim$3x and $\sim$4x increase in strength and bending stiffness, respectively, but that there is a corresponding $\sim$6x decrease in fracture energy from 180 $J/m^2$ to 30 $J/m^2$. Notably, this reduced fracture energy is accompanied by a ductile-to-brittle transition (DBT) in the failure behavior. Using finite element analysis, we demonstrate that the DBT occurs when the fracture yielding zone size ($r_p$) approaches the sample width, corresponding with a known fracture size-affected transition from flaw-based to strength-based failure. This finding provides a crucial insight that ductility is a size-induced property that occurs when features are reduced below a characteristic fracture length scale and that strength, stiffness, and toughness alone are insufficient predictors of ductility.

cond-mat.soft↗

arXiv2020

Nanofibril-mediated Fracture Resistance of Bone

Natural hard composites like human bone possess a combination of strength and toughness that exceeds that of their constituents and of many engineered composites. This augmentation is attributed to their complex hierarchical structure, spanning multiple length scales; in bone, characteristic dimensions range from nanoscale fibrils to microscale lamellae to mesoscale osteons and macroscale organs. The mechanical properties of bone have been studied, with the understanding that the isolated microstructure at micro- and nano-scales gives rise to superior strength compared to that of whole tissue, and the tissue possesses an amplified toughness relative to that of its nanoscale constituents. Nanoscale toughening mechanisms of bone are not adequately understood at sample dimensions that allow for isolating salient microstructural features, because of the challenge of performing fracture experiments on small-sized samples. We developed an in-situ three-point bend experimental methodology that probes site-specific fracture behavior of micron-sized specimens of hard material. Using this, we quantify crack initiation and growth toughness of human trabecular bone with sharp fatigue pre-cracks and blunt notches. Our findings indicate that bone with fatigue cracks is two times tougher than that with blunt cracks. In-situ data-correlated electron microscopy videos reveal this behavior arises from crack-bridging by nanoscale fibril structure. The results reveal a transition between fibril-bridging (~1 $μ$m) and crack deflection/twist (~500 $μ$m) as a function of length-scale, and quantitatively demonstrate hierarchy-induced toughening in a complex material. This versatile approach enables quantifying the relationship between toughness and microstructure in various complex material systems and provides direct insight for designing biomimetic composites.

cond-mat.mtrl-sci↗