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Abstract Knitting turns yarn, a 1D material, into a 2D fabric that is flexible, durable, and can be patterned to adopt a wide range of 3D geometries. Like other mechanical metamaterials, the elasticity of knitted fabrics is an emergent property of the local stitch topology and pattern that cannot solely be attributed to the yarn itself. Thus, knitting can be viewed as an additive manufacturing technique that allows for stitch-by-stitch programming of elastic properties and has applications in many fields ranging from soft robotics and wearable electronics to engineered tissue and architected materials. However, predicting these mechanical properties based on the stitch type remains elusive. Here we untangle the relationship between changes in stitch topology and emergent elasticity in several types of knitted fabrics. We combine experiment and simulation to construct a constitutive model for the nonlinear bulk response of these fabrics. This model serves as a basis for composite fabrics with bespoke mechanical properties, which crucially do not depend on the constituent yarn. 

In this paper we give a brief overview of the geometry of involute gears, from a mathematical more than an engineering perspective. We also list some of the many variant geared mechanisms and discuss some of our 3D printed mechanisms. 

We present our current progress on a virtual reality sandbox experience equipped with a toolset to create interactive vector fields and vector calculus operations. The aim of the project is to empower the student’s understanding of vector field and assist in the development of their intuition. The source code for this project is open-source and available at https://github.com/OthmanAlrawi/Visualizing-Vector-Fields. 

We describe a method of rendering real-time scenes in Nil geometry, and use this to give an expository account of some interesting geometric phenomena. You can play around with the simulation at 3-dimensional.space/nil.html. 

In this paper we outline a topological framework for constructing 2-periodic knitted stitches and an algebra for joining stitches together to form more complicated textiles. Our topological framework can be constructed from certain topological “moves" which correspond to “operations" that knitters make when they create a stitch. In knitting, unlike Jacquard weaves, a set of n loops may be combined in topologically nontrivial ways to create n stitches. We define a swatch as a mathematical construction that captures the topological manipulations a hand knitter makes. Swatches can capture the topology of all possible 2-periodic knitted motifs: standard patterns such as garter and ribbing, cables in which stitches connect one row of loops to a permutation of those same loops on the next row much like operators of a braid group, and lace or pieces with shaping which use increases and decreases to disrupt the underlying square lattice of stitches. 

We describe a method of rendering real-time scenes in Nil geometry, and use this to give an expository account of some interesting geometric phenomena. You can play around with the simulation at 3-dimensional.space/nil.html.