Managing indeterminacy

Bobbin lace is a very versatile textile system, comprised of sometimes thousands of individual threads with no predominant hierarchical order to distinguish them. Traditionally, lace is made with round, narrow threads with little bending stiffness. Round threads can bend freely in any direction, facilitating any pattern or geometric ‘move’ the lacemaker desires. Various combinations of “cross-twist” braiding stitches can be modulated spatially and topologically to create lace designs ranging from periodic “grounds” to free-form figures. In both cases, bobbin lace stitches are small and plentiful. Gaps between threads are minimized with tension such that capstan friction keeps the resulting textile intact.

In our elastic lace networks, we intentionally invert some of these identifying features of lace. Traditionally known for its delicacy and small size, we upheld the topological frameworks while dramatically changing material and length scale. Using stiff, elastic ribbons required adding fasteners at strand intersections to force face-to-face connections and ensure that the networks didn’t slide apart. We exaggerated spaces between strands to drive larger intersection angles, which we knew to create pronounced out-of-plane effects. In doing so, we moved lace from the mm scale to the cm and later meter scales; from the flaccid to the rigid; from dense to sparse; and from the decorative to the structural.

In practice, working with lace networks in this way posed many challenges. In a design, the most stubborn of these challenges was dealing with indeterminacy. While we had instructions for generating specific topological configurations with this material system, its high complexity meant we couldn't predict the final shape. This posed an interesting new politics to the practice of building, adopting a bottom-up, stitch-by-stitch, fabrication-oriented approach as opposed to the familiar, deterministic top-down model. Accordingly, we launched a study of how to build lace networks in 3D space without a predictive model using 6-axis industrial robots — a bold move considering that lace is thought of as one of the most intricate and virtuosic of the textile arts, which has historically evaded mechanical reproduction.

To briefly summarize this area of work, we leveraged the repetitive aspect of lace-making to design an assembly process for these complex spatial lace structures without a predictive model. Our process used two robots equipped with wrist-mounted depth sensors that took turns grasping and ‘looking.’ The vision system enabled the identification of nodes and gripping planes in 3D space for which a robust predictive model was intractable, given the mechanical complexity and large degree of spatial error inherent to long, floppy ribbons that often interacted unexpectedly with the environment. We took advantage of the lightweight, soft nature of these structures to design an assembly sequence that let a structure of indeterminate shape evolve around the robots confined to a specific work area.

Concurrently, we planned an exhibition featuring a large-scale lace structure that would test the aesthetic effects of this system at an aggressive scale, where one could effectively walk between lace stitches. Here, we ran into trouble with our headless model. In practice, we needed an accurate idea of what we were building to plan for material costs, to know whether the structure would fit in our gallery space, and what it would look like aesthetically. Engrossed in our conceptual framework of bottom-up design, I was struck by the simplicity of those basic needs in design. This was underscored at the larger scale, where the magnitude of every decision extends deeply into the budget, materials, and labor. We actually couldn’t afford to be so thoroughly and ideologically experimental.

Further, designing elastic lace networks was challenging even at the local level. Bending into 3D space, the elastic strips had a preferred direction for where they would travel, while the lace pattern prescribed another order. This conflict — or frustration — between elasticity and geometric constraint lies at the heart of what makes these networks interesting; however, it was difficult to decide on a particular intersection angle or node-to-node length on the fly, knowing that the spatial effects would be felt in adjacent modules, affecting the shape of what came before and what was to come. Along these lines, typical strategies such as temporary pinning and gluing of strips in smaller sketch models were not effective because every move required simultaneous adjustment of its neighbors.

Grappling with these challenges, at one juncture, we introduced yet another inversion in the project: a contradiction of our own initial logic, to devise a simple and low-computational-cost method for designing with lace. Our method would enable both creative modulation and design of an approximate target shape and a surprisingly accurate means of predicting the final network shape. Our method returned the distances between nodes on each strip, which were used for generating digital cut files for the assembly of a large-scale lace structure.

The method

Like many endeavors, the first step was to narrow the scope. Lace patterns can be classified as ‘open’ or ‘closed’-stitch patterns, comprised of single cross-twist (CT) or double cross-twist-cross-twist (CTCT) stitch units. For context, a single twist action makes a bigon. An interlaced bigon is formed by a closed CTCT stitch. Different lace patterns can have the same sequence of stitches yet arrive at a different design by changing the order in which thread groups are worked. Inspired by this nuance of lacemaking, we decided to focus on CTCT patterns that are comprised of interlaced bigon unit cells yet tile these units in different configurations. True to bobbin lace, our design would accommodate continuous transitions between these patterns.

To approach the problem of designing such a network in 3D space, we abstracted the interlaced bigon unit cell as a planar, four-sided surface, drawn by connecting the four outer vertices assumed to sit together in-plane, such that the dome-like shape of the module sits above or below the plane depending on orientation. With unit cells represented as planar tiles, we then studied how these tiles were connected. The simpler of the two patterns, torchon ground, makes a checkerboard pattern. Rose ground is geometrically frustrated, connecting three corners together in some places. Tiles can be regular and spatially ordered or irregular. Modulating the valency, angle, and size of the tiles made for a simpler, more intuitive design process. Quadrilaterals could easily be cut out of paper, taped, glued, or strung without invoking the complexity of interlaced ribbons. Additionally, this purely geometric representation was straightforward to adapt to digital design tools.

For example, to design our meter-scale structure, I first made a scale model of our gallery space, then composed an irregular planarized lace surface using torchon and rose ground patterns. I 3D scanned the model using a cell phone camera to obtain 3D coordinates of tile vertices. The points were digitally planarized in an optimization step using preexisting tools from the Rhino/Grasshopper/Kangaroo physics simulator framework. To add the elastic strips back to the design, catenaries were drawn to approximate elastica shapes. The catenaries did not require numerical integration to generate. An optimization was run to find the best intersection angle and arc length to minimize kinks and distances at nodes. Local curve segments were then joined to form longer composite curves per lacing pattern rules. The composite curves were then rebuilt as bezier curves to smooth out any lasting kinks. Distances between nodes were extracted and used to generate flat cut sheets for digital prefabrication of each strip. Assembling the structure became a matter of putting together this puzzle of strips, braiding them as one would in traditional lace, relying on pre-drilled holes to set the distances between nodes that ultimately give the lace object its shape.

To test the process, I first assembled a desktop-scale version of the structure using 0.25mm-thick PET film, screwing together each node with a single pin to allow rotation but not sliding. The scale model provided an opportunity to revise connections that seemed overly stressed or looked especially lumpy due to the many approximations made in our modeling process. Surprisingly, there weren’t many of these instances. I ultimately decided to leave the geometry untouched from our digital model, embracing the lumps and irregularly as part of the distorted, ‘geometrically frustrated’ aesthetic.

To make the meter-scale structure, the material choice was limited. The underlying physical dilemma exacerbates issues of cost and fabrication: as elastic structures increase in length scale, gravity plays an increasingly significant role. To resist gravity, elastic members must be stiff. However, to deform largely without imparting physical damage, the strips must be soft and thin. We opted for ~3mm-thick fiberglass, which has a high stiffness-to-weight ratio and a large elastic range. Fiberglass is also robust in extreme climate conditions, which is what we were facing in our gallery space: a single-pane glass cube built at Princeton in the 1950s to house architectural experiments by Buckminster Fuller. Visionary, exposed, and also seriously leaking to the elements! Fiberglass could stand up to those conditions and also fit in our budget. The catch was that we were required to outsource the cutting and drilling of holes for environmental safety, which turned out to be not only doable by CNC milling thanks to our geometric model, but also desirable to offset some of our labor tasks.

In a later work, I repeated this method to make a desktop-scale lace model for an exhibition in Japan. This time, the analytical target shape required generating the geometry entirely computationally. In the final piece, the lumpiness from the various approximations remains, becoming more apparent with wider strips. Note that the numerical solution of an ideal interlaced bigon unit is also lumpy due to the forced face-to-face meeting of inner nodes. Learn more about this model here.

Continue reading about other areas of this project:

← Or, head back to the Lace in Space project page