Researchers from Carnegie Mellon have been working to make strides in improving new ways to model telescoping structures, specifically in making curves. Their goal is to continue where original telescope makers left off, leaving a legacy of technology that the research team sees as still ‘relatively unexplored.’ They have created new models, both mathematical and computational, for exploring this technology that has been with us for so long (made famously attractive by pirates), and appreciated in so many different applications.
Christopher Yu, Keenan Crane, and Stelian Coros detail their study, and results, in a recently published paper, ‘Computational Design of Telescoping Structures.’
“Telescoping structures are valuable for a variety of applications where mechanisms must be compact in size and yet easily deployed. So far, however, there has been no systematic study of the types of shapes that can be modeled by telescoping structures, nor practical tools for telescopic design,” state the researchers in their paper.
Their focus is on piecewise helical space curves with torsional impulses. During the research project, the team went on to make a system for users to explore structures capable of telescoping. Sketches and meshes from users were used to create a curve skeleton. The team makes applications in animation, fabrication, and robotics.
The fundamental shape for a telescoping shell is a solid (top) swept along a helical path called the medial curve. Any such shape (bottom) can slide along itself via a continuous screw motion.
Although research has been scant on such a subject, the researchers point out that those involved in creating innovation for spaceflight have been motivated to develop applications like robots and bridges. Previous work has focused on:
- Deployable structures
- Compact storage
- Computational folding
- Geometry of space curves
- Mesh skeletonization
In working with piecewise helical curves, the team’s goals were outlined as the following:
- Approximate given curses as densely-sampled polyline.
- Smooth curvature via heat flow.
- Divide it into segments and compute the best approximation of its torsion by a constant plus impulses.
- Convert each segment into a telescoping shell.
Overview of the skeletonization process. The vertices of the original
model are collapsed first to the skeleton and then to a spline network. After
cleaning, the spline network can be discretized and ultimately converted to
a telescoping structure.
The team found that they were able to achieve optimization by framing curvature and torsion.
“Moreover, since there is no dependence of κ on τ (and vice versa), these functions can be optimized separately,” state the researchers in their paper. “We can avoid drift in the curve endpoints (which may need to connect to other curves) by finding a rotation and uniform scaling that aligns the endpoints of the helical approximation with the endpoints of the given curve.”
The team also had to work to make adjustments for 3D printing. They had to create linear tapings of shell radii for preserving shell connection, as well as making each shell longer.
“To realize given torsional impulses we carve a channel into the interior prole of each parent, and add small protrusions at the base of each child. Together, this geometry guides the extension motion of the child, and allows the child to twist as far as necessary but no further. Finally, we add a small gap between consecutive shells, both to give room for extended shells to rotate, and to accommodate tolerances of 3D printers,” they explain.
They also wanted to make the objects they were creating more interesting, so the team fabricated a network of telescoping chains. This was possible with junctures, or fixed objects to which the curves attach. According to the team, they used ‘basic 3D printing’ for their prototypes, but even at that level they found they were able to produce complex designs.
As for the future, the team will use their previous model to continue to their work. Goals include improving geometric approximation, as well as replacing some of the current junctures with telescoping splitters.
“It is also interesting to consider the conditions under which a cyclical telescope or network of such cycles admits feasible extension/contraction. Finally, mechanical actuation of extension and torsional impulses would yield automatic deployability and controllability, facilitating the aforementioned applications in engineering and robotics,” concluded the team.
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Left: Telescopes designed using the research team’s pipeline. Right: 3D printed physical prototypes.