Computational Design of Telescoping Structures

Abstract

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. We present a novel geometric characterization of telescoping curves, and explore how free-form surfaces can be approximated by networks of such curves. In particular we consider piecewise helical space curves with torsional impulses, which significantly generalize the linear telescopes found in typical engineering designs. Based on this principle we develop a system for computational design and fabrication which allows users to explore the space of telescoping structures; inputs to our system include user sketches or arbitrary meshes, which are then converted to a curve skeleton. We prototype applications in animation, fabrication, and robotics, using our system to design a variety of both simulated and fabricated examples.