Deployable 3D linkages with collision avoidance

We present a pipeline that allows ordinary users to create deployable scissor linkages in arbitrary 3D shapes, whose mechanisms are inspired by Hoberman's Sphere. From an arbitrary 3D model and a few user inputs, our method can generate a fabricable scissor linkage resembling that shape that aims to save as much space as possible in its most contracted state. Self-collisions are the primary obstacle in this goal, and these are not addressed in prior work. One key component of our algorithm is a succinct parameterization of these types of linkages. The fast continuous collision detection that arises from this parameterization serves as the foundation for the discontinuous optimization procedure that automatically improves joint placement for avoiding collisions. While linkages are usually composed of straight bars, we consider curved bars as a means of improving the contractibility. To that end, we describe a continuous optimization algorithm for locally deforming the bars.