  3D printing enables the fabrication of complex architectures by automating
long sequences of additive steps. The increasing sophistication of printers,
materials, and generative design promises to make geometric complexity a
non-issue in manufacturing; however, this complexity can only be realized if a
design can be translated into a physically executable sequence of printing
operations. We investigate this planning problem for freeform direct-write
assembly, in which filaments of material are deposited through a nozzle
translating along a 3D path to create sparse, frame-like structures. We
enumerate the process constraints for different variants of the freeform
assembly process and show that, in the case where material stiffens via a glass
transition, determining whether a feasible sequence exists is NP-complete.
Nonetheless, for topologies typically encountered in real-world applications,
finding a feasible or even optimal sequence is a tractable problem. We develop
a sequencing algorithm that maximizes the fidelity of the printed part and
minimizes the probability of print failure by modeling the assembly as a
linear, elastic frame. We implement the algorithm and validate our approach
experimentally, printing objects composed of thousands of sugar alcohol
filaments with diameters of 100-200 microns. The assembly planner allows the
freeform process to be applied to arbitrarily complex parts, from tissue
engineering and microfluidics at the micrometer scale, to vascularized
functional materials and soft robots at the millimeter scale, to structural
components at the meter scale, thus opening a variety of assembly
possibilities.
