FrameFab

Abstract

Frame shapes, which are made of struts, have been widely used in many fields, such as art, sculpture, architecture, and geometric modeling, etc. An interest in robotic fabrication of frame shapes via spatial thermoplastic extrusion has been increasingly growing in recent years. In this paper, we present a novel algorithm to generate a feasible fabrication sequence for general frame shapes. To solve this non-trivial combinatorial problem, we develop a divide-and-conquer strategy that first decomposes the input frame shape into stable layers via a constrained sparse optimization model. Then we search a feasible sequence for each layer via a local optimization method together with a backtracking strategy. The generated sequence guarantees that the already-printed part is in a stable equilibrium state at all stages of fabrication, and that the 3D printing extrusion head does not collide with the printed part during the fabrication. Our algorithm has been validated by a built prototype robotic fabrication system made by a 6-axis KUKA robotic arm with a customized extrusion head. Experimental results demonstrate the feasibility and applicability of our algorithm.

Freeform Assembly Planning

“…Their planner uses a heuristic to avoid collision and also optimizes against a cost function related to the robustness and speed of the print. 17 However, we find that the constraints and optimality criteria in these processes are not appropriate for ours. We develop an algorithm for our problem starting from a classical assembly planning framework and discuss ways in which this older body of work can simplify approaches to the problems formulated by Wu and Huang.…”

“…In order to estimate ε q , we model the assembly as a linear, elastic frame. 17 is represented as the matrix product of a vector of applied forces and moments [δ i ] and a stiffness matrix [k i,j ]. 33 This system of linear equations can be efficiently solved to find the resulting deflection at each joint in the assembly.…”

“…[4][5][6] If the extruded material can be made to rapidly stiffen after extrusion, a supporting reservoir may be unnecessary, and the material can be deposited in free space. Stiffening mechanisms include UVinduced polymerization, 7,8 thermally induced polymerization, 9 solvent evaporation, 10 shear-thinning, 11 laser sintering, 12 and, in the case of thermoplastics, [13][14][15][16][17] metals, 18 and glasses, [19][20][21] cooling below the melting or glass transition temperature. Freeform patterning, layer-by-layer patterning, and patterning directly onto a flat or curved surface have been broadly termed direct-write assembly in the scientific literature.…”

“…Unstable states are penalized with a scaffolding or reorientation cost, but the planner does not backtrack in search of a sequence that minimizes this cost. The work of Huang et al 17 is an exception: the planner performs a stability test at each state and backtracks if the state fails the test. This required an additional divide-and-conquer approach to achieve an acceptable run time.…”

RoMA

“…WirePrint [23] is the first to achieve wireframe printing with off-the-shelf 3D printers and 3D Cocooner [7] adapts this process to robotic arms. More recently, Wu et al [45] proposed a new algorithm to print arbitrary meshes with a 5 DOF 3D printer and Huang et al [13] proposed to print arbitrary mesh models with a 6 DOF robotic arm. Each of the above systems relies on a precomputed printing order, which remains immutable during the printing process.…”