Optimized Synthesis of Snapping Fixtures
release_amqqfhtqsbg5zn4bn7hy565d74
by
Tom Tsabar, Efi Fogel, Dan Halperin
2020
Abstract
Fixtures for constraining the movement of parts have been extensively
investigated in robotics, since they are essential for using robots in
automated manufacturing. This paper deals with the design and optimized
synthesis of a special type of fixtures, which we call snapping
fixtures. Given a polyhedral workpiece P with n vertices and of constant
genus, which we need to hold, a snapping fixture is a semi-rigid polyhedron
G, made of a palm and several fingers, such that when P and G are well
separated, we can push P toward G, slightly bending the fingers of G on
the way (exploiting its mild flexibility), and obtain a configuration, where
G is back in its original shape and P and G are inseparable as rigid
bodies. We prove the minimal closure conditions under which such fixtures can
hold parts, using Helly's theorem. We then introduce an algorithm running in
O(n^3) time that produces a snapping fixture, minimizing the number of
fingers and optimizing additional objectives, if a snapping fixture exists. We
also provide an efficient and robust implementation of a simpler version of the
algorithm, which produces the fixture model to be 3D printed and runs in
O(n^4) time. We describe two applications with different optimization
criteria: Fixtures to hold add-ons for drones, where we aim to make the fixture
as lightweight as possible, and small-scale fixtures to hold precious stones in
jewelry, where we aim to maximize the exposure of the stones, namely minimize
the obscuring of the workpiece by the fixture.
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