Balancing 3D Models with Movable Masses

1ETH Zurich 2Disney Research 3Dartmouth College

In Proceedings of the Vision, Modeling and Visualization Workshop (VMV), 2016

(From left to right) The Sheared Cylinder, the Muscle Gnome, the Dolphin, the Breakdancing Teddy, and the T Shape are all models whose complex balance is made possible by using movable masses and optimization with our method.


We present an algorithm to balance 3D printed models using movable embedded masses. As input, the user provides a 3D model together with the desired suspension, standing, and immersion objectives. Our technique then determines the placement and suitable sizing of a set of hollow capsules with embedded metallic spheres, leveraging the resulting multiple centers of mass to simultaneously satisfy the combination of these objectives. To navigate the non-convex design space in a scalable manner, we propose a heuristic that leads to near-optimal solutions when compared to an exhaustive search. Our method enables the design of models with complex and surprising balancing behavior, as we demonstrate with several manufactured examples.


Supplemental Video

Text Reference

Romain Prévost, Moritz Bächer, Wojciech Jarosz, Olga Sorkine-Hornung. Balancing 3D Models with Movable Masses. Proceedings of the Vision, Modeling and Visualization Workshop (VMV), October 2016.

BibTex Reference

    author = "Prévost, Romain and Bächer, Moritz and Jarosz, Wojciech and Sorkine-Hornung, Olga",
    title = "Balancing 3{D} Models with Movable Masses",
    booktitle = "Proceedings of the Vision, Modeling and Visualization Workshop (VMV)",
    publisher = "Eurographics Association",
    month = "October",
    year = "2016",
    doi = "10.2312/vmv.20161337"

Copyright Disclaimer

© The Author(s). This is the author's version of the work. It is posted here by permission of The Eurographics Association for your personal use. Not for redistribution. The definitive version is available at