Computational Design and Optimization of Non-Circular Gears
Hao Xu^1
Tianwen Fu^1
Peng Song2
Mingjun Zhou1
Chi-Wing Fu1
Niloy J. Mitra3,4
(^ joint 1st authors)
Adobe Research London


We introduce an automatic method to design non-circular gears, which are optimized not only to resemble the input shapes (left) but also to transfer motion continuously and smoothly (middle). Further, our results can be 3D-printed and put to work in practice (right).


We study a general form of gears known as non-circular gears. These gears can transfer periodic motion with variable speed through their irregular shapes and eccentric rotation centers. To design functional non-circular gears is nontrivial, since the gear pair must have compatible shape to keep in contact during motion and one gear can push the other to rotate under a bounded torque that a motor can exert. We address the challenge by modeling the geometry, kinematics, and dynamics of noncircular gears, formulating the design problem as a shape optimization, and identifying necessary independent variables in the optimization search. Taking a pair of 2D shapes as inputs, our method optimizes them into gears by locating the rotation center on each shape, minimally modifying each shape to form the gear’s boundary, and constructing appropriate teeth for gear meshing. Our optimized gears not only resemble the input shapes, but also require relatively small torque to drive the motion. We demonstrate our method by generating a rich variety of non-circular gears from various inputs, and 3D printing several of them to show the usability.

Our Results


Hao Xu, Tianwen Fu, Peng Song, Mingjun Zhou, Niloy J. Mitra, and Chi-Wing Fu
Computational Design and Optimization of Non-Circular Gears
[Paper] [Code] [Models for 3D Printing]



This work is supported by grants from the Research Grants Council of the Hong Kong Special Administrative Region (Project no. CUHK 14201918 and 14203416), SUTD Start-up Research Grant (Award Number: SRG ISTD 2019 148), ERC Starting Grant, ERC PoC Grant, Google Faculty Award, Royal Society Advanced Newton Fellowship, and gifts from Adobe.