Strain wave gear (SWG) drives were patented in 1959 by C. Walton Musser as a coaxial, compact, and lightweight gear drive providing remarkably large gear ratios without backlash. This outstanding performance requires the use of a flexible gear, as well as a meshing process with two regions of tooth contact as opposed to traditional gear drives, which only mesh in a single region. The latter drives have been studied for centuries under the principles of solid mechanics whereas SWG drives lack strong bodies of literature, principles, and computational tools for their design.

SWG drives include three parts: wave generator, flexible spline, and ring gear. Typically, the wave generator is an elliptical cam surrounded by a flexible race ball bearing which, inserted inside the flexible spline, provides the input motion to the drive. The flexible spline is a cup-shaped spring with external teeth on the open-end which, deflected by the wave generator, mesh with the internal teeth of the ring gear in two regions along the major axis of the drive. This thesis dissertation focuses on understanding the influence of the geometries of the wave generator and tooth profiles of the flexible spline and the ring gear over stresses throughout the operation of SWG drives. In doing so, computational tools have been developed and design recommendations have been formulated. The wave generator geometries simplified, elliptical, and four roller have been implemented based on previous geometries, while an additional geometry called parabolic is newly proposed. For the tooth profiles, the involute, as a generated profile, and the double and quadruple circular arc geometries, as directly-defined profiles, have been implemented. Two- and three-dimensional finite element models have been developed in a custom-made software to generate fully parameterized models based on the design and manufacturing processes of SWG drives. The models are analyzed and the resulting stresses for each design are compared to determine which geometries and micro-geometry modifications are the most influential over the mechanical performance of this type of gear drive.

Significant improvement has been achieved by modifying the geometries of the wave generator and the tooth flanks of the flexible spline and the ring gear. Simplified and parabolic wave generator geometries proved similarly advantageous and the elliptical geometry resulted in the lowest compressive stresses, while the four roller geometry was discarded due to large stresses. The involute tooth profile was proven unsuitable while the directly-defined tooth profiles showed similarly beneficial outcomes when the root geometry was reinforced. The three-dimensional model evidenced the complex state of deflection of the flexible spline due to the cup-shaped spring and the need for micro-geometry modifications to further improve the behavior of SWG drives. Crowning and slope micro-geometry modifications on the wave generator and crowning on the tooth flanks of the flexible spline have been implemented. When combined, these modifications eliminated the areas of stress concentration due to the deflection of the flexible spline and allowed the contact pattern to move closer to the center of the teeth. These improvements resulted in remarkably lower stresses which serve to increase the overall mechanical performance of SWG drives.

Publication Date


Document Type


Student Type


Degree Name

Engineering (Ph.D.)

Department, Program, or Center

Mechanical Engineering (KGCOE)


Alfonso Fuentes-Aznar

Advisor/Committee Member

Hany Ghoneim

Advisor/Committee Member

Marcos Esterman


RIT – Main Campus