Kinematic Fundamentals of Planar Harmonic Drives

Abstract

This paper presents the kinematic model and offers a rigorous analysis and description of the kinematics of planar harmonic drives. In order to reflect the fundamental kinematic principle of harmonic drives, the flexspline of a harmonic drive is assumed to be a ring without a cup. A tooth on the flexspline is a rigid body, and the motion of the tooth is fully governed by the wave generator and the nominal transmission ratio of the harmonic drive. The proposed model depicts the flexspline tooth and the wave generator as a cam-follower mechanism, with the follower executing a combined translating and oscillating motion. With the rigid tooth motion obtained, the conjugate condition between the flexspline and the circular spline is determined, from which the conjugate tooth profile can be derived. In this paper, the motion is governed by geometry, and the flexibility of the flexspline only serves as a spring to maintain the contact between the cam and the follower. For any wave generator and any transmission ratio, the explicit expression of the conjugate condition is presented. For a given circular or flexspline tooth profile, the exact conjugate tooth profile can be obtained. The phenomenon of twice engagement is discussed for the first time.

Dynamic Simulation of Harmonic Gear Drives Considering Tooth Profiles Parameters Optimization

“…The tooth profile at the right side and the continue direction of the profile are written as [8,16]:…”

Deformation Discipline of the Flexspline in Harmonic Drives with Engagement Output

“…Assuming the flexspline tooth profile Mðx f ; y f Þ is known, and the conjugate condition [7] can be written as [2]:…”

“…According to the kinematic model [2], the theoretical deformation function of the ring flexspline is…”

“…The kinematic model presented in [2,3] to describe the motion among the components of a HD and meshing equation used to solve the conjugate tooth profile are based on the theoretical deformation function. The deformation of the flexspline is not only related with the shape of the wave generator and type of HDs, but also with load etc.…”

“…According to the kinematic model and conjugation condition [2], a flexspline tooth profile is given, the conjugate circular spline tooth profile is obtained in term of theoretical deformation of the flexspline. Then, a finite element analysis model of Abaqus for the HD with engagement output is established.…”