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Research Papers

# Kinematic Fundamentals of Planar Harmonic Drives

[+] Author and Article Information
Huimin Dong1

School of Mechanical Engineering, Dalian University of Technology, Dalian 116024, P.R. Chinadonghm@dlut.edu.cn

Kwun-Lon Ting

Center for Manufacturing Research, Tennessee Technological University, Cookeville, TN 38505kting@tntech.edu

Delun Wang

School of Mechanical Engineering, Dalian University of Technology, Dalian 116024, P.R. Chinadlunwang@dlut.edu.cn

1

Visiting scholar (March 2009–April 2010), Center for Manufacturing Research, Tennessee Technological University, Cookeville, TN.

J. Mech. Des 133(1), 011007 (Jan 06, 2011) (8 pages) doi:10.1115/1.4003140 History: Received November 03, 2009; Revised October 22, 2010; Published January 06, 2011; Online January 06, 2011

## 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.

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Copyright © 2011 by American Society of Mechanical Engineers
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## Figures

Figure 1

Kinematic diagrams of HD and PGT

Figure 2

Zero and 1DOF overconstraint linkage

Figure 3

The analogy to the combination of disk cams with a translating knife-edge follower and an oscillating flat face follower

Figure 4

Modeling a FS tooth and the WG: (a) the translating knife-edge follower model and (b) the oscillating flat-face follower model

Figure 5

A point on the FS tooth curve

Figure 6

A point on the CS tooth curve

Figure 7

Relative position between the HD components

Figure 8

Meshing between the FS and CS teeth

Figure 9

Instantaneous transmission ratio ifCW with a fixed WG

Figure 10

The conjugate tooth curves of the FS tooth (◻ and ◼ are first and second conjugate points generated by the CS tooth point rC=62.340 mm, μC=0.355 deg at θ=5.178 deg and θ=35.075 deg)

Figure 11

The motion of the FS tooth relative to the CS in θ∊[0 deg,180 deg]

Figure 12

Positions of the teeth between the FS and CS at one instant

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