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| Harmonic Drive Gearing ---> Principles |
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The unique principle of operation of
gears, from which the name Harmonic Drive is derived, was patented
in 1955, by its inventor, C.Walton Musser. Initially this new gear
concept was applied in aerospace and other highly specific applications. |
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System Components |
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All
harmonic drive products employ the same three basic elements: a Circular
Spline, a Flexspline and a Wave Generator. Although these elements may
take alternate forms depending on their application, the types described
here are typical and representative |
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 WAVE GENERATOR (WG) |
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The Wave Generator is an elliptical cam enclosed in an antifriction ballbearing assembly. It normally functions as the rotating input element. When inserted into the bore of the Flexspline, it imparts its elliptical shape to the Flexspline, causing the external teeth of the Flexspline to engage with the internal teeth of the Circular Spline at two equally spaced areas 180 degrees apart on their respective circumferences, thus forming a positive gear mesh at these points of engagement. |
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FLEXSPLINE (FS) |
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The externally toothed
Flexspline is a nonrigid or flexible, thin-walled, cylindrical cup which
is smaller in circumference and has two less teeth than the Circular
Spline. It is normally the rotating output element but can be utilized
as the fixed, non rotating member when output is through the Circular
Spline. |
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CIRCULAR
SPLINE (CS) |
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The Circular Spline
is a thick-walled, rigid ring with internal spline teeth. It normally
functions as the fixed or non rotating member but can, in certain
applications, be utilized as a rotating output element as well. |
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The Principles of Harmonic Drive Gearing |
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The diagram shows the three basic harmonic drive elements (Circular Spline,
Flexspline and Wave generator) assembled in a normal configuration. Ordinarily,
the Circular Spline is held stationary or fixed and input is through the Wave
generator, while output is via the Flexspline. Under these circumstances,
operation of the harmonic drive unit is as follows.
As the Wave generator is rotated by the primary power source, it imparts
a continuously moving elliptical form or wave-like motion to the Flexspline.
This causes the meshing of the external teeth of the Flexspline with the internal
teeth of the Circular Spline at their two equidistant points of engagement
to progress in a continuous rolling fashion. It also allows for full tooth
disengagement at the two points opposite the minor axis of the Wave Generator.
Since the Flexspline has two less teeth than the Circular Spline and because
full teeth disengagement is made possible by the elliptical shape of the Wave
Generator, each complete revolution of the Wave Generator causes a two tooth
displacement of the Flexspline in relation to the Circular Spline. This displacement
is always in the opposite direction of the rotation of the Wave Generator
(see diagram). for example, if the Wave Generator is rotating in a clockwise
direction, the two-tooth-per-revolution displacement of the Flexspline will
be in a counter-clockwise direction and vice versa. In this way, a basic three
element harmonic drive component set is capable of functioning as a speed
reducer. Input from a main power source through the Wave Generator is at a
high speed, but the two-tooth-per-revolution displacement causes the
Flexspline, which
is the output element, to rotate in the opposite direction of, and at a considerably
slower speed than, the Wave Generator. The reduction ratio which results can
be calculated by dividing the number of teeth on the Flexspline by two (the
difference between the number of teeth on the Circular Spline and the Flexspline).
If a fixed Circular Spline had 202 teeth and an output Flexspline has 200
teeth, the ratio would be 200/(202-200)=100:1 |
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Configurations |
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1. |
Reduction Gearing |
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5. |
Increaser Gearing |
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CS:Fixed
WG:Input
FS:Output
Ratio:i=-ZR/2
Input and output in opposite direction |
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FS:Fixed
CS:Input
WG:Output
Ratio:i=2/ZG
Input and output in same direction. |
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2. |
Reduction Gearing |
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6. |
Increaser Gearing |
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FS:Fixed
WG:Input
CS:Output
Ratio:i=ZG/2
Input and output in same direction. |
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CS:Fixed
FS:Input
WG:Output
Ratio:i=-2/ZR
Input and output in opposite direction. |
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3. |
Reduction Gearing |
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7. |
Differential Gearing |
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WG:Fixed
FS:Input
CS:Output
Ratio:i=ZG/ZR
Input and output in same direction. |
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CS:Main Drive-Input
FS:Main Drive-Output
WG:Control Input
Output Speed:NR=NGx(R+1)/R-NW/R
Numerous differential functions can be obtained by combinations of speeds
and rotations on the three shafts
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4. |
Increaser Gearing |
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8. |
Differential Gearing |
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WG:Fixed
CS:Input
FS:Output
Ratio:i=ZR/ZG
Input and output in same direction. |
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CS:Main Drive-Input
FS:Main Drive-Output
WG:Control Input
Output Speed:NR=NGx(R+1)/R+NW/R
Numerous differential functions can be obtained by combinations of speeds
and rotations on the three shafts. |
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| Where: |
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ZR---Teeth of Flexspline
ZG---Teeth of Circular Spline
NR---Speed of Flexspline |
NG---Speed of Circular Spline
NW---Speed of Wave Generator
R=ZR/2 (R---Transmission Ratio as listed) |
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