A strain-wave drive uses an elliptical wave generator to deform a flexible toothed cup inside a rigid circular spline. With the circular spline fixed, the tooth-count difference makes the flexspline turn slowly in the opposite direction to the input. The animation enlarges the working cross-section so both engagement regions can be followed.
Harmonic Drive Interactive Calculator
Watch the elliptical wave generator move two engagement regions around the flexible toothed rim. Calculate output travel for a chosen number of input turns.
Equation Used
- Wave generator is the input.
- Circular spline is fixed.
- Flexspline is the output.
- Target travel is separate from continuous demonstration playback.
With the circular spline fixed, the flexspline turns opposite the wave generator at a speed fraction set by the tooth-count difference.
The three working components
The gold wave generator rotates inside a flexible bearing and the blue flexspline. Teeth engage near the two ends of its major axis and separate near the minor axis. The surrounding grey circular spline stays fixed.
The orange witness marks material on the output rim. The ellipse orientation follows the fast input while the witness moves slowly backwards. The view is a section at the toothed end of the cup; the cup base and output flange are behind this section.
Applications
Strain-wave gear reducers are used for compact precision motion, including robot joints and positioning axes. The selected product determines its ratio, torque capacity, stiffness, accuracy and life. The diagram explains the three principal components and their relative motion.
Tooth-count relation
For flexspline tooth count Nf and circular spline count Nc=Nf+d, the output-to-input speed ratio with the circular spline fixed is −d/Nf. Reduction magnitude is Nf/d. For Tin input revolutions, output angle is −360dTin/Nf degrees.
The two-lobe illustration uses even tooth-count differences. It shows the kinematic relation, not a guarantee that an arbitrary tooth combination can be manufactured as a working strain-wave gear.
200 and 202 teeth
A 200-tooth flexspline and 202-tooth circular spline give 100:1 reduction. One input revolution moves the output backwards by two teeth, or 3.6°. Five input turns give −18°.
The selected input-turns slider controls this target calculation; continuous playback independently demonstrates successive wave-generator revolutions.
Illustration versus component design
The drawing preserves the fixed ring, two moving engagement regions and correct output direction. Tooth silhouettes and deformation are enlarged for readability. They are not proprietary tooth flanks, an elastic deformation solution or a fatigue assessment. Use manufacturer data for torque, life, bearing loads and permissible input speed.
Questions
Why does the output reverse?
The flexspline has fewer teeth than the fixed circular spline.
What rotates fastest?
The wave generator and the orientation of the deformation wave, not the flexspline material.
Does the grey ring move?
No. This calculator fixes the circular spline.
Technical references
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