Grades 9–12 · Machines
How can a flexible gear turn a fast motor into tiny movements?
A robot joint may need a motor to turn many times while its output moves only a little. Strain-wave gearing achieves a large speed reduction with three main parts: a rigid toothed ring, a flexible toothed cup and an elliptical wave generator inside the cup.
In the diagramA flexible gear takes tiny backward stepsFixed ring: 102 teeth · flexible cup: 100 teethTwo engagement regionsElliptical input1 turnsFlexible output-0.02 turnsOpposite directionEach input revolution shifts the cup back by two teeth.
The wave generator bends the cup slightly into an oval. The cup teeth meet the ring teeth in two opposite regions. As the generator turns, those engagement regions move around the ring. The cup flexes repeatedly rather than remaining a rigid oval.
In a common arrangement the ring is fixed and has two more teeth than the flexible cup. Each full input turn shifts the cup backward by two teeth relative to that ring. With 100 cup teeth and 102 ring teeth, one input turn produces −2/100, or −0.02, output turns. The minus sign means the output turns in the opposite direction.
The reduction magnitude is 50 to 1 in this example. That ratio comes from tooth counts and the fixed-ring arrangement. Actual load capacity, elastic deflection, efficiency and service life require material and contact analysis beyond this geometric explanation.
About this explanation
Starting knowledge: Work with signed ratios, rotation and elastic deformation.
Sources
- Harmonic Drive — Strain Wave Gear Principle