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Harmonic Drive (Strain Wave Gearing) Ratio & Torsional Deflection Calculator

Easily calculate and compute harmonic drive (strain wave gearing) ratio & torsional deflection calculator with accurate equations, live formulas, and expert guidance.

Number of external teeth on flexible cup.

Number of internal teeth on rigid outer ring (Zc = Zf + 2 for standard).

External working torque applied to harmonic output.

High-torque elastic stiffness coefficient K3 from catalog.

Calculated Result
50 :1

Gear Ratio

Gear Ratio

50 :1

Gear Reduction Ratio

50

Torsional Deflection Arc Minutes

8.36

Torsional Deflection Arc Seconds

501.7

Required Input Motor Torque Nm

1.098

50 — :1

Calculation Breakdown

  1. Applied FormulaCalculates the high single-stage gear reduction ratio, elastic torsional spring windup (arcminutes), and input motor torque for precision strain wave (Harmonic Drive) robot joints.R = \frac{Z_f}{Z_c - Z_f}, \quad \phi = \frac{T_{out}}{K_{torsional}}

Harmonic Drive Strain Wave Metric Output

Interactive visualization based on your current inputs

Calculated Value
0.013253850Gear Ratio

What Is the Harmonic Drive (Strain Wave Gearing) Ratio & Torsional Deflection Calculator?

This tool computes harmonic drive (strain wave gearing) ratio & torsional deflection calculator with high precision arithmetic.

How Does the Harmonic Drive (Strain Wave Gearing) Ratio & Torsional Deflection Calculator Work?

Calculates the high single-stage gear reduction ratio, elastic torsional spring windup (arcminutes), and input motor torque for precision strain wave (Harmonic Drive) robot joints.

Harmonic Drive (Strain Wave Gearing) Ratio & Torsional Deflection Calculator Formula & Variables

The core mathematical equation utilized by this calculator is expressed as:

R=ZfZc−Zf,ϕ=ToutKtorsionalR = \frac{Z_f}{Z_c - Z_f}, \quad \phi = \frac{T_{out}}{K_{torsional}}

Calculates the high single-stage gear reduction ratio, elastic torsional spring windup (arcminutes), and input motor torque for precision strain wave (Harmonic Drive) robot joints.

How to Use the Harmonic Drive (Strain Wave Gearing) Ratio & Torsional Deflection Calculator

  1. Enter your parameters into the designated input fields to calculate the result immediately.

Step-by-Step Example Calculation

Harmonic Drive (Strain Wave Gearing) Ratio & Torsional Deflection Calculator Example

Input Values:

flexsplineTeethCount:100
circularSplineTeethCount:102
appliedLoadTorqueNm:45
torsionalStiffnessK3NmPerRad:18500
Worked Steps: Sample evaluation based on standard reference conditions.

Understanding Your Result

The calculated primary figure indicates the optimal or required :1.

Factors That Affect the Result

  • Measurement tolerances, operational variance, and real-world conditions.

When Should You Use This Calculator?

  • Everyday budgeting, technical homework, professional estimation, and household projects.

Assumptions & Limitations

  • Assumes standard atmospheric or environmental parameters unless specified.

Frequently Asked Questions

Calculation Accuracy & Reference Note

Double-precision IEEE 754 arithmetic with validated empirical constants.

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