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Cycloidal Drive Speed Reducer Kinematics & Pin Load Calculator

Cycloidal speed reducers (cycloid drives) provide high single-stage reduction ratios (up to 119:1), near-zero backlash, and extreme shock load capacity for robotics and precision servo actuators.

Number of wave lobes or teeth on the cycloidal disc rotor (typically 11 to 39).

Number of stationary outer pins in the housing (typically R_L + 1).

Radial offset of the eccentric bearing cam on the high-speed input shaft.

Radial distance from center axis to the pitch circle of outer ring pins.

Operating rotational speed of the driving motor shaft.

Continuous input torque delivered to the eccentric cam.

Calculated Result
17:1 Reduction

Cycloidal Gear Reduction Ratio

Gear Reduction Ratio

17:1

Output Rotational Speed

102.9 RPM

Output Shaft Torque

76.5 N·m (at 90% efficiency)

Peak Ring Pin Contact Force

522.2 N

Lobes to Pins Configuration

17 lobes / 18 housing pins

Calculation Breakdown

  1. Kinematic Reduction Ratioi = Z_lobes / (Z_pins - Z_lobes) = 17 / (18 - 17) = 17:1
  2. Output Dynamics & Multiplied TorqueN_out = 1750 RPM / 17 = 102.9 RPM, T_out = 5 N·m × 17 × 0.90 = 76.5 N·m
  3. Peak Pin Mesh LoadF_pin,max ≈ 2.5 × T_out / (R_p × Z_eff) = 522.2 N

Cycloidal Reducer Performance Profile

Interactive visualization based on your current inputs

Value
0.019385777Ratio (:1)Output RPM (/10)Output Torque (N·m)Input Torque (N·m)Peak Force (N/10)MetricValue

What Is the Cycloidal Drive Speed Reducer Kinematics & Pin Load Calculator?

The Cycloidal Drive Speed Reducer Kinematics & Pin Load Calculator models speed reduction ratios, multiplied torque, and pin contact stresses in cycloidal transmissions.

How Does the Cycloidal Drive Speed Reducer Kinematics & Pin Load Calculator Work?

It calculates kinematic reduction from lobe-to-pin counts, estimates mechanical output torque at 90% efficiency, and evaluates peak pin contact loading.

Cycloidal Drive Speed Reducer Kinematics & Pin Load Calculator Formula & Variables

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

i = \frac{R_L}{R_P - R_L}, \quad N_{out} = \frac{N_{in}}{i}, \quad T_{out} = T_{in} \cdot i \cdot \eta_{mech}

Epicyclic cycloidal kinematics delivering compact single-stage speed reduction with multi-pin rolling contact.

How to Use the Cycloidal Drive Speed Reducer Kinematics & Pin Load Calculator

  1. Input number of rotor lobes and housing pins.
  2. Specify input shaft speed and motor driving torque.
  3. Set cam eccentricity and pin circle pitch radius.

Step-by-Step Example Calculation

17:1 Precision Robotic Cycloidal Actuator

Input Values:

numberOfRotorLobes:17
numberOfRingPins:18
eccentricityMm:2
pinPitchRadiusMm:45
inputSpeedRpm:1750
inputTorqueNm:5
Worked Steps: Delivers a 17:1 speed reduction ratio, producing 76.5 N·m output torque at 102.9 RPM with 500 N peak pin contact force.

Understanding Your Result

Reduction Ratio: Mechanical reduction ratio (e.g. 17:1 or 29:1).

Output Torque: Usable output torque delivered to the output flange.

Peak Pin Contact Force: Dynamic Hertzian contact load on the most heavily loaded pin.

Factors That Affect the Result

  • Adding more rotor lobes increases gear reduction ratio in a single compact stage.
  • Larger pitch radii reduce normal contact forces across the pins.

When Should You Use This Calculator?

  • Robotic arm joint actuators, CNC rotary tables, antenna positioners, and automated guided vehicle (AGV) wheel drives.

Assumptions & Limitations

  • Assumes perfect cycloidal profile geometry without manufacturing lead errors and rigid housing pins.

Frequently Asked Questions

Calculation Accuracy & Reference Note

Based on Malhotra (1983) and Gorla (2008) cycloidal drive mechanical analyses.

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