Modeling Load-, Velocity-, and Temperature-Dependent Transmission Errors of Cycloidal Drives for Industrial Robots Using Fourier Series

📅 2026-09-24
📈 Citations: 0
✨ Influential: 0
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🤖 AI Summary
This study addresses the significant transmission errors and degraded path accuracy of cycloidal reducers in industrial robots operating under varying load, speed, and temperature conditions. For the first time, it systematically investigates an error modeling approach under multi-factor coupling. Through high-precision measurements and signal processing on a single-joint platform, key harmonic frequencies are identified. A mapping model is then proposed that combines Fourier series fitting for periodic features with polynomial regression, revealing the intrinsic relationship between harmonic frequencies and mechanical characteristics. Experimental results demonstrate that this dynamic compensation model achieves an average root-mean-square error of only 0.026 mrad. By effectively supporting feedforward control strategies, the proposed method significantly enhances robotic path tracking accuracy.
📝 Abstract
Industrial robots are rarely used for machining tasks due to their limited path accuracy. This accuracy is mainly limited by inaccuracies in the drive trains. Compliance and transmission errors occur in the joint gearboxes. While transmission errors have been extensively studied for strain wave gears, there is little research on these errors in cycloidal drives. This gearbox type is commonly used in industrial robots for medium to heavy payloads. It is proposed to model the mainly periodic transmission errors using a Fourier series where amplitude and phase are defined as a polynomial function of the main influence factors load-torque, velocity, and temperature. Measurements of the transmission errors were conducted using an experimental setup representing a single robot joint. In the evaluation of the measurement data, harmonic frequencies were related to mechanical properties of the cycloidal drive. These frequencies were used to identify the parameters of the polynomial Fourier series model. Compared to validation measurements, the derived model shows an average root mean square error of 0.026 mrad. It is proposed to use the output of the resulting model in a feedforward control approach to compensate the transmission errors and to increase the path accuracy of industrial robots.
Problem

Research questions and friction points this paper is trying to address.

transmission error
cycloidal drive
industrial robot
path accuracy
load-velocity-temperature dependence
Innovation

Methods, ideas, or system contributions that make the work stand out.

Cycloidal Drives
Transmission Errors
Fourier Series
Industrial Robots
Feedforward Control
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Christian J. E. Bauer
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Marcel Dzubba
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