cs.ROSep 24, 2026

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

Authors: Christian J. E. Bauer, Valentin Kamm, Marcel Dzubba, Lukas Steinle, Armin Lechler, Alexander Verl

Organizations: Institute for Control Engineering of Machine Tools and Manufacturing Units (ISW), University of Stuttgart, 70174 Stuttgart, Germany

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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.

Figures & tables

Fig. 1 : Transmission errors θTE\theta_{\mathrm{TE}} without mean for 1000 N m1000\text{\,}\mathrm{N}\text{\,}\mathrm{m} load torque, −2.5 \SIUnitSymbolDegree/s-2.5\text{\,}\mathrm{\SIUnitSymbolDegree}\text{/}\mathrm{s} velocity and 27 \SIUnitSymbolCelsius27\text{\,}\mathrm{\SIUnitSymbolCelsius} lubricant temperature dependent on the angle θ\theta .
Fig. 2 : Experimental setup with 1) cycloidal drive, 2) input-side motor, 3) temperature sensor, 4) torque sensor, 5) coupling, and 6) load-side motor (presented in [ 33 ] ).
ComponentSymbolFactor
Teeth of input gearz_{1}2424
Teeth of spur gearsz_{2}9696
Lobes of cycloidal discz_{3}4545
Pins of cycloidal discz_{4}4646
Planetary gear stage reduction ratiou_{1}44
Cycloidal gear stage reduction ratiou_{2}4646
TABLE I : Gearbox Components and Factors of a Nabtesco RH380-N Cycloidal Drive [ 34 ]

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