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Flexsplines in harmonic gear reducers are usually characterized by a large number of teeth, small modulus, and poor stiffness, which makes them difficult to measure using conventional gear measuring centers. In order to efficiently evaluate the quality of flexsplines in harmonic gear reducers, a rapid measurement method for flexspline pitch using offset point laser sensors (PLS) is proposed. This paper investigates the principle of measuring the tooth flank of the flexspline under the offset of the PLS, establishes a model for collecting and analyzing gear surface data, builds an experimental system, calibrates the six pose parameters of the sensor using the geometric features of the flexspline’s outer circular surface, and completes the reconstruction of the left and right gear surfaces of the flexspline based on the measured data. In the experiment, the gear surface obtained by the proposed method is largely consistent with that measured by the video imaging method, and the repeatability of both single pitch deviation and cumulative pitch deviation is within ±3 µm.

To improve the measuring accuracy of circular encoders in special applications, self-calibration of the circular encoder is necessary. The commonly used self-calibration method, namely the Equal Division Average (EDA) method, requires a large number of reading heads and cannot be used when the structural space is limited. In this paper, a self-calibration method for a circular encoder based on two reading heads with adjustable positions (TRAP) is proposed. This TRAP method uses two reading heads to simulate multiple reading heads, which can be used to achieve self-calibration of circular encoders in limited space. This paper investigates the principle of simulating multiple reading heads with two reading heads, designs and builds an experimental system, and obtains and analyzes experimental data. The experimental results show that the peak-valley value of the angle measurement error is reduced from 252.41″ to 18.82″ after self-calibration with the TRAP method, and the repeatability of multiple self-calibration experimental results is less than 0.75″. The TRAP method breaks through the limitation of the number of reading heads that can be installed during the self-calibration of the circular encoder and can effectively suppress the angle measurement error of the circular encoder.