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Absolute Position Coding Method for Angular Sensor—Single-Track Gray Codes

School of Mechanical and Electrical Engineering, Guangzhou University, Guangzhou 510006, China
School of Mechanical, Electronic and Control Engineering, Beijing Jiaotong University, Beijing 100044, China
State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
Author to whom correspondence should be addressed.
Sensors 2018, 18(8), 2728;
Received: 29 June 2018 / Revised: 16 August 2018 / Accepted: 17 August 2018 / Published: 19 August 2018
(This article belongs to the Special Issue Smart Sensors and Smart Structures)
PDF [4636 KB, uploaded 20 August 2018]


Single-track Gray codes (STGCs) is a type of absolute position coding method for novel angular sensors, because it has single-track property over traditional Gray codes and mono-difference over linear feedback shift register codes. However, given that the coding theory of STGCs is incomplete, STGC construction is still a challenging task even though it has been defined for more than 20 years. Published coding theories and results on STGCs are about two types of STGC, namely, necklace and self-dual necklace ordering, which are collectively called as k-spaced head STGCs. To find a new code, three constraints on generating sequences are proposed to accelerate the searching algorithm, and the complete searching result of length-6 STGCs is initially obtained. Among the entire 132 length-6 STGCs, two novel types of STGCs with non-k-spaced heads are found, and the basic structures of these codes with the general length n are proposed and defined as twin-necklace and triplet-necklace ordering STGCs. Furthermore, d-plet-necklace ordering STGC, which unifies all the known STGCs by changing the value of d, is also defined. Finally, a single-track absolute encoder prototype is designed to prove that STGCs are as convenient as the traditional position coding methods. View Full-Text
Keywords: absolute position sensing; absolute position coding; absolute encoder; Gray code; single-track Gray code; necklace absolute position sensing; absolute position coding; absolute encoder; Gray code; single-track Gray code; necklace

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Zhang, F.; Zhu, H.; Bian, K.; Liu, P.; Zhang, J. Absolute Position Coding Method for Angular Sensor—Single-Track Gray Codes. Sensors 2018, 18, 2728.

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