A Relation Spectrum Inheriting Taylor Series: Muscle Synergy and Coupling for Hand
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There are two famous function decomposition methods in math: 1) Taylor Series and 2) Fourier Series. The Fourier series developed into the Fourier spectrum, which was applied to signal analysis. However, Because a function without a functional expression cannot be solved for its Taylor series, Taylor Series has rarely been used in engineering. Here we have solved this problem, learned from Fourier, developed Taylor series, constructed a relation spectrum, and applied it to system analysis. Specific engineering application: the knowledge of the intuitive link between muscle activity and the finger movement is vital for the design of commercial prosthetic hands that do not need user pre-training. However, this link has yet to be understood due to the complexity of human hand. In this study, the relation spectrum was developed for the first time and applied to analyze the muscle-finger system. We established controllable and human-readable polynomial neural network (CR-PNN) models for six degrees of freedom ( DOFs) in 8 subjects. Multiple fingers may be controlled by a single muscle, or multiple muscles may control a single finger. Thus, the research is based on two aspects: muscle synergy and muscle coupling for hand. The research gave the relation spectrum of the muscle-finger system and the knowledge of muscle coupling. The article is very short but significant. The contributions of this paper can be divided into two parts: (1) The findings of hand can contribute to design prosthetic hands. (2) The relation spectrum using CR-PNN can provide a reference for analyzing complex systems in multiple areas. (We're strong believers in Open Source, and provide CR-PNN code for others. GitHub: https://github.com/liugang1234567/CR-PNN#cr-pnn. )
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