A Relation Spectrum Inheriting Taylor Series: Muscle Synergy and Coupling for Hand

There are two famous function decomposition methods in math: Taylor Series and Fourier Series. Fourier series developed into Fourier spectrum, which was applied to signal decomposition\analysis. However, because the Taylor series whose function without a definite functional expression cannot be solved, Taylor Series has rarely been used in engineering. Here, we developed Taylor series by our Dendrite Net, constructed a relation spectrum, and applied it to model or system decomposition\analysis. Specific engineering: 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 applied to analyze the muscle-finger system. One single muscle actuates multiple fingers, or multiple muscles actuate one single finger simultaneously. Thus, the research was in muscle synergy and muscle coupling for hand. This paper has two main contributions. (1) The findings of hand contribute to designing prosthetic hands. (2) The relation spectrum makes the online model human-readable, which unifies online performance and offline results. Code (novel tool for most fields) is available at https://github.com/liugang1234567/Gang-neuron.