  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.
