Define \textunderscore to mimic look of standard underscore

Question

I noticed that the look of the underscore _ differs greatly from the look of \textunderscore

How can I redefine \textunderscore to look like the standard underscore of the set font? I want to avoid changing the catcode, so redefining it seems to be the best option to me.

\documentclass{minimal}

\catcode`\_11%

\begin{document}

{\ttfamily
\textunderscore _ 
}

\end{document} 

Answer 1

\documentclass{article}

\begin{document}

\fontencoding{TU}\selectfont
\textrm{[\_][\string_]} \texttt{[\_][\string_]}

\fontencoding{T1}\selectfont
\textrm{[\_][\string_]} \texttt{[\_][\string_]}

\fontencoding{OT1}\selectfont
\textrm{[\_][\string_]} \texttt{[\_][\string_]}
\end{document}

Ideally \textunderscore (\_) would simply access the _ character in the current font, and that is what happens in encodings that have _. The original TeX encoding as used in the minimal class example in the question does not have _ at all, the slot is taken with the accent character as seen in the image. Just the tt font has _ to allow verbatim, but for OT1 LaTeX defines \_ as a tex-drawn rule independent of the font.