I would not do it like this. Rather, I'd use a pic which I put multiple times along a path using decorations. Note that I did not tune your code, rather focus on the methods "putting sth in a pic" and "repeating it in a decoration". However, I really like your clever idea of using layers here!
\documentclass[tikz,border=3.14mm]{standalone}
\usetikzlibrary{calc}
\usetikzlibrary{math}
\usetikzlibrary{decorations.markings}
\tikzset{pics/.cd,
link/.style={code={\begin{scope}
\tikzmath{%Some math to define and position the link components
\lp = 0.5in;
\re = 0.3299*\lp;
\rc = 0.4284*\lp;
\Th = 41.25;
\Thc = 90 - \Th;
\Tp = \Thc;
\Tn = \Thc;
}
\fill[gray!#1] (0,0)%(\xs,\ys)
arc(\Tp:360-\Tn):\re)
arc(180-\Tn:\Tp:\rc)
arc(-180+\Tp:180-\Tn:\re)
arc(-\Tn:-180+\Tp:\rc)
-- cycle;
\end{scope}
}}}
\begin{document}
\begin{tikzpicture}
\pgfdeclarelayer{top}
\pgfsetlayers{main,top}
\pgfonlayer{main}
\path[decorate,decoration={markings,
mark=between positions 0 and 1 step 2.9in
with {\pic[scale=0.1]{link=30};}
}] (0,0) -- (9in,0);
\endpgfonlayer
\pgfonlayer{top}
\path[decorate,decoration={markings,
mark=between positions 0 and 1 step 2.9in
with {\pic[scale=0.1]{link=80};}
}] (1.45in,0) -- (9in,0);
\endpgfonlayer
\end{tikzpicture}
\end{document}
ADDENDUM: I was just curious if it is possible to make TikZ draw a chain along a path. And I think that the answer is yes. The following post is not at all polished. In particular, I replaced your nice link by a simpler, less fancy version. The only reason is that this thing is centered around (0,0). If you come up with a shape which has a somewhat more intuitive parametrization, this can be used as well. I also did not yet pay too much attention to the requirement that the path closes. I copied this example to have a path that is somewhat reminiscent of a bicycle chain, yet the details of the path are not crucial. The only thing which might be important is that this routine will find points on the curve which are separated by a given distance (the dimension of the link minus twice the radius of its circle). This is done by computing appropriate intersections (and selecting "cleverly" the relevant one).
\documentclass[tikz,border=3.14mm]{standalone}
\usetikzlibrary{calc}
\usetikzlibrary{decorations.markings,intersections}
\tikzset{pics/.cd,
mylink/.style={code={
\fill[gray!#1] (-0.6,0.6) to[out=-50,in=-110,looseness=0.7] (0.6,0.6)
arc(140:-140:0.9)
-- (0.6,-0.6) to[out=110,in=50,looseness=0.7] (-0.6,-0.6) arc(-40:-320:0.9);
}}}
\begin{document}
\begin{tikzpicture}
\pgfdeclarelayer{top}
\pgfsetlayers{main,top}
% tangents are from https://tex.stackexchange.com/a/7209/121799
\pgfmathsetmacro{\rone}{10}
\pgfmathsetmacro{\rtwo}{8}
\pgfmathsetmacro{\mid}{\rone/(\rone + \rtwo)}
\pgfmathsetmacro{\out}{\rone/(\rone - \rtwo)}
\node[circle,minimum size=2 * \rone cm,inner sep=0pt] (c1) at (21.1,0) {};
\node[circle,minimum size=2 * \rtwo cm,inner sep=0pt] (c2) at (0,0) {};
\path (c1.center) -- node[coordinate,pos=\mid] (mid) {} (c2.center);
\path (c1.center) -- node[coordinate,pos=\out] (out) {} (c2.center);
% \draw[red] (tangent cs:node=c2,point={(out)}) -- (tangent cs:node=c1,point={(out)});
% \draw[red] (tangent cs:node=c2,point={(out)},solution=2) -- (tangent cs:node=c1,point={(out)},solution=2);
% end https://tex.stackexchange.com/a/7209/121799
\path[name path=chain,postaction={decorate,decoration={markings,
mark=at position 0 with {\xdef\clen{\pgfdecoratedpathlength}}}},
draw=blue,thick] let
\p1=($(tangent cs:node=c2,point={(out)})-(c2.center)$),
\n1={atan2(\y1,\x1)},
\p2=($(tangent cs:node=c1,point={(out)})-(c1.center)$),
\n2={atan2(\y2,\x2)},
\p3=($(tangent cs:node=c1,point={(out)},solution=2)-(c1.center)$),
\n3={atan2(\y3,\x3)},
\p4=($(tangent cs:node=c2,point={(out)},solution=2)-(c2.center)$),
\n4={atan2(\y4,\x4)} in
(tangent cs:node=c2,point={(out)}) --
(tangent cs:node=c1,point={(out)}) arc(\n2:\n3:\rone)
-- (tangent cs:node=c2,point={(out)},solution=2) arc(\n4:\n1+360:\rtwo);
\coordinate (p0pt) at (tangent cs:node=c2,point={(out)});
\path[name path=c0] (p0pt) circle (2.9in);
\fill[name intersections={of=chain and c0,total=\t}] foreach \i in {1,...,\t}
{(intersection-\i) circle(3pt) node[below] {\i}};
\path (intersection-1) coordinate (p1pt);
\pgfmathsetmacro{\Nmax}{int(\clen/(2.6cm))}
\typeout{\Nmax}
\foreach \X [evaluate=\X as \Y using {int(\X-1)},evaluate=\X as \Z using {int(\X+1)}] in {1,...,\Nmax} % \Nmax
{
\path[name path=c\X] (p\X pt) circle (2.6cm);
\fill[name intersections={of=chain and c\X,total=\t}] foreach \i in {1,...,\t}
{let
\p1=($(intersection-\i)-(p\Y pt)$),\n1={ifthenelse(int(veclen(\x1,\y1)/1pt)<10,int(-1),int(\Z/1pt))}
in %\pgfextra{\typeout{\X:\i:\n1}}
(intersection-\i) coordinate (p\n1) };
\ifodd\X
\pgfonlayer{main}
\path let \p1=($(p\X pt)-(p\Z pt)$),\n1={atan2(\y1,\x1)}
in ($(p\X pt)!0.5!(p\Z pt)$) pic[rotate=\n1]{mylink=30};
\endpgfonlayer
\else
\pgfonlayer{top}
\path let \p1=($(p\X pt)-(p\Z pt)$),\n1={atan2(\y1,\x1)}
in ($(p\X pt)!0.5!(p\Z pt)$) pic[rotate=\n1]{mylink=80};
\endpgfonlayer
\fi
}
\pgfonlayer{top}
\path let \p1=($(p\Nmax pt)-(p1pt)$),\n1={atan2(\y1,\x1)}
in ($(p\Nmax pt)!0.5!(p1pt)$) pic[rotate=\n1]{mylink=80};
\endpgfonlayer
\end{tikzpicture}
\end{document}
And one can animate this as well:
\documentclass[tikz,border=3.14mm]{standalone}
\usetikzlibrary{calc}
\usetikzlibrary{decorations.markings,intersections}
\tikzset{pics/.cd,
mylink/.style={code={
\fill[gray!#1] (-0.6,0.6) to[out=-50,in=-110,looseness=0.7] (0.6,0.6)
arc(140:-140:0.9)
-- (0.6,-0.6) to[out=110,in=50,looseness=0.7] (-0.6,-0.6) arc(-40:-320:0.9);
}}}
\begin{document}
\foreach \nn in {0,...,9}
{\begin{tikzpicture}
\pgfdeclarelayer{top}
\pgfsetlayers{main,top}
% tangents are from https://tex.stackexchange.com/a/7209/121799
\pgfmathsetmacro{\rone}{10}
\pgfmathsetmacro{\rtwo}{8}
\pgfmathsetmacro{\mid}{\rone/(\rone + \rtwo)}
\pgfmathsetmacro{\out}{\rone/(\rone - \rtwo)}
\node[circle,minimum size=2 * \rone cm,inner sep=0pt] (c1) at (21.1,0) {};
\node[circle,minimum size=2 * \rtwo cm,inner sep=0pt] (c2) at (0,0) {};
\path (c1.center) -- node[coordinate,pos=\mid] (mid) {} (c2.center);
\path (c1.center) -- node[coordinate,pos=\out] (out) {} (c2.center);
% \draw[red] (tangent cs:node=c2,point={(out)}) -- (tangent cs:node=c1,point={(out)});
% \draw[red] (tangent cs:node=c2,point={(out)},solution=2) -- (tangent cs:node=c1,point={(out)},solution=2);
% end https://tex.stackexchange.com/a/7209/121799
\path[name path=chain,postaction={decorate,decoration={markings,
mark=at position 0 with {\xdef\clen{\pgfdecoratedpathlength}
\pgfmathsetmacro{\Nmax}{int(\clen/(2.6cm))}
\xdef\Nmax{\Nmax}},
mark=at position {2*\nn/(10*(\Nmax))} with {\coordinate (start) at (0,0);}
}},
draw=blue,thick] let
\p1=($(tangent cs:node=c2,point={(out)})-(c2.center)$),
\n1={atan2(\y1,\x1)},
\p2=($(tangent cs:node=c1,point={(out)})-(c1.center)$),
\n2={atan2(\y2,\x2)},
\p3=($(tangent cs:node=c1,point={(out)},solution=2)-(c1.center)$),
\n3={atan2(\y3,\x3)},
\p4=($(tangent cs:node=c2,point={(out)},solution=2)-(c2.center)$),
\n4={atan2(\y4,\x4)} in
(tangent cs:node=c2,point={(out)}) --
(tangent cs:node=c1,point={(out)}) arc(\n2:\n3:\rone)
-- (tangent cs:node=c2,point={(out)},solution=2) arc(\n4:\n1+360:\rtwo);
\coordinate (p0pt) at (start) ;% (tangent cs:node=c2,point={(out)});
\path[name path=c0] (p0pt) circle (2.9in);
\fill[name intersections={of=chain and c0,total=\t}] foreach \i in {1,...,\t}
{(intersection-\i) circle(3pt) node[below] {\i}};
\path (intersection-1) coordinate (p1pt);
\typeout{\nn:\Nmax}
\foreach \X [evaluate=\X as \Y using {int(\X-1)},evaluate=\X as \Z using {int(\X+1)}] in {1,...,\Nmax} % \Nmax
{
\path[name path=c\X] (p\X pt) circle (2.6cm);
\fill[name intersections={of=chain and c\X,total=\t}] foreach \i in {1,...,\t}
{let
\p1=($(intersection-\i)-(p\Y pt)$),\n1={ifthenelse(int(veclen(\x1,\y1)/1pt)<10,int(-1),int(\Z/1pt))}
in %\pgfextra{\typeout{\X:\i:\n1}}
(intersection-\i) coordinate (p\n1) };
\ifodd\X
\pgfonlayer{main}
\path let \p1=($(p\X pt)-(p\Z pt)$),\n1={atan2(\y1,\x1)}
in ($(p\X pt)!0.5!(p\Z pt)$) pic[rotate=\n1]{mylink=30};
\endpgfonlayer
\else
\pgfonlayer{top}
\path let \p1=($(p\X pt)-(p\Z pt)$),\n1={atan2(\y1,\x1)}
in ($(p\X pt)!0.5!(p\Z pt)$) pic[rotate=\n1]{mylink=80};
\endpgfonlayer
\fi
}
\pgfonlayer{top}
\path let \p1=($(p\Nmax pt)-(p1pt)$),\n1={atan2(\y1,\x1)}
in ($(p\Nmax pt)!0.5!(p1pt)$) pic[rotate=\n1]{mylink=80};
\endpgfonlayer
\end{tikzpicture}}
\end{document}
