Why are there jumping frames when I increase the radius?

Make sure you know how to use \pgfresetboundingbox or \pgfinterruptboundingbox.

Playing code

This is basically the example of show path construction in the manual. In addition to curves I showed the support points so it can be seen that it is the support points that exceeds the frame.

\documentclass[tikz]{standalone}
\usetikzlibrary{decorations.pathreplacing}
\begin{document}
\pgfmathsetmacro{\r}{2.1}
\tikzset{
    decoration={
        show path construction,
        moveto code={
            \fill[red](\tikzinputsegmentfirst)circle(2pt)
                node[fill=none,below]{moveto};},
        lineto code={
            \draw[blue,->](\tikzinputsegmentfirst)--(\tikzinputsegmentlast)
                node[pos=.5,auto]{lineto};
        },
        curveto code={
            \draw[green!75!black,dashed](\tikzinputsegmentfirst)--(\tikzinputsegmentsupporta)
                (\tikzinputsegmentlast)--(\tikzinputsegmentsupportb);
            \draw[green!75!black,->](\tikzinputsegmentfirst)..controls
                (\tikzinputsegmentsupporta)and(\tikzinputsegmentsupportb)
                ..(\tikzinputsegmentlast)node[pos=.5,auto]{curveto};
        },
        closepath code={
            \draw[orange,->](\tikzinputsegmentfirst)--(\tikzinputsegmentlast)
                node[pos=.5,auto]{closepath};
        }
    }
}
\foreach \j in {0,5,...,119}{
    \tikz[scale=3]{
        \draw[line width=1.2](-2.2,-2.2)rectangle(2.2,2.2)(0,0)circle(.25);
        \foreach\i in{0,1,2}{
            \draw[rotate=\i*120,decorate](\j:\r)arc(\j:90+\j:\r)--(90+\j:.3)arc(90+\j:\j:.3)--cycle;
        }% 
    }
}%
\end{document}

See also

• tikz bounding box / cropping: too much space for curves
• Bounding box is larger than expected when drawing a curved path
• Why do coordinates in Bezier curves add to the padding in TikZ?
• What type of curve is used by Tikz when I "bend" an edge?

Use a circle of radius \r (plus something) for calculating the bounding box.

\useasboundingbox overrides automatic BBox calculation which includes invisible path components, such as control points of curves.

\documentclass[tikz]{standalone}
\begin{document}
\pgfmathsetmacro{\r}{1.95}
\foreach \j in {0,10,20,...,110}{%
\begin{tikzpicture}%
% \draw (-2.2,-2.2) rectangle (2.2,2.2);%
  \useasboundingbox (0,0) circle (\r+0.01);                   
 \draw(0,0) circle (.25);%
 \foreach \i in {0,1,2}{\draw[rotate=\i*120] (\j:\r) arc (\j:90+\j:\r) -- (90+\j:.3) arc (90+\j:\j:.3) -- cycle;}%
\end{tikzpicture}}%
\end{document}