[Tex/LaTex] How to make this free body diagram with a non-straight force line using tikzpicture environment

tikz-pgftikz-styles

Please consider the following MWE adapted from this fantastic example of Kjell Magne Fauske's free body diagram:

\documentclass{article}

\usepackage{tikz}           % From http://www.texample.net/tikz/examples/free-body-diagrams/
\usetikzlibrary{scopes}
\begin{document}

\def\iangle{0} % Angle of the inclined plane

\def\down{-90}
\def\arcr{0.5cm} % Radius of the arc used to indicate angles

\begin{tikzpicture}[
    scale=4,
    force/.style={->,draw=blue,fill=blue},
    axis/.style={densely dashed,gray,font=\small},
    M/.style={rectangle,draw,fill=lightgray,minimum size=0.5cm,thin},
    m/.style={rectangle,draw=black,fill=lightgray,minimum size=0.3cm,thin},
    plane/.style={draw=black,fill=blue!10},
    string/.style={draw=red, thick},
    pulley/.style={thick},
]

    %% Free body diagram of M
    \begin{scope}[rotate=\iangle]
        \node[M,transform shape] (M) {};
        % Draw axes and help lines

        {[axis,->]
            \draw (0,-1) -- (0,2) node[right] {$+y$};
            \draw (M) -- ++(2,0) node[right] {$+x$};    % mental note for me: change "right" to "above"
        }

        % Forces
        {[force,->]
            % Assuming that Mg = 1. The normal force will therefore be cos(alpha)
            \draw (M.center) -- ++(0,{cos(\iangle)}) node[above right] {$\vec N$};
            \draw (M.west) -- ++(-1,0) node[left] {$\vec f_r$};
        }

    \end{scope}
    % Draw gravity force. The code is put outside the rotated
    % scope for simplicity. No need to do any angle calculations. 
    \draw[force,->] (M.center) -- ++(0,-1) node[below] {$\vec P$};
    %%
\end{tikzpicture}

\end{document}

With your huge help, I would like to know how to

add a line with slope (e.g. with an inclination of 53º <- with the label and the correct slope). Note that the source already has a code for the angle, it may be the same in this case;
make proportional axis and not "from wherever you are, go above/right by 2", e.g. a 30 ~ 40% more long than the length of the force lines (I ask this because if scale=4 then the axis lines are too large than the force lines);
aditionally add a "floor" with black diagonal lines (maybe this Milo's excellent answer or this marmot's awesome response helps?);
the friction force line f_r in front of the body and not behind;
the possibility of descompose the forces that are not horizontal/vertical (maybe with the same style of the axis line, idk, be creative with format!).

I want something like this:

If possible, I would like you to keep the code format of the MWE so that I do not have to adapt to another code style, but add to the current one.

If you think that the colors are monotonous you can propose darker grays or other styles!

Many thanks!

Best Answer

My humble attempt using arrows (which got superseded by arrows.meta; see below for a version using that library), decoration.markings and angles libraries.

\documentclass[tikz,border=2mm]{standalone} 

\usetikzlibrary{arrows,decorations.markings,angles}

\def\Fangle{53}
\def\Flength{5}
\def\iangle{20}
\def\Plength{2}
\def\Gwidth{5}
\def\Gthick{3pt}
\def\Gstep{4pt}
\def\coordwd{1}
\usepackage{siunitx}

\begin{document}
\begin{tikzpicture}
  [
    ,force/.style={>=latex',->,draw=blue,fill=blue}
    ,force component/.style={>=latex',->,draw=gray,fill=gray}
    ,M/.style={rectangle,draw,fill=lightgray,minimum size=0.5cm,thin}
    ,note/.style={font=\small}
    ,ground/.style={black,postaction={ground hatch}}
    ,ground hatch/.style=
      {
        decorate,
        decoration=
          {
            ,markings
            ,mark =
              between positions 0 and 1 step \Gstep
              with{\draw[darkgray] (-\Gthick,-\Gthick) -- (0,0);}
          }
      }
    ,my angles/.style=
      {
        ,draw=green!70!black
        ,->
        ,angle radius=9mm
        ,angle eccentricity=1.3
        ,pic text=#1
        ,font = \small
      }
    ,coord/.style={dashed,gray,>=latex',->,transform shape}
  ]
  \begin{scope}[rotate=\iangle]
    \node[M,transform shape] (M) {};
    \draw[force] (M.center) ++(\Fangle+90:\Flength) coordinate (F)
      --node[at start,above left,note]{$\vec{F}$} (M.center);
    \draw[force component] (F)
      --node[at end,above left,gray,note,transform shape,rotate=-90]
        {$\Vert\vec{F}\Vert\cos\SI{\Fangle}{\degree}$}
      (F|-M.center) coordinate (fr);
    \draw[force component] (F) 
      --node[at end,above left,gray,note,transform shape]
        {$\Vert\vec{F}\Vert\sin\SI{\Fangle}{\degree}$}
      (F-|M.center) coordinate (N);
    \draw[force] (M.center)
      --node[at end,below,note]{$\vec{f}_r$} (fr);
    \draw[force] (M.center)
      --node[at end,right,note]{$\vec{N}$} (N);
    \draw[ground] (M.south) ++(-\Gwidth/2,0) -- ++(\Gwidth,0) coordinate (G);
    \path (M.center) coordinate (Mc)
      pic[my angles=\SI\Fangle\degree]
      {angle=N--Mc--F};
    \draw[coord] (N) --node[at end,above]{$+y$} ++(0,\coordwd);
    \draw[coord] (M.east) --node[at end,right]{$+x$} ++(\coordwd,0);
  \end{scope}
  \draw[force] (M.center) --node[at end,below,note]{$\vec{P}$} ++(0,-\Plength);
  \draw[dashed,darkgray] (M.south) -- ++(2,0) coordinate (H);
  \path (M.south) coordinate (Ms)
    pic[my angles=\SI\iangle\degree]
    {angle=H--Ms--G};
\end{tikzpicture}
\end{document}

Changing the 53° label to the position you want, also using arrows.meta instead of arrows:

\documentclass[tikz,border=2mm]{standalone} 

\usetikzlibrary{arrows.meta,decorations.markings,angles}

\def\Fangle{53}
\def\Flength{5}
\def\iangle{20}
\def\Plength{2}
\def\Gwidth{5}
\def\Gthick{3pt}
\def\Gstep{4pt}
\def\coordwd{1}
\usepackage{siunitx}

\begin{document}
\begin{tikzpicture}
  [
    ,force/.style={>=Stealth,->,draw=blue,fill=blue}
    ,force component/.style={>=Stealth,->,draw=gray,fill=gray}
    ,M/.style={rectangle,draw,fill=lightgray,minimum size=0.5cm,thin}
    ,note/.style={font=\small}
    ,ground/.style={black,postaction={ground hatch}}
    ,ground hatch/.style=
      {
        decorate,
        decoration=
          {
            ,markings
            ,mark =
              between positions 0 and 1 step \Gstep
              with{\draw[darkgray] (-\Gthick,-\Gthick) -- (0,0);}
          }
      }
    ,my angles/.style=
      {
        ,draw=green!70!black
        ,->
        ,angle radius=9mm
        ,angle eccentricity=1.3
        ,pic text=#1
        ,font = \small
      }
    ,coord/.style={dashed,gray,>=Stealth,->,transform shape}
  ]
  \begin{scope}[rotate=\iangle]
    \node[M,transform shape] (M) {};
    \draw[force] (M.center) ++(\Fangle+90:\Flength) coordinate (F)
      --node[at start,above left,note]{$\vec{F}$} (M.center);
    \draw[force component] (F)
      --node[at end,above left,gray,note,transform shape,rotate=-90]
        {$\Vert\vec{F}\Vert\cos\SI{\Fangle}{\degree}$}
      (F|-M.center) coordinate (fr);
    \draw[force component] (F) 
      --node[at end,above left,gray,note,transform shape]
        {$\Vert\vec{F}\Vert\sin\SI{\Fangle}{\degree}$}
      (F-|M.center) coordinate (N);
    \draw[force] (M.center)
      --node[at end,below,note]{$\vec{f}_r$} (fr);
    \draw[force] (M.center)
      --node[at end,right,note]{$\vec{N}$} (N);
    \draw[ground] (M.south) ++(-\Gwidth/2,0) -- ++(\Gwidth,0) coordinate (G);
    \path (M.center) coordinate (Mc)
      pic[my angles=\SI\Fangle\degree]
      {angle=fr--F--Mc};
    \draw[coord] (N) --node[at end,above]{$+y$} ++(0,\coordwd);
    \draw[coord] (M.east) --node[at end,right]{$+x$} ++(\coordwd,0);
  \end{scope}
  \draw[force] (M.center) --node[at end,below,note]{$\vec{P}$} ++(0,-\Plength);
  \draw[dashed,darkgray] (M.south) -- ++(2,0) coordinate (H);
  \path (M.south) coordinate (Ms)
    pic[my angles=\SI\iangle\degree]
    {angle=H--Ms--G};
\end{tikzpicture}
\end{document}

Related Solutions

[Tex/LaTex] TikZ: Drawing an arc from an intersection to an intersection

A solution which allows to draw intersection segments of any two intersections is available as tikz library fillbetween.

This library works as general purpose tikz library, but it is shipped with pgfplots and you need to load pgfplots in order to make it work:

\documentclass{standalone}

\usepackage{tikz}
\usepackage{pgfplots}
\usetikzlibrary{fillbetween}

\begin{document}

\begin{tikzpicture}

\draw [name path=red,red] (120:1.06) circle (1.9);
%\draw [name path=yellow,yellow] (0:1.06) circle (2.12);
\draw [name path=green,green!50!black] (0:0.77) circle (2.41);
\draw [name path=blue,blue] (0:0) circle (1.06);

% substitute this temp path by `\path` to make it invisible:
\draw[name path=temp1, intersection segments={of=red and blue,sequence=L1}];
\draw[red,-stealth,ultra thick, intersection segments={of=temp1 and green,sequence=L3}];

\end{tikzpicture}

\end{document}

enter image description here

The key intersection segments is described in all detail in the pgfplots reference manual section "5.6.6 Intersection Segment Recombination"; the key idea in this case is to

create a temporary path temp1 which is the first intersection segment of red and blue, more precisely, it is the first intersection segment in the Left argument in red and blue : red. This path is drawn as thin black path. Substitute its \draw statement by \path to make it invisible.
Compute the desired intersection segment by intersecting temp1 and green and use the correct intersection segment. By trial and error I figured that it is the third segment of path temp1 which is written as L3 (L = left argument in temp1 and green and 3 means third segment of that path).

The argument involves some trial and error because fillbetween is unaware of the fact that end and startpoint are connected -- and we as end users do not see start and end point.

Note that you can connect these path segments with other paths. If such an intersection segment should be the continuation of another path, use -- as before the first argument in sequence. This allows to fill paths segments:

\documentclass{standalone}

\usepackage{tikz}
\usepackage{pgfplots}
\usetikzlibrary{fillbetween}

\begin{document}

\begin{tikzpicture}

\draw [name path=red,red] (120:1.06) circle (1.9);
%\draw [name path=yellow,yellow] (0:1.06) circle (2.12);
\draw [name path=green,green!50!black] (0:0.77) circle (2.41);
\draw [name path=blue,blue] (0:0) circle (1.06);

% substitute this temp path by `\path` to make it invisible:
\draw[name path=temp1, intersection segments={of=red and blue,sequence=L1}];
\draw[red,fill=blue,-stealth,ultra thick, intersection segments={of=temp1 and green,sequence=L3}]  
    [intersection segments={of=temp1 and green, sequence={--R2}}]
;

\end{tikzpicture}

\end{document}

enter image description here

[Tex/LaTex] Drawing rectilinear curves in Tikz, aka an Etch-a-Sketch drawing

\draw (20,12) -- ++(2,0) -- ++(0,2) -- ++(-3,0) -- ++(45:3);

Use ++ before each new incremental coordinate to make it relative to the last one and put the pencil there.

Here's a complete example:

\documentclass{article}
\usepackage{tikz}
\begin{document}
\tikz\draw (20,12) -- ++(2,0) -- ++(0,2) -- ++(-3,0) -- ++(30:3) {[rounded corners=10pt]-- ++(5,0) -- ++(0,-6)} -- ++(-7,0) -- cycle;
\end{document}

Of course, combining this with the -| or |- path operators can simplify the code even further; the following two pieces of code produce the same result:

\tikz\draw (20,12) -- ++(2,0) -- ++(0,2) -- ++(3,0) -- ++(0,1) -- ++(1,0) -- ++(0,-3) -- ++(2,0);\par\bigskip

and

\tikz\draw (20,12) -| ++(2,2) -| ++(3,1) -- ++(1,0) |- ++(2,-3);

I don't think that defining commands in this case adds anything; in fact, I think it reduces the functionality of the existing syntax (which is already simple). The example demonstrates that you can use, for example, polar coordinates and modify (up to TikZ limitations) the path attributes midways; even if the current question doesn't require this, it's a good thing to have the possibility to do those kind of modification if they are required.

Best Answer

Related Solutions

[Tex/LaTex] TikZ: Drawing an arc from an intersection to an intersection

[Tex/LaTex] Drawing rectilinear curves in Tikz, aka an Etch-a-Sketch drawing

Related Question