mar/content/case_experiment_scara.tex

%&tex
    \subsection{Feature Selection}
        The implementation of the end-effector proofed to be impractical.
        This means that only two features are left.
        The updated table in \autoref{tab:featurestab2} shows that the next step would be the SCARA.
        The SCARA has a higher risk/time factor and covers more tests.
        \begin{table}[]
            \caption{}
            \label{tab:featurestab2}
            \begin{tabular}{|l|l|l|l|l|l|}
                \hline
                Feature      & Dependees   & Tests  & Risk   & Time    & Risk/Time  \\ \hline
                SCARA        & -           & 3      & 40\%   & 10 days & 4          \\ \hline
                End-effector & SCARA       & 2      & 60\%   & 8 days  & 7.5        \\ \hline
                Carriage     & -           & 2      & 30\%   & 10 days & 3          \\ \hline
            \end{tabular}
        \end{table}

    \subsection{Rapid Development}
        At the end of this implementation the SCARA is able to write the first characters
        This will be achieved by working through different levels of detail.
        Where each level adds more detail to the model.
        The levels that are implemented are as follow:
        \begin{enumerate}
            \item Basic kinematics model, no physics.
            \item Basic physics model, ideal 2D physics.
            \item Basic Motor behavior, 2D physics with non-ideal DC-motor.
            \item Basic control law, path planning.
            \item Advanced motor behavior, 2D physics with stepper motor behavior.
            \item Advanced physics model, 3D physics with complex dynamics with Lie-algebra.
            \item Marker lifting behavior, servo lifts marker of the board.
        \end{enumerate}
        This mainly describes the different level of physics detail.
        Together with the physics model there will be a solid 3D CAD model.
        The CAD model helps to check with dimensions and possible collisions of objects.

        \subsubsection{Basics}
            \begin{marginfigure}
                    \centering
                    \begin{tikzpicture}
                            \tikzstyle{arrow} = [-latex,ultra thick]
                    
                    % draw roof
                    \fill[pattern = north east lines] ($ (0,0) + (-1,0) $) rectangle ($ (0,0) + (1,0.5) $);
                    \draw[thick] ($ (0,0.5) + (-1,0) $) -- ($ (0,0.5) + (1,0) $);
                    
                    %draw arm and joints
                            \fill (0,0.5) circle (0.2);  
                            \draw[thick] (0,0.5) to node[midway,right,draw=none] {$a$} (-1.5,3.5);  
                            \fill (-1.5,3.5) circle (0.2); 
                            \draw[thick] (-1.5,3.5) to node[midway,above,draw=none] {$b$}(1.51,4.26);		
                            
                            %draw mass
                            \draw (1.7,4.32) circle (0.2) node {$m$};
                            
                            %draw arc
                    %\draw[dashed,gray] (-1.5,3.5) -- ++(2.5,0);
                    %\draw (1,0.5) arc (0:116:1cm) node[above,midway] {$\theta$};	

                    %\draw [arrow] (c.south) -- +(0,-1cm) node[midway,right,draw=none] {$F_{g} = m \cdot g$};
                    \end{tikzpicture}
                    \caption{Basic kinematics of the SCARA}
                    \label{fig:scaraarm}
            \end{marginfigure}
            The first four detail steps are just creating the basics dynamics of the SCARA as shown in \autoref{fig:scaraarm}
            It start with the kinematics model that is used to test the forward and inverse kinematics of the design.
            It gave a general idea of angles and arm lengths that are required in the design.
            The second detail iteration adds the basic physics of the model.
            This model was in the form of a double pendulum, with to powered joints.
            The ideal motors in the joints made it that it could move with almost infinite speed.
            To get a better idea of the forces in the model, the ideal motors are replaced with a beter motor model.
            As the system did not operate with infinite gain anymore it the path planning was updated as well.
            A simple PID controller was implemented to make SCARA follow a square path.
            
            Now that the model forms a basic with the non-ideal motors, basic physics and a controllaw, it can be used to make some estimates.
            The model followed the required path in the specified amount out time.
            With this, the minimum required torque could be calculated.
            Which is then used to dimension the motors.

        \subsubsection{Advanced Model}
            The basic model contains all elementary components and detail can be added for different components.
            The first step was to improve the motor models.
            Up to now it was a primitive model with a source of effort, resistance and gyrator in series.
            For the design it was decided to go with a stepper motor.
            The advantage of a stepper motor is the holding torque, such that the motor can be forced in a certain angle.
            With the new motors the controller was updated, to accommodate for the behavior of the steppers.

            The next step was to upgrade the model to a full three dimensional dynamics.
            Although the SCARA model itself is valid in only two dimensions, having the SCARA suspended from wires required the full dimensions.
            The dynamics of the SCARA are based on a serial link structure \autocite{dresscher_modeling_2010}.
            This allowed for a simple, yet quick implementation of the dynamics.

        \subsubsection{3D modeling}
            With a full dynamics model in 20-sim, the next step was to design the system in OpenSCAD.
            Although 20-sim has a 3D editor, it is significantly easier to build components with OpenSCAD.
            Furthermore, for prototyping the OpenSCAD objects can be exported for 3D printing.
            The model made it possible to check component clearance and get an idea of size.
            The model is shown in \autoref{fig:scad_carriage}.
            \begin{figure}
                \centering
                \includegraphics[width=0.8\linewidth]{graphics/scad_carriage.png}
                \caption{Rendered 3D model of the SCARA}
                \label{fig:scad_carriage}
            \end{figure}

    \subsection{Variable Approach}