%&tex
    As the previous development cycle was aborted prematurely, the development cycle is repeated for the next feature.

    \subsection{Feature Selection}
        The implementation of the end-effector proofed to be impractical.
        This means that only two features are left.
        \autoref{tab:featurestab2} shows an updated feature comparison.
        Compared with the previous feature selection in \autoref{tab:firstfeatureselection}, the number of tests for the SCARA decreased and the Risk/Time increased.
        This is because \autoref{test_tool_change} relied on both the SCARA and the End-effector which is no longer applicable.
        Based on the feature comparison, the next component to implement is the SCARA.

        \begin{table}[]
            \caption{Comparison of the two remaining features in the design process. This table is an updated version of \autoref{tab:firstfeatureselection}.}
            \label{tab:featurestab2}
            \begin{tabular}{|l|l|l|l|l|l|}
                \hline
                Feature      & Dependees   & Tests  & Risk   & Time    & Risk/Time  \\ \hline
                SCARA        & -           & 2      & 50\%   & 12 days & 4.2        \\ \hline
                Carriage     & -           & 2      & 30\%   & 10 days & 3          \\ \hline
            \end{tabular}
        \end{table}

        \subsubsection{Evaluation}
            The feature selection for the second cycle is an updated selection process of the first cycle (\autoref{sec:case_feature_selection_1}).
            This resulted in a quick and effortless feature selection process.

    \subsection{Rapid Development for SCARA}
        The goal is to present a functional model of the SCARA.
        The specifications state that it must be able to write three characters within 2 seconds.
        And to pass \autoref{test1} it must draw a \SI{50}{\milli\meter} by \SI{70}{\milli\meter} rectangle within 1 second.
        The basic design principle is based on the initial design as shown in \autoref{fig:combined}.
        For the lowest detail level of the design, I decided on a kinematics model.
        The model is stays very simple as it does not implement any physics.
        However, the model enables me to tinker with the design parameters, such as the lengths of the linkages and joint angles.
        In the following steps, the level of detail is gradually increased to arrive at a competent model.
        Planning all the different steps in advance is difficult as design decisions still need to be made.
        Nonetheless, I can describe at least the following levels of detail for the model:
        \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.
        \end{enumerate}
        After these steps the optimal order of implementation for the levels of detail becomes vague.
        However, the following elements are required to make a competent model:
        \begin{itemize}
            \item Improved motor model
            \item 3D physics model
        \end{itemize}
        When the first design decisions made, the succeeding levels of detail for these and other elements are laid out.


        \subsubsection{Evaluation}
            The current steps in the rapid development are difficult to perform.
            There is, unsurprisingly, lack of a clear vision of the end-product.
            Which makes an explicit description of all the different levels of detail unfeasible.
            However, it was still possible to describe the initial steps in the level of detail of the design.
            The remaining elements, that are essential to the design, will take shape in a later stage of the development.
            Apart from this small deviation, the deliverables of this step are a good start of this development cycle.

    \subsection{Variable Detail Approach}
        The following steps is to increase the level of detail of the model.
        The initial model together with the set of steps in the detail level is inherited from the previous design step.
        To start, I will implement the basic model and implement the different levels of detail.
        Based on the model after those steps, it is possible to make more detailed design decisions.
        The decisions make it possible to plan the subsequent levels of detail.
        Implementing these details as well, results in a competent model.

        \subsubsection{Basic Kinematics Model}
            \begin{marginfigure}
                    \centering
                    \includegraphics[width=0.9\linewidth]{graphics/scara_arm_kinematics.pdf}
                    \caption{Basic kinematics of the SCARA. The arm consists of two linkages $a$ and $b$; two joints $\alpha$ and $\beta$; and a point mass $m$ which represents the end-effector/tool.}
                    \label{fig:scaraarm}
            \end{marginfigure}
            The development starts with a basic model model as shown in \autoref{fig:scaraarm}.
            It consists of the forward and inverse kinematics of the design.
            With this kinematics model it was easy to find a good configuration of the SCARA.
            I tested if the SCARA could reach the required operating area, to be able to satisfy specification \ref{threecharspec}.
            The operating area is not a couple of centimeters away from the base of the SCARA.
            This is to avoid the singularity point that lies at the base of the SCARA.
            Resulting in longer arms than strictly necessary but this reduces the operating angles of the joints allowing for simpler construction.
            
            At this point, there are already multiple design decisions made about the position of the operating area and the arm lengths.
            The second detail iteration adds the basic physics of the model.
            This model was in the form of a double pendulum, with two attenuated joints.
            The ideal motors in the joints made gave the SCARA almost unlimited acceleration.
            As the one of the goals is to get an indication on what the required torque for these joints is, the ideal motors are replaced with basic DC-motors.
            Implementing a simple PID-controller allowed the SCARA to follow the rectangular path as described in system test \ref{test1}.
            Based the simulation, it was possible to determine minimum specifications of the motors.
            The motors must be able to deliver at least \SI{0.2}{\newton\meter} of torque and reach an angular velocity of at least \SI{12}{\radian\per\second}.

            \begin{marginfigure}
                \centering
                \includegraphics[width=0.9\linewidth]{graphics/scara_20sim_model.png}
                \caption{3D plot of the current implementation. The rectangular shapes represent are the linkages and implemented as rigid bodies. 
                The sphere on the origin and the one between both linkages represent the actuated joints.
                There is no inertia implemented for these joints.}
                \label{fig:scara_20sim}
            \end{marginfigure}
            
            The current implementation can be seen in \autoref{fig:scara_20sim}.
            Now that the model forms a basic with the non-ideal motors, basic physics and a control law, it can be used to make some estimates.
            The model was configured to follow the required path in the specified amount out time according to System Test \ref{test1}.
            The torque required gave a rough estimate of the required actuation force of the motors.
        
        \subsubsection{Detailed design decisions}
            The basic model gave some good insight and information about the dynamic behavior of the system.
            However, the current configuration is very simple but requires a motor in the joint.
            In \autoref{fig:scaradesign}, this setup is shown as configuration 1.
            The disadvantage is that a motorized joint is heavy and has to be accelerated with the rest of the arm.
            Other configurations in \autoref{fig:scaradesign} move the motor to a static position.
            Configuration 2 is a double arm setup, but has quite limited operating range, caused by a singularity region in the system when both arms at the top are in line with each other.
            Configuration 3 also has such a singularity, but due to the extended top arm this point of singularity is outside of the operating range.
            However, this configuration requires one axis with two motorized joints on it.
            Even though this is possible, it does increase the complexity of the construction.
            By adding an extra linkage, the actuation can be split as shown in configuration 4.
            \begin{figure}
                \centering
                \includegraphics[width=0.875\linewidth]{graphics/scara_design.pdf}
                \caption{Four different SCARA configurations. The colored circles mark which of the joints are actuated. Configuration 3 has two independently actuated joints on the same position.}
                \label{fig:scaradesign}
            \end{figure}

            The actuation of the arm is done with stepper motors, which have the advantage over DC-motors with their holding torque.
            The holding torque removes the need of a feedback controller to compensate for external forces.
            Instead, the stepper motors can be fully operated with a feedforward controller.
            However, they are heavier and more expensive.
            The additional mass is beneficial as increased inertia of the base, reducing the displacement due to the reaction force of the SCARA acceleration.
            The extra costs are easily compensated as it saves development time due to the simplified control law, and the removed need for extra angle sensors used in feedback control.

            Due to the aborted implementation of the end-effector, the SCARA must also lift the marker of the board.
            The chosen configuration of the SCARA makes it possible to add an extra joint in the linkage.
            As the marker only needs to be moved a couple of millimeters from the board, a simple servo suffices.

        \subsubsection{Implementing details}
            The new concrete design decisions, make it possible to plan the next steps of adding detail.
            The following steps are an addition to the steps as described in the previous section:
            \begin{enumerate}
                \setcounter{enumi}{4}
                \item Stepper motor behavior.
                \item Updating physics model to 3D physics.
                \item Marker lifting behavior, servo lifts marker of the board.
            \end{enumerate}
            Starting with replacing the DC-motor with a stepper motor model, which is based on a model by \textcite{karadeniz_modelling_2018}.
            The controller is updated as well, to accommodate for the behavior of the steppers.
            The next step is to implement a dynamic model of configuration 4 in \autoref{fig:scaradesign}.
            The dynamics of the SCARA are based on a serial link structure \autocite{dresscher_modeling_2010}.
            This serial link structure makes it easy to add and extend joints, bodies and mass points to the system.
            Therefore, the last detail, the marker lifting, was added without any difficulty.
            The servo is connected via a linkage with the marker such that it rotates away from the board.

        \subsubsection{Component Design}
            At this point the development has reached a detailed design together with a dynamic model representing that design.
            The dynamic model is a useful tool to test and evaluate the system behavior.
            However, it does not include the shapes of the components and can therefore not be used to evaluate clearance or collision between components.
            By implementing the design using CAD software, it is possible to search for collisions.
            Furthermore, this model can than also be used to print the custom parts.
            For the mechanical part I used OpenSCAD as CAD software, based on prior experience with the software.
            With this it was possible to implement all the custom components as well as the \ac{ots}-components.
            Using the inverse kinematics model from the basic design of the SCARA, the angles were directly applied on the components in system.
            Allowing me to change the configuration of the SCARA and inspect the clearance between each component.
            Following the rectangular path as defined in \autoref{test1} revealed that collisions occurred between parts.
            These collisions were resolved by adding an indentation in one linkage and moving another linkage.
            These changes are shown in \autoref{fig:scad_clearance}
            The complete setup with the custom parts and the \ac{ots}-components, such as stepper motors, servo and marker, is shown in \autoref{fig:scad_carriage}.
            \begin{figure}
                \centering
                \includegraphics[width=0.8\linewidth]{graphics/scad_scara_circles.png}
                \caption{
                    CAD of the SCARA configuration, with the end-effector orientated in the lower left corner of the operating area. 
                    The configuration has been adapted at the two circled points, to resolve collisions in this orientation. 
                    An indentation was made to ensure that the arm could make the required corner.
                    Furthermore, the bottom linkage has been moved from above to below the actuated joints, as this linkage would otherwise collide with the end-effector.
                }
                \label{fig:scad_clearance}
            \end{figure}

            \begin{figure}
                \centering
                \includegraphics[width=0.8\linewidth]{graphics/scad_carriage.png}
                \caption{Rendered 3D model of the SCARA, including steppers, marker and servo.}
                \label{fig:scad_carriage}
            \end{figure}

        \subsubsection{Evaluation}
            The complete development was rather smooth.
            However, this was not without deviating from the original design plan.
            The different levels of detail could not be defined before the start of the development but had to be updated midway.

            In total there are seven predefined levels of detail in the design.
            Meaning that there must also be seven test cycles.
            However, I noticed that this number was significantly higher.
            During the design, running the simulation of the dynamics is easy.
            Resulting in extremely short feedback loops, sometimes even minutes.
            For example, changing the arm lengths and evaluate the new behavior.
            Did it improve? Is this as expected?
            Implicitly, the system was very often tested and changed based on test results.

    \subsection{Conclusion}
        With the development of the SCARA completed.
        Following the design plan, the development has to be repeated for the design of the Cable bot.
        However, the evaluation of the development until this point resulted in enough information to draw conclusions about the design plan.
        I expect that executing this development a third time is not beneficial to the case study, given the additional effort.
        Time is better spent on the realization of a prototype and improving the current design method.
        Therefore, the next section will go into the construction of the prototype instead of the development of the Cable bot.

