\section{Methodology}
\label{sec:methodology}
\subsection{Research Approach}
Because of the controversial findings about the impact of key actuation forces
on speed \cite{akagi_keyswitch, loricchio_force_speed} and the fact, that
keyboard related work can increase the risk for \gls{WRUED} \cite{ccfohas_wrued,
  pascarelli_wrued}, we decided to further investigate possible effects of
different actuation forces and even a keyboard equipped with non-uniform
actuation forces on speed, error rate and satisfaction. To our best knowledge,
to this date, there is no published work about the influence of a keyboard with
non-uniform actuation forces on these metrics. Therefore, we first asked
seventeen people about their preferences, experiences and habits related to
keyboards to get a better understanding on what people might prefer as a
baseline for the design of the adjusted keyboard (keyboard with non-uniform
actuation forces) and to complement the findings obtained through our literature
review. Further, we collected information about available mechanical keyswitches
on the market. Additionally, we conducted a small preliminary experiment with 6
subjects, where we measured the peak forces each individual finger of the right
hand was able to apply to distinct keys in different locations. We then created
the design for the adjusted keyboard based on those measurements. Lastly, an
experiment with twenty-four participants was conducted, where we compared the
performance and user satisfaction while using four different keyboards,
including our adjusted keyboard, to values obtained with the participant's own
keyboards.

\subsection{Preliminary telephone interview}
Some of the studies we found that researched implications of actuation force on
speed, preference or other metrics were published between 1984 and 2010. That is
why we wanted to ascertain if and how, with the advance of technology in recent
years and especially the capabilities modern smartphones offer, keyboard usage
has changed. Further, we wanted to gather information about the preference of
key resistance, keyswitch type and experiences with \gls{WRUED}. Therefore, we
conducted a structured interview with seventeen volunteers (59\% females) via
telephone. The age of the subjects ranged between 22 and 52 with a mean age of
29 years. The professions of subjects were distributed among medical workers,
students, office employees, computer engineers and community workers. The first
question we asked was \textit{``Which keyboard in terms of actuation force would
  be the most satisfying for you to use in the long run?''}. Thirteen (76\%) out
of the seventeen subjects mentioned, that they would prefer a keyboard with
light actuation force over a keyboard with higher resistance. The next question
\textit{``Have you ever had pain when using a keyboard and if so, where did you
  have pain?''} yielded, that 41\% of those polled experienced pain at least
once while using a keyboard. The areas affected described by the seven who
already experienced pain were the wrist \underline{and} forearm (3 out of 7),
wrist only (2 out of 7), fingers (1 out of 7) and forearm only (1 out of 7). The
results for the third question \textit{``Which keyboard are you currently using
  and for how many hours a day on average?''} were in line with the statements
we found during our literature review \cite{ergopedia_keyswitch,
  peery_3d_keyswitch}. Nine answered that they use a notebook (scissor-switches,
membrane), six stated that they use an external keyboard with rubber dome
switches and only two responded that they use a keyboard featuring mechanical
keyswitches. The average, self-reported, usage ranged between half an hour and
10 hours with a mean of 4.71 hours. It is important to note, that a study by
Mikkelsen et al. found, that self-reported durations related to computer work
can be inaccurate \cite{mikkelsen_duration}. The last question \textit{``Which
  tasks do you still prefer to perform with a keyboard rather than your mobile
  phone?''} revealed, that all of the subjects preferred to use a keyboard when
entering greater amounts of data (emails, applications, presentations,
calculations, research), but also surprisingly 41\% preferred to use a keyboard
to write instant messages (chatting via Whatsapp
Web\footnote{\url{https://web.whatsapp.com/}}, Signal
Desktop\footnote{\url{https://signal.org/download/}}, Telegram
Desktop\footnote{\url{https://desktop.telegram.org/}}).

\subsection{Market analysis of available mechanical keyswitches}
\label{sec:market_forces}
To gather information about available actuation forces, we collected the product
lines of keyswitches for all well known manufacturers, namely
Cherry\footnote{\url{https://www.cherrymx.de/en/mx-original/mx-red.html}},
Kailh\footnote{\url{https://www.kailhswitch.com/mechanical-keyboard-switches/}},
Gateron\footnote{\url{http://www.gateron.com/col/58459?lang=en}},
Matias\footnote{\url{http://matias.ca/switches/}},
Razer\footnote{\url{https://www.razer.com/razer-mechanical-switches}} and
Logitech\footnote{\url{https://www.logitechg.com/en-us/innovation/mechanical-switches.html}}. Since
some of the key actuation forces listed on the manufacturers or resellers
websites were given in cN and most of them in g or gf, the values were adjusted
to gram to reflect a trend that is within a margin of ± 2 g of accuracy. The
results shown in Figure \ref{fig:keyswitches_brands} are used to determine the
minimum, maximum and most common actuation force for broadly available
keyswitches. According to our findings, the lowest commercially available
actuation force is 35 g ($\approx$ 0.34 \gls{N}) the most common one is 50 g
($\approx$ 0.49 \gls{N}) and the highest resistance available is 80 g ($\approx$
0.78 \gls{N}).

\begin{figure}[ht]
  \centering
  \includegraphics[width=0.8\textwidth]{images/keyswitches_brands}
  \caption{Available actuation forces for keyswitches of major keyswitch manufacturers}
  \label{fig:keyswitches_brands}
\end{figure}

\subsection{Preliminary study of finger strength}
To evaluate the impact of an adjusted keyboard (keyboard with non-uniform
actuation forces) on performance and satisfaction we first needed to get an
understanding on how to distribute keyswitches with different actuation forces
across a keyboard. Our first idea was to use a similar approach to the keyboard
we described in Section \ref{sec:lr_sum}, were the force required to activate
the keys decreased towards the left and right ends of the keyboard. This rather
simple approach only accounts for the differences in finger strength when all
fingers are in the same position, but omits possible differences in applicable
force depending on the position a finger has to enter to press a certain key.
To detect possible differences in peak force depending on the position of the
fingers, we conducted an experiment with six volunteers (50\%
females). Subject's ages ranged from 20 to 26 with a mean age of 24 years. The
subjects were all personal contacts. Subjects professions were distributed as
follows: computer science students (3/6), physiotherapist (1/6), user experience
consultant (1/6) and retail (1/6). All Participants were given instructions to
exert maximum force for approximately one second onto the key mounted to the
measuring device described in Section \ref{sec:force_meas_dev}. We also used a
timer to announced when to press and when to stop. We provided a keyboard to
every participant, which was used as a reference for the finger position before
every measurement. To reduce order effects, we used a balanced latin square to
specify the sequence of rows (top, home, bottom) in which the participants had
to press the keys \cite{bradley_latin_square}. Additionally, because there were
only six people available, we alternated the direction from which participants
had to start in such a way, that every second subject started with the little
finger instead of the index finger. An example of four different positions of
the finger while performing the measurements for the keys \textit{Shift, L, I}
and \textit{Z} can be observed in Figure \ref{fig:FM_example}.

\begin{figure}[ht]
  \centering
  \includegraphics[width=1.0\textwidth]{images/FM_example}
  \caption{Prototype of the force measuring device used to gather data about the
    maximum applicable force to a key with different finger positions. The
    positions for certain keys are simulated by aligning the wrist pad (left
    picture) to the scale of the device. The four different positions for the
    keys \textit{Shift, L, I, Z} (right pictures) are color coded according to
    the keys on the scale}
  \label{fig:FM_example}
\end{figure}

The results of the measurements are given in Table \ref{tbl:finger_force}. The
median of the means (15.47 N) of all measurements was used to calculate the
actuation forces in gram for the keyswitches later incorporated in the layout
for adjusted keyboard. We used Eq. (\ref{eq:N_to_g}) and
Eq. (\ref{eg:actuation_forces}) to calculate the gram values for each measured
keyswitch.

\begin{equation}
  \label{eq:N_to_g}
  GFR = \frac{50 g}{M_{maf}} = \frac{50 g}{14.47 N} = 3.23 \frac{g}{N}
\end{equation}

\begin{equation}
  \label{eq:actuation_forces}
  AF_{key} = GFR * MAF_{key}
\end{equation}

With $M_{maf}$ the median of the means of applicable forces, $50 g$ the most
commonly found actuation force on the market (Section \ref{sec:market_forces}),
$GFR_{key}$ the gram to force ratio, $MAF_{key}$ the median of applicable force
for a specific key and $AF_{key}$ the actuation force for that specific key in
grams.

An example where we calculated the theoretical actuation force for the \textit{P}
key can be seen in Eq. (\ref{eq:force_example}).

\begin{equation}
  \label{eq:force_example}
  AF_{P} = GFR * MAF_{P} = 3.23 \frac{g}{N} * 10.45 N \approx 33.75 g
\end{equation}

Because there are only certain spring

% Custom spring stiffness
% https://www.engineersedge.com/spring_comp_calc_k.htm


\begin{table*}[]
  \centering
  \ra{1.3}
  \begin{tabularx}{13cm}{?l^l^l^l^l^l^l^l}
    \toprule
    \multicolumn{8}{c}{\textbf{Bottom Row}}\\
    \rowstyle{\itshape}
    \emph{Key}                 & ↑     & -     & :     & ;     & M     & N     & B    \\
    \midrule
    \emph{Mean Force (N)}      & 11.23 & 10.84 & 14.22 & 15.34 & 16.38 & 15.6  & 14.36\\
    \emph{Actuation Force (g)} & 36.05 & 34.8  & 45.65 & 49.24 & 52.58 & 50.08 & 46.1\\
  \end{tabularx}
  \begin{tabularx}{13cm}{?l^l^l^l^l^l^l^X}
    \multicolumn{8}{c}{\textbf{Home Row}}\\
    \rowstyle{\itshape}
    \emph{Key}                 & Ä     & Ö     & L     & K     & J     & H     &\\
    \midrule
    \emph{Mean Force (N)}      & 11.88 & 12.27 & 15.84 & 18.56 & 17.78 & 18.43 &\\
    \emph{Actuation Force (g)} & 38.13 & 39.39 & 50.85 & 59.58 & 57.07 & 59.16 &\\
  \end{tabularx}
  \begin{tabularx}{13cm}{?l^l^l^l^l^l^l^l}
    \multicolumn{8}{c}{\textbf{Top Row}}\\
    \rowstyle{\itshape}
    \emph{Key}                 & +     & Ü     & P     & O     & I     & U     & Z    \\
    \midrule
    \emph{Mean Force (N)}      & 10.8  & 10.7  & 10.45 & 14.34 & 17.95 & 17.0  & 16.8 \\
    \emph{Actuation Force (g)} & 34.67 & 34.35 & 33.54 & 46.03 & 57.62 & 54.57 & 53.93\\
    \bottomrule
  \end{tabularx}
  \caption{Maximum force measurements for all digits of the right hand in
    different positions. The mean force of six participants is shown in the
    first row of each table and the resulting actuation force for the
    corresponding keyswitch in the following row. The columns indicate the label
    of the scale on the measuring device which can be seen in Figure
    \ref{fig:FM_example}. \textit{↑} stands for the shift key.}
\end{table*}