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The cable-based positioning systems result in a end-effector with a large range and high velocities. |
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A basic setup can be seen in \autoref{fig:cablebotdrawing}. |
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This given setup contains two cables that are motorized. |
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The big advantage of this system is that it scales good, as the cables can have almost any length. |
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The big advantage of this system is that it scales well, as the cables can have almost any length. |
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\begin{figure} |
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\centering |
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\includegraphics[width=10.8cm]{graphics/cablebot.pdf} |
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@@ -25,7 +25,7 @@ |
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\begin{marginfigure} |
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\centering |
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\includegraphics[width=3.74cm]{graphics/cable_angle.pdf} |
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\caption{Illustrating the limit for horizontal acceleration $a$, for different angles to compensate for gravitational acceleration $g$. |
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\caption{Illustrating the limit for pure horizontal acceleration $a$, for different angles to compensate for gravitational acceleration $g$. |
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The red arrow represents the acceleration as a result of the pulling force of the cable, which is vectorized in a vertical acceleration that compensates $g$ and a vertical acceleration $a$.} |
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\label{fig:cable_angle} |
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\end{marginfigure} |
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@@ -33,8 +33,8 @@ |
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Although it is possible to achieve high velocities, this system is limited by the gravitational acceleration. |
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In case of vertical acceleration, the maximum downward acceleration or upward deceleration is limited by \SI{9.81}{\meter\per\second\squared}. |
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The horizontal acceleration depends on the relative angle of the suspending cable. |
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The closer the end-effector is below the cable pulley, the lower the vertical acceleration becomes. |
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\autoref{fig:cable_angle} illustrates the vertical acceleration for different angles. |
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The closer the end-effector is below the cable pulley, the lower the pure horizontal acceleration becomes. |
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\autoref{fig:cable_angle} illustrates the horizontal acceleration for different angles. |
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A possible solution to this is to add one or two additional wires to the system. |
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These can pull on the system to 'assist' the gravitational force. |
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@@ -48,8 +48,8 @@ |
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Because each slider covers a single X or Y axis, the control and dynamics of this system are rather simple. |
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The biggest challenge is in the construction of the system, especially when the size of the system is increased. |
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The larger system requires bigger length sliders, which are expensive. |
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Another difficulty is the actuation of both horizontal sliders, if these sliders do not operate synchronous, the vertical slider will rotate. |
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However, this is slider is not allowed to rotate, thus probably breaking the system. |
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Another difficulty is the actuation of both horizontal sliders, if these sliders do not operate synchronous, the vertical slider rotates. |
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However, the construction of the slider is not able to rotate, resulting in damage to the system. |
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\begin{figure} |
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\centering |
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\includegraphics[width=8.74cm]{graphics/plotter.pdf} |
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@@ -106,14 +106,21 @@ |
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\subsubsection{Choice of system} |
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The previous sections have shown four different configurations. |
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These configurations are compared in \autoref{tab:initial_design}. |
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Each of the systems are scored on range, dimension, speed, scaling and the interesting dynamics. |
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Each of the systems are scored on range, speed, cost, obstruction, effective area, and the interesting dynamics. |
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The range scores the system on the practical dimension of the system, larger is better. |
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The cable and cartesian configuration scale very well, the cables or slider rails can be made longer without real difficulty. |
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The SCARA or polar configuration run into problems with the arm lengths, as forces scale quadratically with their length. |
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The dimension looks at the number of states that require control and is for all systems defined as 2.5D. |
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The half dimension is the binary state for the marker on or off the board. |
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Except for the cable bot, all configurations score sufficient on speed. |
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The cable bot can be quick, but is limited in acceleration, and depends on the type of cable configuration. |
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For the cost, all systems fit within the €200 budget, except for the Cartesian setup. |
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All systems require some DC or stepper motors, but the cartesian setup also requires linear sliders which are expensive for longer distances. |
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The obstruction score depends on the capability of the system to move away from the text on the board, such that the system does not obstruct the written tweet. |
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For the scalability, only the cable bot scores high. |
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The cables make it possible to easily change the operating range of the system, only requiring reconfiguration. |
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The cartesian system scales poor because the length of the sliders is fixed, and longer sliders are expensive. |
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For the Polar system and SCARA, the forces on the joints scale quadratically with the length of the arms. |
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However, the SCARA can be build with counter balance making it scale less worse than the Polar system. |
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With the effective area, the system is scored on the area it requires to operated versus the writable area. |
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The last one, how interesting or challenging are the dynamics. |
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The cartesian configuration is trivial, both sliders operate completely separate from each other and the position coordinates can be mapped one to one with the sliders. |
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For the other configuration, some inverse kinematics are required to get from desired position to the control angles of the system. |
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@@ -125,20 +132,23 @@ |
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\cline{2-6} |
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& Cable bot & Cartesian & Polar & SCARA & Combined \\ \hline |
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\multicolumn{1}{|l|}{Range} & + + & + & - - & - & + + \\ \hline |
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\multicolumn{1}{|l|}{Dimension} & 2.5 & 2.5 & 2.5 & 2.5 & 4.5 \\ \hline |
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\multicolumn{1}{|l|}{Speed} & - & + & + & + + & + \\ \hline |
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\multicolumn{1}{|l|}{\begin{tabular}[c]{@{}l@{}}Interesting\\ dynamics\end{tabular}} & + & - - & + & + & + + \\ \hline |
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\multicolumn{1}{|l|}{Cost} & + + & - - & + & + & + \\ \hline |
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\multicolumn{1}{|l|}{Obstruction} & - & + & + & + & - \\ \hline |
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\multicolumn{1}{|l|}{Scalability} & + + & - & - - & - & + \\ \hline |
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\multicolumn{1}{|l|}{\begin{tabular}[c]{@{}l@{}}Effective\\ area\end{tabular}} & + + & + & - - & + & + + \\ \hline |
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\multicolumn{1}{|l|}{\begin{tabular}[c]{@{}l@{}}Interesting\\ dynamics\end{tabular}} & - & - - & - & + & + + \\ \hline |
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\end{tabular} |
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\end{table} |
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Based on the dimension, all configurations fail to meet the required four state minimum. |
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By combining two configurations, it is possible to meet the minimum of four states. |
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To get the best system, I decided to combine a 'speed' and a 'range' configuration. |
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This results in a system that has both properties. |
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Combining anything with the cartesian configurations, creates just a moving base for the other configurations. |
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Together with the trivial dynamics, this option is discarded. |
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Suspending the SCARA of the polar configuration with cables creates very interesting dynamics, as moving the end-effector also influences the cables. |
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From both options, the SCARA is quicker and scales better with range than the polar. |
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Therefore, the SCARA is chosen above the polar configuration to be combined with the cable bot. |
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Based on this comparison, I decided to disqualify the cartesian and polar system. |
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The cartesian has no interesting dynamics and is expensive to build at a large enough scale. |
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The polar system is just not feasible, the arm length required to cover the writing area results forces that are too large. |
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Making the joint that can deliver the torque for that arm and also providing enough speed is just out of the scope of this case study. |
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The two remaining configurations also contain some downsides. The cable bot is slow, and the arm length for the SCARA is also likely to cause problems. |
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Therefore, I decided to combine both systems: a cable bot system that moves a small SCARA along the whiteboard. |
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The small SCARA is quick while the cable bot gives the system an enormous range. |
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Resulting in a system that scores high on all criteria except obstruction. |
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The grading for the combined system is shown in the most right column in \autoref{tab:initial_design}. |
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\begin{figure} |
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@@ -157,9 +167,10 @@ |
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In hind sight, it would have been useful to have this information during the specifications step. |
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However, as the specifications step are mainly on the "what" to solve, and specifically not on "how" to solve it, this information was avoided on purpose during the specifications step. |
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This step did result in a initial design that can be used in the next steps. |
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However, I noticed that none of the previous steps gave some implementation threshold. |
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For the problem description and the specifications steps this was a minimum implementation level. |
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This step was a optimal implementation level, the minimum was reached rather quick. |
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But at what level of implementation needs this step to be concluded? |
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A related question: Would a simple dynamic model of the initial design be a useful insight or a waste of time? |
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This step did result in an initial design that can be used in the next steps. |
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However, I noticed that none of the previous steps have a clear start or end. |
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For the problem description and the specification steps the question is when all required information is collected. |
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In the initial design it is always possible continue researching design options to come up with an even better design. |
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Especially with complex system, it is unrealistic to create complete specifications before making design decissions. |
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Resulting in the question: at what point do we have enough information and must we move to the next design step? |
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This is also known as the \emph{requirement versus design paradox} \autocite{fitzgerald_collaborative_2014}. |