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Rename footnotes

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Thomas Dehaeze 2025-02-04 14:23:48 +01:00
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@ -265,8 +265,8 @@ To do so, a precisely machined mounting tool (Figure ref:fig:test_nhexa_center_p
#+end_subfigure
#+end_figure
The mechanical tolerances of the received plates were checked using a FARO arm[fn:1] (Figure ref:fig:test_nhexa_plates_tolerances) and were found to comply with the requirements[fn:2].
The same was done for the mounting tool[fn:3].
The mechanical tolerances of the received plates were checked using a FARO arm[fn:test_nhexa_1] (Figure ref:fig:test_nhexa_plates_tolerances) and were found to comply with the requirements[fn:test_nhexa_2].
The same was done for the mounting tool[fn:test_nhexa_3].
The two plates were then fixed to the mounting tool, as shown in Figure ref:fig:test_nhexa_mounting_tool_hexapod_top_view.
The main goal of this "mounting tool" is to position the flexible joint interfaces (the "V" shapes) of both plates so that a cylinder can rest on the 4 flat interfaces at the same time.
@ -293,7 +293,7 @@ The main goal of this "mounting tool" is to position the flexible joint interfac
The quality of the positioning can be estimated by measuring the "straightness" of the top and bottom "V" interfaces.
This corresponds to the diameter of the smallest cylinder which contains all points along the measured axis.
This was again done using the FARO arm, and the results for all six struts are summarized in Table ref:tab:measured_straightness.
The straightness was found to be better than $15\,\mu m$ for all struts[fn:4], which is sufficiently good to not induce significant stress of the flexible joint during assembly.
The straightness was found to be better than $15\,\mu m$ for all struts[fn:test_nhexa_4], which is sufficiently good to not induce significant stress of the flexible joint during assembly.
#+name: tab:measured_straightness
#+caption: Measured straightness between the two "V" shapes for the six struts. These measurements were performed twice for each strut.
@ -395,8 +395,8 @@ Finally, the multi-body model representing the suspended table was tuned to matc
<<ssec:test_nhexa_table_setup>>
The design of the suspended table is quite straightforward.
First, an optical table with high frequency flexible mode was selected[fn:5].
Then, four springs[fn:6] were selected with low spring rate such that the suspension modes are below 10Hz.
First, an optical table with high frequency flexible mode was selected[fn:test_nhexa_5].
Then, four springs[fn:test_nhexa_6] were selected with low spring rate such that the suspension modes are below 10Hz.
Finally, some interface elements were designed, and mechanical lateral mechanical stops were added (Figure ref:fig:test_nhexa_suspended_table_cad).
#+name: fig:test_nhexa_suspended_table_cad
@ -407,7 +407,7 @@ Finally, some interface elements were designed, and mechanical lateral mechanica
** Modal analysis of the suspended table
<<ssec:test_nhexa_table_identification>>
In order to perform a modal analysis of the suspended table, a total of 15 3-axis accelerometers[fn:7] were fixed to the breadboard.
In order to perform a modal analysis of the suspended table, a total of 15 3-axis accelerometers[fn:test_nhexa_7] were fixed to the breadboard.
Using an instrumented hammer, the first 9 modes could be identified and are summarized in Table ref:tab:test_nhexa_suspended_table_modes.
The first 6 modes are suspension modes (i.e. rigid body mode of the breadboard) and are located below 10Hz.
The next modes are the flexible modes of the breadboard as shown in Figure ref:fig:test_nhexa_table_flexible_modes, and are located above 700Hz.
@ -2159,10 +2159,10 @@ end
* Footnotes
[fn:7]PCB 356B18. Sensitivity is $1\,V/g$, measurement range is $\pm 5\,g$ and bandwidth is $0.5$ to $5\,\text{kHz}$.
[fn:6]"SZ8005 20 x 044" from Steinel. The spring rate is specified at $17.8\,N/mm$
[fn:5]The 450 mm x 450 mm x 60 mm Nexus B4545A from Thorlabs.
[fn:4]As the accuracy of the FARO arm is $\pm 13\,\mu m$, the true straightness is probably better than the values indicated. The limitation of the instrument is here reached.
[fn:3]The height dimension is better than $40\,\mu m$. The diameter fitting of 182g6 and 24g6 with the two plates is verified.
[fn:2]Location of all the interface surfaces with the flexible joints were checked. The fittings (182H7 and 24H8) with the interface element were also checked.
[fn:1]FARO Arm Platinum 4ft, specified accuracy of $\pm 13\mu m$
[fn:test_nhexa_7]PCB 356B18. Sensitivity is $1\,V/g$, measurement range is $\pm 5\,g$ and bandwidth is $0.5$ to $5\,\text{kHz}$.
[fn:test_nhexa_6]"SZ8005 20 x 044" from Steinel. The spring rate is specified at $17.8\,N/mm$
[fn:test_nhexa_5]The 450 mm x 450 mm x 60 mm Nexus B4545A from Thorlabs.
[fn:test_nhexa_4]As the accuracy of the FARO arm is $\pm 13\,\mu m$, the true straightness is probably better than the values indicated. The limitation of the instrument is here reached.
[fn:test_nhexa_3]The height dimension is better than $40\,\mu m$. The diameter fitting of 182g6 and 24g6 with the two plates is verified.
[fn:test_nhexa_2]Location of all the interface surfaces with the flexible joints were checked. The fittings (182H7 and 24H8) with the interface element were also checked.
[fn:test_nhexa_1]FARO Arm Platinum 4ft, specified accuracy of $\pm 13\mu m$