tdehaeze/phd-test-bench-flexible-joints
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Rename footnotes

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Thomas Dehaeze 2025-02-04 14:24:09 +01:00
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@ -154,7 +154,7 @@ During the detailed design phase, specifications in terms of stiffness and strok
| Bending Stroke | $> 1\,\text{mrad}$ | 24.5 | | Bending Stroke | $> 1\,\text{mrad}$ | 24.5 |
After optimization using a finite element model, the geometry shown in Figure ref:fig:test_joints_schematic has been obtained and the corresponding flexible joint characteristics are summarized in Table ref:tab:test_joints_specs. After optimization using a finite element model, the geometry shown in Figure ref:fig:test_joints_schematic has been obtained and the corresponding flexible joint characteristics are summarized in Table ref:tab:test_joints_specs.
This flexible joint is a monolithic piece of stainless steel[fn:1] manufactured using wire electrical discharge machining. This flexible joint is a monolithic piece of stainless steel[fn:test_joints_1] manufactured using wire electrical discharge machining.
It serves several functions, as shown in Figure ref:fig:test_joints_iso, such as: It serves several functions, as shown in Figure ref:fig:test_joints_iso, such as:
- Rigid interfacing with the nano-hexapod plates (yellow surfaces) - Rigid interfacing with the nano-hexapod plates (yellow surfaces)
- Rigid interfacing with the amplified piezoelectric actuator (blue surface) - Rigid interfacing with the amplified piezoelectric actuator (blue surface)
@ -595,13 +595,13 @@ An overall accuracy of $\approx 5\,\%$ can be expected with this measurement ben
As explained in Section ref:ssec:test_joints_meas_principle, the flexible joint's bending stiffness is estimated by applying a known force to the flexible joint's tip and by measuring its deflection at the same point. As explained in Section ref:ssec:test_joints_meas_principle, the flexible joint's bending stiffness is estimated by applying a known force to the flexible joint's tip and by measuring its deflection at the same point.
The force is applied using a load cell[fn:2] such that the applied force to the flexible joint's tip is directly measured. The force is applied using a load cell[fn:test_joints_2] such that the applied force to the flexible joint's tip is directly measured.
To control the height and direction of the applied force, a cylinder cut in half is fixed at the tip of the force sensor (pink element in Figure ref:fig:test_joints_bench_side) that initially had a flat surface. To control the height and direction of the applied force, a cylinder cut in half is fixed at the tip of the force sensor (pink element in Figure ref:fig:test_joints_bench_side) that initially had a flat surface.
Doing so, the contact between the flexible joint cylindrical tip and the force sensor is a point (intersection of two cylinders) at a precise height, and the force is applied in a known direction. Doing so, the contact between the flexible joint cylindrical tip and the force sensor is a point (intersection of two cylinders) at a precise height, and the force is applied in a known direction.
To translate the load cell at a constant height, it is fixed to a translation stage[fn:3] which is moved by hand. To translate the load cell at a constant height, it is fixed to a translation stage[fn:test_joints_3] which is moved by hand.
Instead of measuring the displacement directly at the tip of the flexible joint (with a probe or an interferometer for instance), the displacement of the load cell itself is measured. Instead of measuring the displacement directly at the tip of the flexible joint (with a probe or an interferometer for instance), the displacement of the load cell itself is measured.
To do so, an encoder[fn:4] is used, which measures the motion of a ruler. To do so, an encoder[fn:test_joints_4] is used, which measures the motion of a ruler.
This ruler is fixed to the translation stage in line (i.e. at the same height) with the application point to reduce Abbe errors (see Figure ref:fig:test_joints_bench_overview). This ruler is fixed to the translation stage in line (i.e. at the same height) with the application point to reduce Abbe errors (see Figure ref:fig:test_joints_bench_overview).
The flexible joint can be rotated by $90^o$ in order to measure the bending stiffness in the two directions. The flexible joint can be rotated by $90^o$ in order to measure the bending stiffness in the two directions.
@ -675,7 +675,7 @@ A closer view of the force sensor tip is shown in Figure ref:fig:test_joints_pic
#+end_src #+end_src
** Load Cell Calibration ** Load Cell Calibration
In order to estimate the measured errors of the load cell "FC2231", it is compared against another load cell[fn:5]. In order to estimate the measured errors of the load cell "FC2231", it is compared against another load cell[fn:test_joints_5].
The two load cells are measured simultaneously while they are pushed against each other (see Figure ref:fig:test_joints_force_sensor_calib_picture). The two load cells are measured simultaneously while they are pushed against each other (see Figure ref:fig:test_joints_force_sensor_calib_picture).
The contact between the two load cells is well defined as one has a spherical interface and the other has a flat surface. The contact between the two load cells is well defined as one has a spherical interface and the other has a flat surface.
@ -1164,8 +1164,8 @@ colors = colororder;
* Footnotes * Footnotes
[fn:5]XFL212R-50N from TE Connectivity. The measurement range is $50\,N$. The specified accuracy is $1\,\%$ of the full range [fn:test_joints_5]XFL212R-50N from TE Connectivity. The measurement range is $50\,N$. The specified accuracy is $1\,\%$ of the full range
[fn:4]Resolute\texttrademark{} encoder with $1\,nm$ resolution and $\pm 40\,nm$ maximum non-linearity [fn:test_joints_4]Resolute\texttrademark{} encoder with $1\,nm$ resolution and $\pm 40\,nm$ maximum non-linearity
[fn:3]V-408 PIMag\textsuperscript{\textregistered} linear stage is used. Crossed rollers are used to guide the motion. [fn:test_joints_3]V-408 PIMag\textsuperscript{\textregistered} linear stage is used. Crossed rollers are used to guide the motion.
[fn:2]The load cell is FC22 from TE Connectivity. The measurement range is $50\,N$. The specified accuracy is $1\,\%$ of the full range [fn:test_joints_2]The load cell is FC22 from TE Connectivity. The measurement range is $50\,N$. The specified accuracy is $1\,\%$ of the full range
[fn:1]The alloy used is called /F16PH/, also refereed as "1.4542" [fn:test_joints_1]The alloy used is called /F16PH/, also refereed as "1.4542"