tdehaeze/digital-brain
1
0
Fork 0
Code Issues Pull Requests Releases Wiki Activity

Update Content - 2024-12-17

Browse Source
This commit is contained in:
Thomas Dehaeze
2024-12-17 15:37:17 +01:00
parent 4d585dd592
commit 4fb2b6c969
86 changed files with 1314 additions and 711 deletions
Download Patch File Download Diff File Expand all files Collapse all files

12
content/article/mcinroy02_model_desig_flexur_joint_stewar.md
View File

@@ -40,11 +40,11 @@ This short paper is very similar to (<a href="#citeproc_bib_item_1">McInroy 1999
{{< figure src="/ox-hugo/mcinroy02_leg_model.png" caption="<span class=\"figure-number\">Figure 1: </span>The dynamics of the ith strut. A parallel spring, damper, and actautor drives the moving mass of the strut and a payload" >}}
The strut can be modeled as consisting of a parallel arrangement of an actuator force, a spring and some damping driving a mass (Figure [1](#figure--fig:mcinroy02-leg-model)).
The strut can be modeled as consisting of a parallel arrangement of an actuator force, a spring and some damping driving a mass ([Figure 1](#figure--fig:mcinroy02-leg-model)).
Thus, **the strut does not output force directly, but rather outputs a mechanically filtered force**.
The model of the strut are shown in Figure [1](#figure--fig:mcinroy02-leg-model) with:
The model of the strut are shown in [Figure 1](#figure--fig:mcinroy02-leg-model) with:
- \\(m\_{s\_i}\\) moving strut mass
- \\(k\_i\\) spring constant
@@ -136,12 +136,12 @@ This section establishes design guidelines for the spherical flexure joint to gu
{{< figure src="/ox-hugo/mcinroy02_model_strut_joint.png" caption="<span class=\"figure-number\">Figure 2: </span>A simplified dynamic model of a strut and its joint" >}}
Figure [2](#figure--fig:mcinroy02-model-strut-joint) depicts a strut, along with the corresponding force diagram.
[Figure 2](#figure--fig:mcinroy02-model-strut-joint) depicts a strut, along with the corresponding force diagram.
The force diagram is obtained using standard finite element assumptions (\\(\sin \theta \approx \theta\\)).
Damping terms are neglected.
\\(k\_r\\) denotes the rotational stiffness of the spherical joint.
From Figure [2](#figure--fig:mcinroy02-model-strut-joint) (b), Newton's second law yields:
From [Figure 2](#figure--fig:mcinroy02-model-strut-joint) (b), Newton's second law yields:
\begin{equation}
f\_p = \begin{bmatrix}
@@ -269,6 +269,6 @@ By using the vector triple identity \\(a \cdot (b \times c) = b \cdot (c \times
## Bibliography {#bibliography}
<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
<div class="csl-entry"><a id="citeproc_bib_item_1"></a>McInroy, J.E. 1999. “Dynamic Modeling of Flexure Jointed Hexapods for Control Purposes.” In <i>Proceedings of the 1999 Ieee International Conference on Control Applications (Cat. No.99ch36328)</i>, nil. doi:<a href="https://doi.org/10.1109/cca.1999.806694">10.1109/cca.1999.806694</a>.</div>
<div class="csl-entry"><a id="citeproc_bib_item_2"></a>———. 2002. “Modeling and Design of Flexure Jointed Stewart Platforms for Control Purposes.” <i>Ieee/Asme Transactions on Mechatronics</i> 7 (1): 95–99. doi:<a href="https://doi.org/10.1109/3516.990892">10.1109/3516.990892</a>.</div>
<div class="csl-entry"><a id="citeproc_bib_item_1"></a>McInroy, J.E. 1999. “Dynamic Modeling of Flexure Jointed Hexapods for Control Purposes.” In <i>Proceedings of the 1999 IEEE International Conference on Control Applications (Cat. No.99CH36328)</i>. doi:<a href="https://doi.org/10.1109/cca.1999.806694">10.1109/cca.1999.806694</a>.</div>
<div class="csl-entry"><a id="citeproc_bib_item_2"></a>———. 2002. “Modeling and Design of Flexure Jointed Stewart Platforms for Control Purposes.” <i>IEEE/ASME Transactions on Mechatronics</i> 7 (1): 95–99. doi:<a href="https://doi.org/10.1109/3516.990892">10.1109/3516.990892</a>.</div>
</div>