Update Content - 2020-10-15

content/article/mcinroy99_dynam.md

@@ -4,7 +4,7 @@ author = ["Thomas Dehaeze"]
 draft = false
 +++
 
-### Backlinks {#backlinks}
+Backlinks:
 
 -   [Identification and decoupling control of flexure jointed hexapods]({{< relref "chen00_ident_decoup_contr_flexur_joint_hexap" >}})
 
@@ -12,7 +12,7 @@ Tags
 : [Stewart Platforms]({{< relref "stewart_platforms" >}}), [Flexible Joints]({{< relref "flexible_joints" >}})
 
 Reference
-: ([McInroy 1999](#org5efb28a))
+: ([McInroy 1999](#orgfc7fa52))
 
 Author(s)
 : McInroy, J.
@@ -20,7 +20,7 @@ Author(s)
 Year
 : 1999
 
-This conference paper has been further published in a journal as a short note ([McInroy 2002](#org4990a96)).
+This conference paper has been further published in a journal as a short note ([McInroy 2002](#org7752c60)).
 
 
 ## Abstract {#abstract}
@@ -42,22 +42,22 @@ The actuators for FJHs can be divided into two categories:
 1.  soft (voice coil), which employs a spring flexure mount
 2.  hard (piezoceramic or magnetostrictive), which employs a compressive load spring.
 
-<a id="org5279430"></a>
+<a id="orgd835559"></a>
 
 {{< figure src="/ox-hugo/mcinroy99_general_hexapod.png" caption="Figure 1: A general Stewart Platform" >}}
 
-Since both actuator types employ force production in parallel with a spring, they can both be modeled as shown in Figure [2](#org6b356c7).
+Since both actuator types employ force production in parallel with a spring, they can both be modeled as shown in Figure [2](#org26f1840).
 
 In order to provide low frequency passive vibration isolation, the hard actuators are sometimes placed in series with additional passive springs.
 
-<a id="org6b356c7"></a>
+<a id="org26f1840"></a>
 
 {{< figure src="/ox-hugo/mcinroy99_strut_model.png" caption="Figure 2: The dynamics of the i'th strut. A parallel spring, damper and actuator drives the moving mass of the strut and a payload" >}}
 
 <a id="table--tab:mcinroy99-strut-model"></a>
 <div class="table-caption">
   <span class="table-number"><a href="#table--tab:mcinroy99-strut-model">Table 1</a></span>:
-  Definition of quantities on Figure <a href="#org6b356c7">2</a>
+  Definition of quantities on Figure <a href="#org26f1840">2</a>
 </div>
 
 | **Symbol**                   | **Meaning**                                |
@@ -74,11 +74,11 @@ In order to provide low frequency passive vibration isolation, the hard actuator
 | \\(v\_i = p\_i - q\_i\\)     | vector pointing from the bottom to the top |
 | \\(\hat{u}\_i = v\_i/l\_i\\) | unit direction of the strut                |
 
-It is here supposed that \\(f\_{p\_i}\\) is predominantly in the strut direction (explained in ([McInroy 2002](#org4990a96))).
+It is here supposed that \\(f\_{p\_i}\\) is predominantly in the strut direction (explained in ([McInroy 2002](#org7752c60))).
 This is a good approximation unless the spherical joints and extremely stiff or massive, of high inertia struts are used.
 This allows to reduce considerably the complexity of the model.
 
-From Figure [2](#org6b356c7) (b), forces along the strut direction are summed to yield (projected along the strut direction, hence the \\(\hat{u}\_i^T\\) term):
+From Figure [2](#org26f1840) (b), forces along the strut direction are summed to yield (projected along the strut direction, hence the \\(\hat{u}\_i^T\\) term):
 
 \begin{equation}
   m\_i \hat{u}\_i^T \ddot{p}\_i = f\_{m\_i} - f\_{p\_i} - m\_i \hat{u}\_i^Tg - k\_i(l\_i - l\_{r\_i}) - b\_i \dot{l}\_i
@@ -168,6 +168,6 @@ In the next section, a connection between the two will be found to complete the
 
 ## Bibliography {#bibliography}
 
-<a id="org5efb28a"></a>McInroy, J.E. 1999. “Dynamic Modeling of Flexure Jointed Hexapods for Control Purposes.” In _Proceedings of the 1999 IEEE International Conference on Control Applications (Cat. No.99CH36328)_, nil. <https://doi.org/10.1109/cca.1999.806694>.
+<a id="orgfc7fa52"></a>McInroy, J.E. 1999. “Dynamic Modeling of Flexure Jointed Hexapods for Control Purposes.” In _Proceedings of the 1999 IEEE International Conference on Control Applications (Cat. No.99CH36328)_, nil. <https://doi.org/10.1109/cca.1999.806694>.
 
-<a id="org4990a96"></a>———. 2002. “Modeling and Design of Flexure Jointed Stewart Platforms for Control Purposes.” _IEEE/ASME Transactions on Mechatronics_ 7 (1):95–99. <https://doi.org/10.1109/3516.990892>.
+<a id="org7752c60"></a>———. 2002. “Modeling and Design of Flexure Jointed Stewart Platforms for Control Purposes.” _IEEE/ASME Transactions on Mechatronics_ 7 (1):95–99. <https://doi.org/10.1109/3516.990892>.