tdehaeze/stewart-simscape
1
0
Fork 0
Code Issues Pull Requests Releases Wiki Activity

Remove useless latex headings

Browse Source
This commit is contained in:
Thomas Dehaeze
2020-02-14 14:24:20 +01:00
parent de392e5c40
commit a83598d7dd
6 changed files with 190 additions and 218 deletions
Download Patch File Download Diff File Expand all files Collapse all files

12
org/cubic-configuration.org
View File

@@ -45,15 +45,15 @@ This configuration is now widely used (cite:preumont07_six_axis_singl_stage_acti
According to cite:preumont07_six_axis_singl_stage_activ, the cubic configuration offers the following advantages:
#+begin_quote
This topology provides a uniform control capability and a uniform stiffness in all directions, and it minimizes the cross-coupling amongst actuators and sensors of different legs (being orthogonal to each other).
This topology provides a *uniform control capability* and a *uniform stiffness* in all directions, and it *minimizes the cross-coupling amongst actuators and sensors of different legs* (being orthogonal to each other).
#+end_quote
In this document, the cubic architecture is analyzed:
- In section [[sec:cubic_conf_stiffness]], we study the link between the Stiffness matrix and the cubic architecture and we find what are the conditions to obtain a diagonal stiffness matrix
- In section [[sec:cubic_conf_above_platform]], we study cubic configurations where the cube's center is located above the mobile platform
- In section [[sec:cubic_conf_stiffness]], we study the *uniform stiffness* of such configuration and we find the conditions to obtain a diagonal stiffness matrix
- In section [[sec:cubic_conf_above_platform]], we find cubic configurations where the cube's center is located above the mobile platform
- In section [[sec:cubic_conf_size_analysis]], we study the effect of the cube's size on the Stewart platform properties
- In section [[sec:cubic_conf_coupling_cartesian]], we study the dynamic coupling of the cubic configuration in the cartesian frame
- In section [[sec:cubic_conf_coupling_struts]], we study the dynamic coupling of the cubic configuration from actuators to sensors of each strut
- In section [[sec:cubic_conf_coupling_cartesian]], we study the dynamics of the cubic configuration in the cartesian frame
- In section [[sec:cubic_conf_coupling_struts]], we study the dynamic *cross-coupling* of the cubic configuration from actuators to sensors of each strut
- In section [[sec:functions]], function related to the cubic configuration are defined. To generate and study the Stewart platform with a Cubic configuration, the Matlab function =generateCubicConfiguration= is used (described [[sec:generateCubicConfiguration][here]]).
* Stiffness Matrix for the Cubic configuration
@@ -605,7 +605,7 @@ We here suppose that there is one relative motion sensor in each strut ($\delta\
Thanks to the Jacobian matrix, we can use the "architecture" shown in Figure [[fig:local_to_cartesian_coordinates]] to obtain the dynamics of the system from forces/torques applied by the actuators on the top platform to translations/rotations of the top platform.
#+begin_src latex :file local_to_cartesian_coordinates.pdf :post pdf2svg(file=*this*, ext="png") :exports both
#+begin_src latex :file local_to_cartesian_coordinates.pdf
\begin{tikzpicture}
\node[block] (Jt) at (0, 0) {$\bm{J}^{-T}$};
\node[block, right= of Jt] (G) {$\bm{G}$};

2
org/static-analysis.org
View File

@@ -41,7 +41,7 @@
* Coupling
What causes the coupling from $F_i$ to $X_i$ ?
#+begin_src latex :file coupling.pdf :post pdf2svg(file=*this*, ext="png") :exports both
#+begin_src latex :file coupling.pdf
\begin{tikzpicture}
\node[block] (Jt) at (0, 0) {$J^{-T}$};
\node[block, right= of Jt] (G) {$G$};

6
org/stewart-architecture.org
View File

@@ -449,7 +449,7 @@ This Matlab function is accessible [[file:../src/generateGeneralConfiguration.m]
Joints are positions on a circle centered with the Z axis of {F} and {M} and at a chosen distance from {F} and {M}.
The radius of the circles can be chosen as well as the angles where the joints are located (see Figure [[fig:joint_position_general]]).
#+begin_src latex :file stewart_bottom_plate.pdf :exports results
#+begin_src latex :file stewart_bottom_plate.pdf
\begin{tikzpicture}
% Internal and external limit
\draw[fill=white!80!black] (0, 0) circle [radius=3];
@@ -993,7 +993,7 @@ A simplistic model of such amplified actuator is shown in Figure [[fig:actuator_
- $v_{m}$ represents the absolute velocity of the top part of the actuator
- $d_{m}$ represents the total relative displacement of the actuator
#+begin_src latex :file actuator_model_simple.pdf :post pdf2svg(file=*this*, ext="png") :exports results
#+begin_src latex :file actuator_model_simple.pdf
\begin{tikzpicture}
\draw (-1, 0) -- (1, 0);
@@ -1094,7 +1094,7 @@ A simplistic model of such amplified actuator is shown in Figure [[fig:amplified
- $v_{m,i}$ represents the absolute velocity of the top part of the actuator
- $d_{m,i}$ represents the total relative displacement of the actuator
#+begin_src latex :file iff_1dof.pdf :post pdf2svg(file=*this*, ext="png") :exports results
#+begin_src latex :file iff_1dof.pdf
\begin{tikzpicture}
% Ground
\draw (-1.2, 0) -- (1, 0);