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Thomas Dehaeze
2025-12-02 15:08:20 +01:00
parent be49c57495
commit 9231f43cbb
5 changed files with 111 additions and 111 deletions
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@@ -117,10 +117,10 @@
#+end_src
** Geometry
The Delta Robot geometry is defined as shown in Figure ref:fig:delta_robot_schematic.
The Delta Robot geometry is defined as shown in Figure [[fig:delta_robot_schematic]].
The geometry is fully defined by three parameters:
- =d=: Cube's size (i.e., the length of the cube edge)
- =d=: Cube's size (i.e., the length of the cube edge) eqref:eq:detail_kinematics_cubic_s
- =a=: Distance from cube's vertex to top flexible joint
- =L=: Distance between two flexible joints (i.e., the length of the struts)
@@ -207,15 +207,15 @@ Jacobian matrix between actuator displacement and top platform displacement.
There are three actuators in the following directions $\hat{s}_1$, $\hat{s}_2$ and $\hat{s}_3$;
\begin{equation}\label{eq:detail_kinematics_cubic_s}
\hat{\bm{s}}_1 = \begin{bmatrix} \frac{-1}{\sqrt{6}} \\ \frac{-1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} \end{bmatrix} \quad
\hat{\bm{s}}_2 = \begin{bmatrix} \frac{\sqrt{2}}{\sqrt{3}} \\ 0 \\ \frac{1}{\sqrt{3}} \end{bmatrix} \quad
\hat{\bm{s}}_1 = \begin{bmatrix} \frac{-1}{\sqrt{6}} \\ \frac{-1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} \end{bmatrix}\quad
\hat{\bm{s}}_2 = \begin{bmatrix} \frac{\sqrt{2}}{\sqrt{3}} \\ 0 \\ \frac{1}{\sqrt{3}} \end{bmatrix}\quad
\hat{\bm{s}}_3 = \begin{bmatrix} \frac{-1}{\sqrt{6}} \\ \frac{ 1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} \end{bmatrix}
\end{equation}
\begin{equation}
\boldsymbol{J} = \begin{bmatrix}
\hat{\boldsymbol{s}}_1^T \\ \hat{\boldsymbol{s}}_2^T \\ \hat{\boldsymbol{s}}_3^T
\end{bmatrix}
\bm{J} = \begin{bmatrix}
\hat{\bm{s}}_1^T \\ \hat{\bm{s}}_2^T \\ \hat{\bm{s}}_3^T
\end{bmatrix}
\end{equation}
#+begin_src matlab
@@ -227,11 +227,11 @@ J = [s1' ; s2' ; s3']
#+end_src
\begin{equation}
d\mathcal{L} = J d\mathcal{L}
d\mathcal{L} = J d\mathcal{L}
\end{equation}
\begin{equation}
d\mathcal{X} = J^{-1} d\mathcal{L}
d\mathcal{X} = J^{-1} d\mathcal{L}
\end{equation}
The achievable workspace is a cube whose edge length is equal to the actuator stroke.