Workspace analysis In this part, we

Workspace analysis
In this part, we would like to analyze the size of the workspace of both Delta and Delta
inverse robots taking into account geometric limitations. The procedure used to compute the
workspace of the manipulators taking into account geometric limitations is very simple.
Firstly, we discretize the Cartesian space into n points (the discretization step is fixed to 0.02
m). For a point Q to belong to the workspace of the desired manipulator, it should comply
with the geometric limitations, namely:
- values of angle θi
computed using the inverse geometric models have to be comprised
between 0° and 90°;
- for the Delta inverse robot, values of angle αi
computed using the inverse geometric
models comprised of between -90° and 90° in order to avoid interferences with the
base;
- the altitude of the platform has not to be superior to z = -0.3 m in order to avoid
interferences with the base.
Thus, the workspaces of both manipulators can be computed. The results are presented in the
figure 5. For these two robots, the following parameters are used, which correspond to the
parameters of the SurgiScope®
developed by company ISIS: Rb = 0.25 m, Rp = 0.2 m, Lp =
0.95 m, Lb = 0.75 m. It can be seen that, taking into account only the geometric limitations of
the manipulators, the workspace of the Delta inverse robot (1.81 m3
) is larger than the
workspace of the Delta robot (1.48 m3
).