Game Development Reference
in robotics. We distinguish between open kinematic chain robots (serial architecture)
and closed chain robots (parallel architecture, refer to examples below).
The application work space is the space where the X configuration (position and/or
orientation) of the end effector (here, the robot gripper), its speed V , acceleration a and
forces F exerted on it are represented. The articular space is the space used to represent
the situation of all the bodies of the robot, i.e. the articular variables (generally, only
the motorised articulations are taken into account): q art , speeds
q art , accelerations
and the articular torques τ art .
Geometric dimensioning: The first criterion considered in the dimensioning of the
haptic interfaces is the work space, which is all the configurations that the robot can
achieve. There are various methods to determine it.
We can travel through the space of the accessible articular configurations and trace
all the associated positions of the end effector. For each configuration, the position
of the robot gripper is calculated using the direct geometric model of the robot,
which is written as:
f ( q art )
This first approach provides configurations that are appropriately distributed in
the articular space. However, the associated positions in the application work
space are arranged less regularly.
To obtain a better distribution of the achievable operational configurations, it is
possible to travel through the Cartesian space and test each position to find out
whether it is valid. For this, we use the opposite geometric model written as:
q art =
g ( X )
The point considered belongs to the work space of the manipulator if and only if
there is a solution to equation 8.2, i.e. a corresponding articular configuration.
These models help to optimise the structure of the robot and its geometry, particu-
larly the arrangement of the articulations and the length of the segments. To calculate
the work space, we also take into account the collisions between the segments of
the robot, which helps to optimise their geometry. This requires having a sufficiently
advanced CAD design description to have a realistic collisions model. It is thus impor-
tant to simultaneously carry out the theoretical dimensioning of the robot and its
design. By repeating this procedure for the different structures, we can select the one
which is most suitable to the given specifications.
Kinematic singularities: There are configurations in which a robot cannot be com-
pletely controlled. These are referred to as singular configurations or singularities.
They are divided into two types:
Serial singularities: The movement of the end effector cannot be controlled in
certain directions because of these singularities. This movement restriction of the
effector is accompanied by an internal movement in a branch of the robot. This
type of singularity occurs in serial robots and the elementary branches of parallel
robots. They are mostly local in nature;