Game Development Reference
In-Depth Information
the handle in free space in all directions. To study it, we shall introduce the dynamic
model of the manipulator written as:
τ mot +
τ ext =
A ( q )
· ¨
q
+
C ( q ,
q )
˙
· ˙
q
+
Q ( q )
(8.11)
In free space, the motor torques τ mot are considered to be zero while the vector Q ( q )of
the centrifugal forces and Coriolis is ignored because the robot gripper is operated by
the user at a relatively low speed. Finally, the vector Q ( q ) of the gravitational forces is
also ignored because most of the haptic interfaces are statically balanced. The dynamic
model is thus written in a simplified manner:
τ ext =
A ( q )
· ¨
q
(8.12)
Equation 8.12 can be expressed at the operational level thanks to the static model and
to the derivative of the kinematic model. If we ignore the terms involving the speeds,
which are relatively low, we obtain:
F
=
M
·
γ
(8.13)
To study the mass and inertia felt by the person who operates the interface, we use the
concept of apparent mass ellipsoid which is defined as the image of the operational
forces produced by a normalised acceleration of 1m/s 2 . Its equation is written as:
2
γ
=
1
(8.14)
i.e.
F T
M T ) 1
·
( M
·
·
F
=
1
(8.15)
This ellipsoid helps to calculate the mass and inertia felt by the operator in all directions
in a given configuration. It can be used to study the dynamic homogeneity of the robot
and adjust its parameters to obtain better performance and to calculate the maximum
apparent inertia and mass that must be less than the value stated in the specifications.
Note: The same type of ellipsoid can be used to study the apparent stiffness seen by the
user. For this, it suffices to replace γ with dX and M with K in equations 8.13 to 8.15.
8.3.2.3 Optimisation
Modelling and dimensioning tools can be used in a simultaneous or sequential man-
ner to optimise the performance of the haptic interfaces. The algorithms developed
will depend on the case concerned and the importance accorded to each criterion. To
the extent possible, we would prefer using simple algorithms, at least on the prop-
erly controlled structures, which help to understand the development of performance
according to the parameters of the robot rather than “black boxes'' providing a unique
optimal solution. This helps to integrate the design constraints that appear during CAD
designing of the interface and which are not taken into account initially.