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.

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