Game Development Reference
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τ 2
F 2
τ mot 2
τ max
τ min
τ 1
F 1
τ mot 1
F d
|| F || 2
F T · F F d
T ·( G · G T ) ·
F d
τ
τ
Figure 8.4 Force dimensioning ellipsoids
This ellipsoid defines the required motor torques so that the robot can apply identical
and adequate force and torques in all directions. For this, it suffices to take motors
and reducers with a torque higher than the maximum values of the ellipsoid. These
values are given by its containing box (Figure 8.4).
Stiffness dimensioning : The third criterion is stiffness K of the haptic interface
defined by equation 8.9:
F
=
K
·
dX
(8.9)
This breaks down into a control stiffness K c , which is an image of the maximum gains
of the servomechanisms at the operational level ensuring their stability, transmission
stiffness K t and a mechanical stiffness K s that comes from the flexibility inherent to
any mechanical structure.
With these stiffnesses, roughly considered to be acting in a series, the overall
apparent stiffness of the interface is controlled by equation 8.10:
( K 1
c
K 1
t
K 1
s
) 1
K
=
+
+
(8.10)
The transmission stiffness K t can be optimised by limiting the length of the transmis-
sions.
The mechanical stiffness K s can be maximised during CAD designing by playing
on the shape of the parts and materials used. Finally, the control stiffness K c defined
by F
dX is deducted from the maximum stiffness of the servomechanisms of
the motors K mot which is equal to the proportional term of their servomechanisms
( ô mot =
=
K c ·
G T
G . It can be maximised by
selecting coders with a sufficient resolution (which increase K mot ) or by selecting suit-
able reduction ratios, as the motor stiffness is multiplied in this case by the square of
the reduction ratio.
Dynamic dimensioning : The last criterion is the apparent mass of the robot defined
in a given configuration as the highest mass perceived by the operator when he moves
K mot ·
dq mot ) using the equation K c =
·
K mot ·
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