Game Development Reference

In-Depth Information

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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