full Paper - Nguyen Dang Binh

number all over the workspace when links’ sizes and interface
position were changed. In Fig. 3, the best-case solution
is graphically represented. The workspace areas have
been coloured by the value of the condition number (c). The
colour type changes at each tenth of unit. Central area has
values between 0.9 and 1, second area values range between
0.8 and 0.9 and the third area values range between 0.7 and
0.8. More than 90% of the overall workspace has c>0.9
Figure 3: Workspace evaluation
In Fig. 4, the haptic desktop workspace in case of length of
link 1 equal to 300mm and length of link 2 equal to 270mm
is shown. Two capstans are used for reducing the inertia of
moving masses and for introducing a reduction ratio. These
reduction ratios have been dimensioned to obtain a condition
number in the middle of the workspace equal to 1.
4. COMPONENT CHOICE AND CONTROL DESIGN
The kinematics of the haptic interface has been determined
according to the chosen link lengths and the following equations
describe end-effector’s coordinates referred to the central
pivoting joint:
Massimo Bergamasco / Future trends and Applications, Education
Xee L2 cos q2 L1 cos q1 (1)
Yee L2 sin q2 L1 sin q1 (2)
From (1) and (2) and are the lengths of link 1 and link 2
while and are the angles referred to the joints. On the other
hand, the end-effector’s coordinates referred to the motors,
and can be computed as follows:
q1 r1
θ1
R1
(3)
33
Figure 4: Workspace of the haptic interface.
q2 r2
θ2
R2
From (3) and (4) and are the rotations of the two actuators,
and are the radii of motor pulleys and and are the radii
of the capstans. Using the above relationships it was possible
to identify the commercial components to be used within the
haptic device (motor type and size, sensors,Ě). The homogeneity
of the conditioning number has allowed us to size out
the design by using the workspace centre as reference point.
Maxon motor 3557024CR was used for actuation. With this
solution the Haptic Interface can generate on user’s hand up
to 3 N of continuous forces and 5 N of peak forces. To detect
device motion 1024cpr optical encoders with a 4X decoding
were adopted. Such a choice leads to a spatial sensitivity of
about 30um at workspace centre (pixel size is about 300um).
Figure 5: Square box with all electronic components inside.
This control system was implemented on the same architecture
of the target application system. This device was
made by an embedded PC (PIII 1.4GHz 256Mb RAM). Specific
I/O board for detecting the encoder position and for
generating the DAC command to be forwarded to drivers
were implemented on the ISA and PC104 busses offered by
the embedded board. The desktop backside was designed in
order to host motors, power supply, hard disk, power drivers,
mother boards and IO boards, all within a minimal regular
square box as shown in figure 5. The high integration
achieved has allowed us to implement all control procedures
(4)
c­ The Eurographics Association 2005.