Biomedical Engineering Reference
In-Depth Information
researchers have tried to maintain the stability by fine tuning a stable linear PID
controller and the function of the fuzzy logic was the tuner (Ibrahim, 2002; Moon
and Lee, 2003; Deskur et al. , 1998).
In the above review, there are 17 rehabilitation robots for upper limbs and
only five robots have dimension of movements less than 3. Yet, we decided to
develop a planar robot based on the following reasons, (1) the design of controller
and therapeutic trajectories becomes more difficult as the DoF and movement
dimension increase and (2) the knowledge about how to design the beneficial
movement trajectories, especially in 3D, is currently lacking.
9.2 OUR PLANAR REHAB ROBOT FOR UPPER LIMBS
We have devoted ourselves to develop a 2-DoF robot specialized for rehabilitation
of the upper limbs in the horizontal plane in the past 10 years (Ju et al. , 2001;
Wu et al. , 2002; Ju et al. , 2005) ( Fig. 9.1a ) . Our robot system consists of a robot
mechanism, motion controller, position and force/torque sensors, and a personal
computer ( Fig. 9.1b ) . During the rehabilitation, the subject's hand grasps a clamp
that allows free pronation/supination. The commands calculated by the personal
computer are sent to drivers of two AC motors of the robot. The inputs to the
controller, consisting of end-point force and position information, are used both for
closed-loop control and for later off-line analyses. We adopt the five-bar-link drive
mechanism (Asada et al. , 1984) for constructing the robot ( Fig. 9.1c ) . The motors
are located at the base (origin of X-Y coordinate system), in order to minimize the
inertial loading of the whole robot system. The main advantage of the design is
that when the physical configuration of the 4 links satisfies the relation of Eq. (1) ,
the dynamic equation of the robot can be theoretically decoupled as Eq. (2) ,
l g 4
l g 3 =
m 4
m 3
l 2
l 1
,
(9.1)
τ 1
τ 2
h 11 0
0
; ¨
θ ¨
=
(9.2)
θ 2
h 22
where m 3 ,m 4 ,l g 3 and l g 4 are the masses and lengths to the centers of mass of
third and fourth links respectively, l 1 and l 2 are lengths of first and second links
respectively,
τ 2 are the input torques of the robot joints respectively, h 11
and h 22 are constants, and
τ 1 and
θ 2 are the angles of first and second links
relative to the horizontal axis (X), respectively. Eq. (2) means that the two axes are
independent and it makes the controller design process simpler. During the design
process, we find that friction has significant effects on the robot performance and
the friction torque can be added to Eq. (2) , as
τ 1
τ 2
θ 1 and
h 11 0
0 h 22
¨
θ ¨
τ f 1
τ f 2
=
+
(9.3)
θ 2
 
 
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