To Design a Small Pneumatic Actuator Driven Parallel
Link Mechanism forShoulder Prostheses for Daily Living Use 111
coordinate system OB 1 - XYZ is located at the center of the Base 1, with the Z-axis directed
along the Backbone 1. The contact points of three pneumatic actuators to Base 1 (B 11 , B 12 , B 13 )
were aligned equiangularly along the peripheral of a circle with a radius rB, and B 11 is on the
X-axis.
The local coordinate system OP 1 - xP 1 yP 1 zP 1 locates at the center of disk Platform 1, h 1 away
from OB 1 along the Z-axis. The contact points of pneumatic actuators to Platform 1 (P 11 , P 12 ,
P 13 ) are on radius rP. In turn, the contact points of three pneumatic actuators to Base 2 (B 21 ,
B 22 , B 23 ) are equiangularly set on circumference of a circle, radius rB, and B 21 is on the xP 1 -
axis. The local coordinate system OP 2 -xP 2 yP 2 zP 2 is set at the center of Platform 2, and the
distance from OP 1 is h 2. The contact points (P 21 , P 22 , P 23 ) are aligned equiangularly along the
peripheral of a circle with a radius rP, and P 21 is on the xP 2 -axis.
Finally, the Rod of length lR is fixed up at OP 2 along the zP 2 -axis.
Suppose the actuators are activated, and their lengths change (expressed discretely: li gets to
li’, i =1, ..., 6). Therefore, h 1 and h 2 are converted to h 1 ’ and h 2 ’, two passive joints (Joint 1) of
Platform 1 and the one (Joint 2) of Platform 2 rotate by , ,,(see Fig. 2, 3), respectively.
Fig. 3. Geometry of the parallel link arm.
At first, the position of OP 1 , P 1 i, P 1 i’(i=1, 2, 3) and the rotation matrix R 1 of Joint 1 in OP 1 -
xP 1 yP 1 zP 1 , i.e. P^1 OP 1 , P^1 P 1 i, P^1 P 1 i’ and P^1 R 1 can be presented as follows: