respectively). Joint 2 was prismatic which slid about its Z2 axis that passed through the

intersection of axes 0 and 1. A robot with this order and configuration of the joints and links is

referred to as a spherical-coordinate manipulator.

 The order of assignment of the coordinate frames on the orange-picking robot is

presented in Figures 5.1 and 5.2. The first coordinate frame (frame 0, labeled Xo, Y and Z )

was assigned to the stationary base of the robot. Frame 1 was attached to the outer link and

positioned to rotate about Zo an angle 81. The third frame (frame 2) was designated to the inner

moving link (link 2) of the robot and allowed to rotate 82 about Z1. The final coordinate frame

(frame 3) was assigned to the sliding tube of the robot and fixed to have linear motion along

axis Z2 which was coincident with Z3. This final frame was positioned in the end-effector of

the robot so that its origin corresponded with the optical lens center of the robot camera. This

arrangement caused the final coordinate frame of the manipulator and the camera's coordinate

frame to be coincident.

 For the orange-picking robot, the joint parameters were specified as variables for

rotation and translation about the axes of motion and as constants to establish the fixed



 frame 0

 Yo, Z, Y2





 frameframe 2 frame 3,






 camera frame
 Xo/, X ^^





 frame 2 frame 3,
 camera frame


Figure 5.1. Kinematic frames of the three degree-of-freedom robot.