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Modeling and Human Performance in Manipulating Parallel Flexible Objects  73



                                   PC                  Parallel port



                                  Monitor

                                             Bead 1
                        Proxy
                                             Bead 2

                               Virtual object



                          Visual & haptic interface







              Fig. 5.3 Experimental setup.

              ¼ 3 kg, m 2 ¼ 3 kg, k 1 ¼ 50 N/m, k 2 ¼ 250 N/m), “connected” to a human
              hand by haptic feedback generated by the PHANToM motors. The hand &
              beads system was at rest at the start point. The subjects were asked to move
              the flexible object and to smoothly stop the hand and the two beads at a tar-
              get point. The subjects made these rest-to-rest movements along a line (in
              the direction from left to right) in the horizontal plane using the PHAN-
              ToM stylus. The traveling distance was set as L ¼ 0.2 m.
                 A simple haptic simulator, including a haptic rendering module, a
              graphics rendering (using VRML objects) module, a simulation loop (with
              a given number of parallel springs/beads), and a history unit, was designed
              and implemented for the experiment. The position of the hand (proxy point
              in Fig. 5.3) as well as of the object (Bead1 and Bead2) were displayed on the
              PC monitor, providing the subject with a real-time visual feedback. The
              object dynamics (5.5), (5.6) were simulated (the fourth-order Runge-Kutta
              method with constant step h ¼ 0.001 s), and the real-time haptic feedback
                              f haptic ðtÞ¼ k 1 ðx 1  x h Þ + k 2 ðx 2  x h Þ,  (5.54)

              was supplied to the subject through the PHANToM stylus.
                 It should be noted that this game-like reaching task posed for the subjects
              is quite different from what one experiences when moving the hand in free
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