【正文】 (LC+LB).Because N1=N2 and we need N1+N2Nbr for the HS to walk, this means that LBLC should be satis?ed. Since the HS cannot move if LC=0, the range of motion is ?nally determined by 0LCLB. In our design, LC+LB≈30mm(the length of the PST), we expect that maximum displacement of the square HS is less than 15 mm. This issue of limitation on the range of motion can nevertheless be solved if the clamping springs are attached to the sapphire rings(not to the HS). III. PERFORMANCE TEST We have tested the room temperature performance of the motor in two extreme cases of moving directions(upward and downward)by measuring its step size and speed as functions of the frequency [Figs. 5(a)and 6(a)for circular and square HS, respectively]and operating voltage[(b)and 6(b)for circular and square HS, respectively]. The pressing forces were set to N1≈N2≈Nbr≈ for circular HS which are much smaller than the blocking forces (Fbl1～ Fbl2～ 2N)of the driving piezoP1 and P2. The maximum step size is m with the measurement conditions being: circular HS, downward stepping with Hz driving frequency. When the moving direction is changed to upward, the step size bees m due to gravity. In case of square HS, the downward and upward step sizes are and , respectively, which is more uniform because of its knife edge contacts with the sapphire rings. All these step sizes are rather large pared with other types of piezoelectric motors9,11,23 with the similar speed of motion is of course closely related to the driving frequency. The maximum driving frequency we set was 50 Hz, at which the speeds for the circular(upward versus downward) and square(upward versus downward)HS were:( versus )and( versus )mm/min. When the driving frequency increases or if the magnitude of the operating voltage drops, the step size diminishes as seen in Figs. 5 and 6. Although we get larger step size from circular HS, we still prefer the square HS owing to its advantages listed earlier. For instance, the travel range using the square HS is 9 mm(as designed)pared with mm for the circular HS(worse than the designed travel range).The performance curves of the square HS motor seen in are also smoother and more consistent than those ()of the circular HS motor. step size(left vertical axis)nd speed(right vertical axis of the motor using the circular HS as functions of (a) frequency(maximum operating voltage=177。200 V maximum operating voltages), respectively. A cut(with diamond saw)through two opposite boundaries of the quadrants is made from the sapphire ring at one end of the PST into about 92% of the tube length toward the other end. The uncut sapphire ring is the base ring, whereas the other is cut into two semi rings which are called clamping semi rings(will clamp hold a mobile HS).Each pair of the neighboring electrodes with no cut in between is wired together, resulting in two semicylindrical electrodes, one is arbitrarily called the ?rst electrode (E1)for convenience and the other, the second electrode(E2).The two halves of the PST that E1 and E2 control are abbreviated as P1 and P2, respectively. The moving part of the motor is a titanium HS that is inserted into the PST as shown in (a).We have studied a circular and a square HS as illustrated in (b). For the circular one(length=45mm,inner diameter=, and outer diameter= mm which can pass through the sapphire rings at the PST ends with a small gap of mm),a wire cut through the axis is made from each end toward the other end with the cutting planes perpendicular to each two cuts do not go through the entire HS and a small length of mm remains uncut at each end. The pair of the HS cut slits having the opening toward the same direction as that of the PST slits is arr