**2. Motion principle**

The inchworm type piezoelectric actuator mimics the motion principle of the real inchworm in nature, as is illustrated in **Figure 1(a)** [6]. Sometimes, it is called one kind of novel bionic actuators. It is found that the natural inchworm moves smoothly by stepping motion form. With the help of the stepping motion form and the piezoelectric technology, large working stroke is easy to be achieved by inchworm actuators through the alternating motion of driving units and clamping units. At the same time, compared with other piezoelectric actuators, the use of clamping unit brings larger output force. The inchworm type piezoelectric actuator usually consists of one driving unit and two clamping units. According to the difference of motion modes, inchworm type piezoelectric actuators could be split into three motion patterns: the "walker" pattern, the "pusher" pattern and hybrid "walker-pusher" pattern.

**Figure 1(b)** shows the motion principle of the "walker" pattern piezoelectric actuator, which is essentially similar to the walking mode of the real inchworm in nature. The "walker" mechanism obtains a large working stroke by repeating the following six steps: (1) in the original position, all piezoelectric elements in the driving unit and clamping units do not work, so there is a gap between the clamping device and the base guider; (2) the piezoelectric element in clamping unit 1 obtains the power, and then clamping unit 1 holds the base guide tightly; (3) the driving unit is extending while the piezoelectric element inside it obtains the power; (4) the clamping unit 2 obtains the power to tightly fix the base guider and the clamping unit 1; (5) the clamping unit 1 loses power to release the base guider; (6) the driving unit returns to its original length. Finally, the clamping unit 2 is de energized to release the base guider in the same original position as in step (1). By repeating these six steps, a large working stroke is achieved gradually [7].

The "push" pattern piezoelectric actuator also needs six steps to obtain a step motion, as shown in **Figure 1(c)**: (1) in the original position, all of the driving and clamping units have no power to fix the slider; (2) the clamping unit 2 obtains the power to hold the slider tightly; (3) the driving unit gets power to push the clamping unit 2, and since the slider is hold by clamping unit 2 tightly, it will move forward for small moving distance; (4) the clamping unit 1 holds the slider; (5) the clamping unit 2 is powered off to release the slider; (6) the driving unit returns to the original length when it loses power. At last, the clamping unit 1 releases the slider to the same condition as in the original position [8].

Hybrid "Walker-pusher" pattern piezoelectric actuator is a hybrid of "Walker" and "pusher" modes. The difference is that the driving unit is inserted into the sliding block, and the clamping unit is assembled in the base in the "Walker-pusher" mode [9].

**Figure 1.** *Motion principles: (a) real inchworm; (b) "walker" pattern; (c) "pusher" pattern.*
