System setup for controllable motion
In this system, a manipulator composed of a parallel structure is utilized for generating 2D circular motion. The manipulator is controlled by two operating systems: a Windows PC and a Linux PC. The Windows PC provides visual feedback from a high-speed camera (Photron FASTCAM MC2). The Linux PC takes charge of the end effector’s motion control by a parallel link actuated by three piezoelectric actuators (NEC TOKIN, AE0203D16). The end effector is composed of a glass needle. By heating and vertically pulling a glass rod (NARISHIGE G-1000) of a 90-mm in length and 1-mm in diameter, we made a sharpen glass needle which has about 23-mm in length, 1-mm in diameter, and less than 1-μm in diameter of tip of end effector.
For accurate positioning of microobjects using water flow, the precise high-speed motions of the end-effector is required. In this work, the target object is a 9.6 μm microbead around the end effector. To estimate the movement of the target, we can apply the rotational flow made by the circular motion. The rotational flow can be generated by the high speed motion (more than 50 Hz). In addition, the flow velocity is changed by the frequency and the amplitude of the circular motion. Thus, the motion with high-accuracy (less than 1 μm) helps to formulate the velocity model clearly.
To generate high-speed motion with high-accuracy positioning, the parallel manipulator is a better solution than serial manipulator owing to its advantages such as high rigidity and positioning accuracy. Thus, we applied the parallel mechanism for this work. The parallel mechanism is a redesigned version of our previous structure [30]. The former version of the microhand was a 3-prismatic–revolute–spherical (PRS) parallel mechanism, while the current mechanism has a 3-prismatic–revolute–revolute (PRR) structure, which is smaller and more rigid. Details of this mechanism are described in [31]. Figure 1 shows the parallel link and the end effector’s camera view. This mechanism is actuated by three piezoelectric actuators as prismatic joints to be extended up to 10.7 μm. The end-effector has three degrees of freedom: two rotational motions (X- and Z-movement) and one translational motion (Y-movement).
Figure 2 shows the control scheme of the parallel link for generating high-speed motion. The displacement of the three PZT actuators determines the 3D position of the end effector, which can be measured by the strain gauges attached to the actuators. The extensions of the PZT actuators are measured by the strain gauges fixed to each PZT actuator; the signals are transferred to the Linux PC through an amplifier (Kyowa MCD-16A) and an analog-to-digital board [Contec AD16-16(PCI)EV]. The 3D position of the end effector can be calculated using the obtained sensor data and compensated by a closed-loop PID controller. The desired voltage determined by computation of the sensor data is applied to each actuator through a digital-to-analog board [Contec DA16-16(LPCI)L] and an amplifier (MATSUSADA, HJPZ-0.15Px3). The desired end effector motion can be generated by using point-to-point movements of an end effector. This motion includes accelerating of the end effector to a necessary speed and decelerating to a stop. The sudden changes in acceleration or deceleration often create residual vibration. This residual vibration can be increased at the high speed motion because the high acceleration increases the abrupt changes of the end effector movement.
To generate the desired end effector motion precisely without the residual vibration, we fixed the length of the end effector at 16 mm and then carried out calibration by changing a calibration matrix. Generally, the longer the length of the end effector is, the more the vibration is. To suppress the vibration at high speed, it is better to select the length of end effector as short as possible. To generate a precise motion at high speed for formulating model clearly, we tried to suppress vibration less than 1 μm. We tested several lengths of end effector (14, 16, 18, 20, and 22 mm) and finally chose the length at 16 mm because the vibration is lower than 1 μm. As a result, we obtained an end-effector workspace of approximately 80 μm in X- and Z-directions and 10 μm in Y-direction. However, in high-speed motion (1 kHz), the vibration was still generated. To reduce the vibration of the end effector, a low-pass filter composed of an RC circuit was applied. Thus, the vibration at the high frequency of 1 kHz was remarkably reduced from over 5 μm to less than 0.5 μm. In this system, the maximum amplitude is approximately 24 μm in the X- and Z-directions at the maximum frequency (1 kHz).
Circular motion of the end effector
To analyze the rotational flow in 3D space, generation of circular motion is mandatory. Using the parallel link, circular motions with different amplitudes and frequencies can be created. The circular motion is designed by the combination of a sine function in the X-direction and a cosine function in the Z-direction. The motion consists of ten steps to make this motion as close as possible to a circular shape. The maximum frequency of the circular motion is 100 Hz because the number of steps is ten and the maximum frequency of the end effector during a step is 1 kHz. After generating 2D circular motion, we observed the end-effector’s motion in the XZ plane through a microscope (Hirox, CX-10C) with a objective lens (OL-140). The experimental setup for observing the circular motion in the XZ plane is shown in Fig. 3.
The motions of the end effector with different parameters were observed. To compare the swirl flow according to amplitude of the end effector, we applied several amplitudes (12, 15, and 21 μm) by holding the frequency constant. We also changed the frequencies from 100 Hz (maximum frequency) to 10 Hz. Figure 4 shows the high-speed motions of the end effector (100 Hz) in different amplitudes captured by a high-speed camera. From these figures, we can see the circular shape with different diameters. From the observed images, we can verify that the concise parallel link is a suitable tool for creating 2D circular motion.
The motions of the end effector with different parameters were observed. To compare the rotational flow according to amplitude of the end effector, we applied several amplitudes (12, 15, and 21 μm) by holding the frequency constant. We also changed the frequencies from 100 Hz (maximum frequency) to 10 Hz. Figure 4 shows the high-speed motions of the end effector (100 Hz) in different amplitudes captured by a high-speed camera. From these figures, we can see the circular shape with different diameters. From the observed images, we can verify that the concise parallel link is a suitable tool for creating 2D circular motion.
Experimental setup for analyzing rotational flow
In this section, the experimental setup for analyzing the rotational flow is described. To verify that the circular motion can generate rotational flow around the end effector, the experiment was conducted using 9.6-μm microbeads in water. By using 9.6-μm microbeads, we can extend this research to the cell manipulation in the future. The experimental setup is shown in Fig. 5. The water stream was observed by a microscope (IX71) with a 10× objective lens that provided a visual space of 512 μm × 512 μm. A high-speed camera that can capture images at 2000 frames per second was applied for tracking the microbeads at high speed. The density and dynamic viscosity of water are 998.2 kg/m3 and 1.003 × 10−3 kg/m s, respectively, at 20 °C [32]. The experiments were executed 250 μm above the substrate.
First, we applied several frequencies (100, 77, 50, 40, 33, and 10 Hz) at a fixed amplitude (21 μm) in order to determine the range of frequencies that can generate a rotational stream. At frequencies lower than 50 Hz, the rotational flow was not observed. On the other hand, when the frequency of the circular motion was 50 Hz or more, the rotational flow was detected despite the same amplitude of the circular motion. The water flow when the end-effector was rotating in a circle at a frequency of 100 Hz is shown in Fig. 6. The images were captured every 0.028 s. A microbead is tracked and the path of the object is shown. As shown in Fig. 6, the microbead is rotating around the end-effector as well as moving toward the root of the end-effector. From the experimental result, we found that the circular motion of the glass needle generates the rotational stream in three dimensions and the low frequency (less than 50 Hz) of the circular motion cannot create the rotational flow. Thus, we utilized three frequencies (50, 77, and 100 Hz) for the experiments. Supplementary video (Additional file 1) shows the rotational flow by the circular motion with three frequencies and amplitudes. From this movie, we can verify that the circular motion of the end effector makes the rotational flow that can control microobjects.
Rotational flow by circular motion
In the previous section, we observed the rotational stream by the circular motion when the frequency was 50 Hz or higher. In addition, the microbeads rotated by the circular motion were not only rotated around the end effector but also moved to the root of the end effector. As a result, the rotational flow can be analyzed by two relationships: the relationship between the angular velocity and the distance from the center of the end effector’s motion, and the relationship between the velocity toward the root of the end effector and the distance from the center of the end effector’s motion.
Figure 7a shows the measurement method of the rotational stream in 3D space. In Fig. 7b, the blue circle indicates the initial position of the microbead and the red circle shows the position of the microbead after one turn (after 0.16 s). Positions in the X-direction of the two circles are almost on the same axis, and the Y-direction is changed. In addition, the distances from the center of the circular motion (\(r_1\) and \(r_2\)) are the same. From this trajectory of the microbead, we can verify the relationship between the flow velocity in three dimensions and the radius of the flow (Fig. 7a). The angular velocities and the velocities toward the root of the end effector can be calculated by the movements of the 9.6-μm microbeads and the time it takes for the object to traverse half a revolution. To be specific, we computed the radius of rotation described in Fig. 7 (\(r_1\) and \(r_2\)) using the movement of the object in the X-direction after a half-turn. The angular velocity and the velocity toward the root of the end effector were calculated by the time it takes for the microbead to make a half-turn and the moving distance in the Y-direction, respectively. Experiments were conducted by changing the frequency and the amplitude of the end effector. In this experiment, we utilized a cone shape of a glass needle. Generally, the thicker the end effector is, the faster the velocity is [26]. Thus, to minimize this influence, we selected a specific region having similar diameter from 8 to 12 μm. The trapped region in Fig. 7b shows the selected region. It is approximately from 80 to 250 μm from needle tip.