This paper presents a release method for micro-objects. To improve position accuracy after release, we propose 3D high-speed end-effector motions. The classical release task focuses on the detachment of a micro-object from an end-effector. The technique utilizes merely the vibration of the end-effector regardless of the pattern of movement. To release different sizes of micro- objects and place them precisely at the desired locations in both air and liquid media, in this paper, we propose high-speed motions by analyzing the adhesion force and movement of micro-objects after separation. To generate high end-effector acceleration, many researchers have applied simple vibration by using an additional actuator. However, in our research, 3D high-speed motion with apt amplitude is accomplished by using only a compact parallel mechanism. To verify the advantages of the proposed motion, we compare five motions, 1D motions (in X-, Y-, and Z-directions) and circular motions (clockwise and counterclockwise directions), by changing the frequency and amplitude of the end-effector. Experiments are conducted with different sizes of microbeads and NIH3T3 cells. From these experiments, we conclude that a counterclockwise circular motion can release the objects precisely in air, while 1D motion in the Y direction and two circular motions can detach the objects at the desired positions after release in a liquid environment.
Manipulation of micro-scale objects is important for diverse applications in industrial, biological, and biomedical research such as in the assembly of biological cells for tissue engineering, development of sensing devices, and micro-surgical systems. In micromanipulation, the adhesion force between an end-effector and a micro-object is significantly different from macro manipulation, which is influenced by the gravitational force. The adhesion force includes van der Waals, electrostatic, capillary, and surface tension forces. These forces make it easy to pick up and transport an object, whereas the release of a micro-object is more difficult.
Diverse methods have been studied in order to release and place micro-scale objects precisely. The release methods can be classified into two strategies: passive release and active release [
On the other hand, active release methods apply external forces to detach micro-objects from an end-effector without making contact with the substrate. These methods reduce the adhesion force by using pressure changes (vacuum tools) [
In this paper, we propose an active release technique using high-speed end- effector motions controlled by a parallel mechanism. The purpose of this research is the release of micro-objects at the desired positions with high placement accuracy by comparing several end-effector motions. Previous dynamic release studies utilized additional mechanisms to generate sufficient acceleration. However, we present a parallel-link mechanism with three degrees of freedom actuated by three PZT actuators. Using this parallel mechanism, 3D end-effector motion at high speed is feasible. Previous experiments using this mechanism from [
The following section describes the release strategy for precise placement. In the third section, an experimental system for releasing micro-objects is explained. The last section presents experimental results by comparing several high-speed motions in different environments. The results show that the proposed motions of the end-effector can release micro-objects at the desired positions with high placement accuracy.
In micromanipulation, the most difficult problem is probably caused by the adhesion effect. To overcome the adhesion phenomenon, the van der Waals, capillary, and electrostatic forces should be taken into account [
F e x t = m p a > 3 2 π R b γ b p (1)
F e x t in (1) from the end-effector should be made larger than the pull-off force by applying the Johnson Kendall Roberts (JKR) contact model for overbalancing the adhesion force between an end-effector and a micro-object [
The computation of the external force ( F e x t ) is dependent on the movement of the end-effector. When the acceleration of the end-effector (a) is high enough, the object can be separated from the end-effector. However, to release the object at a suitable position with small landing area, the control of the release motion is necessary because a large amount of external force cannot guarantee position accuracy after separation [
end-effector and a target object, respectively. Based on the assumed parameters, the pull-off forces are calculated to be 2.03 × 10−5 N in air and 5.37 × 10−6 N in water.
To verify the successful release and precise positioning of an object when using the proposed motions, five motions, including circular motions (clockwise and counterclockwise) and 1D motions (X, Y, and Z) were compared.
One of the important considerations in releasing an adhered object on the planned position is to reduce the velocity of the object before it reaches the substrate. In a micro-scale environment, although the inertial forces from the end- effector’s motion are very small, the accelerations of micro-objects are usually very high. Subsequently, the velocity of the object is able to increase in a very short time and the trajectory of the object could be difficult to control. Finally, the object can jump rapidly out of the visible area. The attachment position between the end-effector and the micro-object are also vital factors for the trajectory of the object after separation. The high-speed camera provides the position of the target object and end-effectors; however, 3D position information, including Z-position, is generally difficult to acquire in a micro-environment. For
this reason, objects can be adhered to an end-effector in several patterns as shown in
To compare the velocity of the released object, we calculate the acceleration of the end-effector according to the motions. 1D motions that can be composed of the sinusoidal curve generate an acceleration which is directly proportional to the displacement in opposing direction. On the other hand, circular motions create a constant speed by changing the direction, which means that the object is accelerating (centripetal acceleration). However, since the initial speed of the motion is zero, we should consider the tangential acceleration and centripetal acceleration together until the desired speed is reached. In this section, the main assumption in order to compare two motions is that the maximum velocity and increased time to maximum velocity of two motions are same. In addition, the amplitude (A) and the angular velocity ( ω n ) of two motions are equal. Accelerations of the 1D motion and the circular motion can be calculated by Equations ((2) and (3)), respectively. A indicates the amplitude and ω n is the angular velocity of the end-effector’s motion. According to Equation (2), when the displacement is maximum, the acceleration is maximum. Moreover, the maximum acceleration of the 1D motion is same as the centripetal acceleration of the circular motion calculated by Equation (3) if t > t 1 . The acceleration of circular motions can be divided by the time ( t 1 ) when the end-effector reaches the maximum velocity. The angular velocity is varied from 0 to ω n until t 1 , so it relies on the time (t). After t 1 , the angular velocity is fixed as ω 2 because the end-effector makes a uniform circular motion. To estimate the acceleration of two different motions, we assume several parameters. For example, f n is assumed to be 100 Hz and A is assumed to be 3 μm. Thus, the maximum velocity and the time to reach the maximum velocity of the 1D motion are calculated to be 1.9 × 10−3 m/s and 5 ms, respectively. Applying these values, we can compute the acceleration of the circular motion until the time t 1 . At that time, the end- effector accelerates to the desired speed (1.9 × 10−3 m/s) and θ is changed from 0˚ to 180˚ in the time interval of 5 ms ( t 1 ). Thus, the tangential acceleration and centripetal acceleration of the circular motion when t1 are calculated to be 0.38 m/s2 and 1.18 m/s2, respectively. After t 1 , the uniform circular motion can be formed, as a result, the centrifugal acceleration of the circular motion and the maximum acceleration of the 1D motion are calculated to be 1.18 m/s2. The external forces ( F e x t ) also can be computed by using Equation (1). m p is assumed to be 2.4 × 10−5 kg. Therefore, the external force of the circular motion is 2.98 × 10−5 N when t 1 and 2.84 × 10−5 N after t 1 , whereas, the force of the 1D motion is constantly changed from 0N to 2.84 × 10−5 N. As a result, the maximum force of the 1D motion is identical with the force of the uniform circular motion.
a 1 = ω 1 2 x (2)
where, x = A sin ( ω 1 t ) , ω 1 = 2 π f 1
a 2 = { ( θ ¨ A ) 2 + ( θ ˙ 2 A ) 2 , t ≤ t 1 ω 2 2 A , t > t 1 (3)
where, ω 2 = 2 π f 2
From estimated values, we can assume trajectories of the released object by two types of motions. Not only to detach the object from the end-effector, but also to reduce the velocity of the object after release, the minimum amount of forces should be applied. In case of the 1D motion, when the end-effector reaches the maximum displacement, the maximum force is applied and then the object will be released. On the other hand, the circular motion produces the same amount of forces before t 1 , thus the object will be released at that time. Obviously, the magnitude of the exerted force of the two motions when the object is released is same as mentioned above. However, the velocity of the object after release can be guessed by considering the direction of applied forces. The force of the 1D motion is exerted on the adhered object in the same direction as the end-effector’s motion, so the object will be released in the same direction of the motion. In contrast, an object adhered to the end-effector that moves in a circular path experiences the centrifugal force directed toward the center of the circular motion and the tangential force. If the object is released, the centrifugal force will be vanished. Subsequently, the object will travel in the tangential direction with a constant speed. Thus, the force for release of the object is slightly reduced, which makes the objects travel shorter distance than the 1D motion.
In addition, the circular motion can release object into the small region in spite of the different contact position. For instance, in case of the 1D motion in the X-direction, when the object adhered to the center part like
Based on the applied force and the direction of the motion, we can estimate the movement of the object after release. 1D motion in the X-direction makes an object move in a straight line in the X-direction, therefore, the object travels with further displacement than the proposed motions and may even be located outside of the workspace. The object released by the 1D motion in Y-direction could be not only dropped into the substrate but also moved in the Y-direction with high velocity. Finally, the object also travels a long distance. The object manipulated by 1D motion in Z-direction could be released in a straight line in the Z-direction and be finally located at the nearest position. However, the object can reach the substrate having high velocity due to the high acceleration and then the object can sometime bump into the substrate rapidly. In contrast, circular motion creates an arc trajectory for an object. As an object moves in circular motion, it constantly changes its direction. After the object is released, it moves in a straight line at constant speed, tangent to the circle at the point where the object is located. Subsequently, the object moves in a parabolic path after release, causing the object to reach the substrate at a lower velocity than the former motions.
In this paper, we conduct the release task in air and liquid media together. F d in Equation (4) indicates the drag force of the fluid on a sphere. μ represents the dynamic viscosity of the medium (air: 1.85 × 10−5, water: 1 × 10−3 Pa⋅s) and V is the relative velocity of the fluid with respect to the object.
F d = − 6 π μ R b V (4)
The drag force is able to reduce the velocity of the object to be applied in the opposite direction. In water, the dynamic viscosity has a stronger influence on the drag force of the fluid than in air. As the result, an object in water will be located at a closer position than in air in spite of the same external forces thanks to the high drag forces [
In this system, a two-fingered micro-hand was utilized for grasping, transporting, and releasing objects. The micro-hand is displayed in
(Dell, XPS600, Pentium 4 at 3.80 GHz) and a Windows PC (Intel Core i7 CPU at 2.93 GHz with 4 GB of RAM). The Linux PC was in charge of manipulating the micro-hand. The motion of the micro-hand was composed by two parts: a global motion and a local motion. The global motion handled the movement of both end-effectors for transporting target objects and positioning the micro-hand. Two motorized stages, a rough stage (Sigma-Koki, TSD-805S) and a fine stage (Sigma-Koki, SFS-H60XYZ), made the micro-hand move in a large workspace with precision positioning. The rough stage actuated by three DC motors was controlled by a stage controller (Sigma-Koki, OMEC-4BG). On the other hand, the fine stage driven by piezo actuators was managed by a controller (Sigma- Koki, Fine-503).
Local motion manipulated the right end-effector controlled by a compact parallel link for grasping and releasing variously sized objects. The displacements of three PZT actuators (NEC TOKIN, AE0203D16) determined the 3D position of the right end-effector through a D/A board (Contec DA16-16(LPCI)L) and an amplifier (MATSUSADA, HJPZ-0.15Px3). For measuring the displacement of the PZT actuators, strain gages were implemented. In addition, the measured outcomes were transferred to the Linux PC through an amplifier (Kyowa MCD- 16A) and A/D converter (Contec AD16-16(PCI)EV). One adjustment stage, operated manually for adjusting the right end-effector with respect to the local motion, moved 6 mm in a 3D direction with a resolution of 3 μm. To realize a large distance between the two end-effectors for grasping tasks, the manual stage was necessary. The two end-effectors of the micro-hand and the target objects were observed under an IX81 motorized inverted optical microscope using an objective lens. The Windows PC displayed the images of the two end-effectors and objects captured by the high-speed camera (Photron FASTCAM MC2). Two fine-tipped glass needles, having a 23-mm length, 1-mm diameter, and tips with less than 1-μm curvature, were mounted in the micro-hand at the end of the parallel link. The structure of two-fingered micro-hand is shown in
In order to detach diverse sizes of objects from the end-effector at the desired locations, the 3D high-speed motions without uncontrollable vibration were applied by using a parallel mechanism. The parallel manipulator was stiffer, faster, and more accurate than the serial mechanism. Therefore, we utilized the parallel mechanism to achieve 3D high-speed motions with precise positioning. The concise parallel link was a modified version of a previous structure [
To analyze the workspace of the parallel mechanism, inverse kinematics and structural analysis are utilized. In inverse kinematics of the mechanism, the length of piezo actuators ( h 1 , h 2 , and h 3 ) can be solved from a position of the end-effector P e ( P e x , P e y , and P e z ). The proposed mechanism in the plane defined by p and the axis of the revolute joint located a distance h 3 is displayed in
P e x = ( E y + L e ) sin α (5)
P e y = h 3 + { p + q + ( E y + L e ) cos α } cos θ (6)
P e z = { p + q + ( E y + L e ) cos α } sin θ (7)
In this equation, we set L e to an extension of E z . Based on
E y sin α + E x cos α + L 3 cos θ 3 + L 4 = B x (8)
p + q + E y cos α = E x sin α + L 3 sin θ 3 + L 5 (9)
With all of the above results, Equations ((5) and (6)), it is possible to find the length of the piezo actuator ( h 3 ). The angle α is calculated by Equation (5), and the angle θ 3 is obtained by substituting α into Equation (8). p and θ are calculated by Equations ((9) and (7)), respectively. Finally, the value of h 3 can be solved by substituting the above parameters into Equation (6).
To solve h 1 and h 2 , we concentrate on two polygons, divided by the p in
L 1 cos θ 1 + E z cos θ / 2 = B z / 2 + p sin θ (10)
h 1 + L 1 sin θ 1 = h 3 + p cos θ + E z sin θ / 2 (11)
L 2 cos θ 2 + E z cos θ + p c o s θ = B z / 2 (12)
h 2 + L 2 sin θ 2 + E z sin θ = h 3 + p cos θ (13)
To find h 1 , h 2 and h 3 , the angles θ 1 , θ 2 , and θ 3 are computed by using Equations ((10), (12), and (8)), respectively.
θ 1 = cos − 1 ( ( B z / 2 + p sin θ − E z cos θ / 2 ) / L 1 ) (14)
θ 2 = cos − 1 ( ( B z / 2 − p sin θ − E z cos θ / 2 ) / L 2 ) (15)
θ 3 = cos − 1 ( ( B x − L 4 − E y sin α − E x cos α ) / L 3 ) (16)
Finally, the value of h 1 , h 2 and h 3 can be found in terms of P e . With all of the calculated results, we find the piezo actuators values in the parallel link.
Based on the above calculations, we get the axial displacement of the workspace. To be specific, the displacement in X-direction is 128 μm (−64 ~ 64 μm) and in Y-direction is 17 μm (0 ~ 17 μm). In the Z-direction, the end-effector can move 110 μm (−55 ~ 55 μm).
To control the movement of the right end-effector precisely, the relationship between the parallel link extension using the strain gages and the positional change of the end-effector using the camera was investigated. The 3D position of the right end-effector managed by the piezo-actuated parallel link was influenced by the length of the end-effector. Thus, at first, we set the length of the end-effector to 16 mm and subsequently performed calibration by obtaining a calibration matrix calculated by the linear relationship between the displacement of the PZT actuators and the positional change of the end-effector in three directions. Finally, we set the displacement of the end-effector to about 80 μm in the X- and Z-directions and 10 μm in the Y-direction. In our system, the displacement of the Y-axis was smaller than in the other directions owing to the mechanism; the movement in the Y-direction was determined by the length of the PZT actuators because it was generated by moving the three piezo actuators,
which could stretch to 10.7 μm simultaneously.
To generate enough force to separate the micro-objects, high-speed motions of the end-effector at high frequency (about 1 kHz) and amplitude were required. The control scheme for the parallel link is shown in
Using this parallel link, we generated five types of high-speed motions
This experiment aimed to release micro-objects at the desired positions using a right end-effector controlled by a parallel link mechanism. For this experiment, 10-, 25-, and 55-μm microbeads and NIH3T3 cells (16 ± 2 μm) were utilized as the target objects. According to the sizes of the objects, different sizes of lens were used. For the 55-μm microbeads, a 10× objective lens was used, allowing a visible space of 512 μm × 512 μm. 25-μm microbeads and biological cells were utilized with a 20× objective lens, allowing a visible space of 256 μm × 256 μm. On the other hand, for the 10-μm microbeads, a 40× objective lens was applied, providing a visual space of 128 μm × 128 μm.
A high-speed camera capable of capturing images at 2000 frames per second to visualize the high-speed motion was applied. Because the maximum frequency of a step in the motions studied was 1 kHz, in order to capture images that identify the direction and the speed of the objects, a high-speed camera that could capture images at over 1000 frames per second was necessary. The release experiments were performed at 20 μm above the substrate to avoid being affected by the motions of the end-effector. Each motion was repeated 8 times, and the performance duration for each motion was 100 ms. Room temperature was set to 24 ˚C. The experiment was performed in different environments; for example, with 55-μm microbeads in air, 10-, 25-, 55-μm microbeads in water, and 16-μm NIH3T3 cells in phosphate-buffered saline (PBS).
According to the sizes of objects and the environment, the range of frequency and amplitude of the end-effector that could release the adhered object was different. To determine the possible frequency and amplitude of the end-effector for release in different environments and different object sizes, the maximum frequency was applied to adhered micro-objects by changing the amplitudes of the end-effector; then, lower frequencies were tested using the same values of amplitude. If the release of microbeads was not achieved or if the object moved outside of the visible area every time, these cases were excluded from the experiment. The ranges of amplitudes and frequencies for the end-effector using circular motions according for different objects in different environments under the proposed conditions are shown in
Specifically, at first, experiments using 55-μm microbeads in air were performed at the maximum frequency (100 Hz). As a result, when the amplitude of the end-effector was smaller than 4 μm, objects did not detach from the end-effector. On the other hand, when the amplitude was larger than 9 μm, objects flew outside of the visible space. Thus, we decided that the useful range of the amplitude of the end-effector was from 4 μm to 9 μm except for 1D motion in the Y-direction. Thereafter, we applied this range of amplitudes at different frequencies (50, 25, 20, and 10 Hz). If the objects were released successfully at the same conditions, the frequency was selected. Finally, we determined that the frequencies of the motions were 50 Hz and 100 Hz. However, in the case of 1D motion in the Y-direction, only two amplitudes (1.2 μm and 2.4 μm) were applied because the maximum movement of the end-effector in the Y direction was 2.4 μm at 100 Hz.
In order to compare the release conditions between air and liquid environments, the same range of amplitudes (4 ~ 9 μm) and frequencies (50 Hz and 100 Hz) in air were applied in the liquid environment. In the liquid environment, the objects were always located in the visible area (in contrast with the case in air); on the other hand, the adhered objects could detach from the end-effector when the amplitude or frequency were too low. For instance, 55-μm microbeads in water detached from the end-effector under the same conditions (amplitudes and frequencies) as in the air environment. However, 10- and 25-μm microbeads
Medium | Target Object | Frequency | Amplitude |
---|---|---|---|
Air | 55 μm microbeads | 50, 100 Hz | 4 ∼ 9 μm |
Water | 55 μm microbeads | 50, 100 Hz | 4 ∼ 9 μm |
25 μm microbeads | 50, 100 Hz | 4.8 ∼ 9 μm | |
10 μm microbeads | 100 Hz | 4.8 ∼ 9 μm | |
PBS | NIH3T3 cells | 100 Hz | 4.8 ∼ 9 μm |
and 16-μm NIH3T3 cells were not released from the end-effector when the amplitude was lower than 4.8 μm at 100 Hz, and even 10-μm microbeads and 16-μm cells could not be detached when the frequency was 50 Hz and the amplitudes were from 4.8 μm to 9 μm. From the results in water, it can be seen that, when the size of the microbeads is smaller, the required external forces calculated by the frequency and the amplitude of the end-effector in Equations ((2) and (3)) for release are larger.
Experiments were conducted in different environments such as air, water, and PBS. First of all, the results of release in air are analyzed. In the environment of air, objects can sometimes move rapidly; as a result, objects can become located outside of the visible area. If microbeads (55-μm) after release moved inside of the visible area (512 μm × 512 μm), the release task was judged as a success; in the opposite case, the task was considered as a failure.
To analyze the results of release tasks in terms of placement accuracy, the position change after release was measured. Each motion was repeated eight times for statistical analysis. To compare every motion, the mean value and standard deviation of the displacement of the microbeads of the eight repeated motions were computed. Figures 9(a)-(c) show the results of the experiments. The bars indicate the mean value and the error bars express the standard deviation. 1D motion in the Y-direction was included in the smallest value of each motion because the maximum values of the amplitude of the end-effector in the Y-axis (1.2 μm in air and 2.4 μm in liquid) were smaller than the smallest values for other motions.
Motion | Amplitude | ||||||
---|---|---|---|---|---|---|---|
1.2 μm | 2.4 μm | 4 μm | 4.8 μm | 6 μm | 9 μm | ||
50 Hz | X-axis | 81 % | 73 % | 72 % | 36 % | ||
Y-axis | 100 % | 59 % | |||||
100 Hz | X-axis | 73 % | 61 % | 57 % | 35 % | ||
Y-axis | 100 % | 0 % |
The position change values of the microbeads for motions in air when the frequency was 100 Hz are shown in
The results of the release task in water are investigated. The same size of microbeads (55-μm) was utilized for analyzing the relationship between the environments of air and water. In this case, the microbeads after release were always placed in the visible area; consequently, the success rate was 100%.
NIH3T3 cells in PBS were utilized to verify the precise release of the proposed motions.
the objects released by the CW motion were placed on the left side of the desired position, while it the objects detached by the CCW motion were not located on the fixed position. In addition, in the case of clockwise circular motion, small amplitude of the end-effector can guarantee more precise positioning, which is different from the case for other motions.
Based on the previous experimental data in different environments (air, water, and PBS), the proposed motions that can improve placement precision after release are verified. To analyze the results of the experiments, at first, different frequencies and amplitudes of the end-effector were examined to ascertain whether release was achieved or not. Then, five motions were applied in order to compare the position accuracy after release. As a result, several outcomes can be obtained.
First, micro-objects in air are located within a larger space than in liquid. To be specific, the objects in air are positioned over 50 μm from the initial position and are not even located in visible areas, whereas the values of the position change of objects in liquid are less than 50 μm. This outcome agrees with the former assumption that the hydrodynamic force in water is stronger than in air owing to the higher dynamic viscosity in the former medium, which hinders the object from moving quickly a short time after separation; finally, the object in water will be located at a closer position than in air.
Second, in every environment, we can find the relationship between the amplitude and the position accuracy: the smaller the amplitude, the better the placement accuracy achieved. This result verified that the external force decided by the amplitude and frequency of the end-effector in Equations (1)-(3) increases with the increase of amplitude. Consequently, the minimum amplitude that is able to detach objects from the end-effector can release micro-objects with high position accuracy.
Finally, for different environments, active release motions with high position accuracy are different. In the case of air, counterclockwise circular motions can release microbeads at the nearest position from the initial position. In the case of water, 1D motion in the Y-direction and circular motions can detach microbeads with small position changes. Lastly, 1D motion in the Y-direction and clockwise circular motions can separate NIH3T3 cells precisely. In the second section, we proposed these motions by analyzing the movement of objects after release. From these experimental results, we verified the assumption that the proposed motions can release and place objects precisely.
To release micro-objects with high position accuracy, a release method using dynamic motions was proposed. This release method was applied for different sizes of objects and different environments (air, water, and PBS). To release micro-objects, the status of a micro-object after release was analyzed in two different environments (air and liquid media). From the analyses, circular motion for the air environment, and circular motion and 1D motion in the Y-direction for the liquid environment are proposed for improving placement accuracy. To verify the efficiency of the proposed motions, five motions, including 1D motion in the X-, Y-, and Z-directions and circular motion (CW, CCW) were applied by comparing the position change after the release of 10-, 25-, and 55-μm microbeads and NIH3T3 cells; we then applied statistical methods. As the result, we verified the fact that the proposed motions can release objects at suitable positions with high position accuracy. In the future, we will extend this approach to the automatic system that can release objects on the precise position.
This work was partially supported by the Grant-in-Aid for Scientific Research (A) (JP16H02321), Grant-in-Aid for Young Scientists (A) (JP16H06076) from the Ministry of Education, Culture, Sports, Science and Technology of Japan.
Kim, E., Kojima, M., Kamiyama, K., Horade, M., Mae, Y. and Arai, T. (2018) High-Speed Active Release End-Effector Motions for Precise Positioning of Adhered Micro-Objects. World Journal of Engineering and Technology, 6, 81-103. https://doi.org/10.4236/wjet.2018.61005