Proceedings of the 1st IEEE International Conference on Nano/Micro Engineered and Molecular Systems January 18 - 21, 2006, Zhuhai, China
Mechanical Design of Compliant Parallel Micromanipulators for Nano Scale Manipulation Qingsong Xu and Yangmin Li∗ Dept. of Electromechanical Engineering, Faculty of Science and Technology, University of Macau Av. Padre Tom´as Pereira S.J., Taipa, Macao SAR, P. R. China E-mail: {ya47401|ymli}@umac.mo nanopositioners with ultra-high precision are in great demands for nano scale manipulation. In the mechanism community, it is well known that parallel manipulators possess inherent advantages over their serial counterparts in terms of high rigidity, high load carrying capacity, high velocity, and high precision, etc [6]. However, as with any mechanical systems composed of conventional joints, traditional parallel manipulators suffer from errors due to backlash, hysteresis, and manufacturing errors in the joints. Thus, it is a major challenge to achieve ultra-high precision using conventional joints. Whereas compliant mechanisms, i.e., flexure hinge-based mechanisms, can be employed into parallel manipulators for ultra-high precision applications thanks to their outstanding characteristics including vacuum compatibility, no backlash property, no nonlinear friction, and ease of manufacture, etc [7]. Such a parallel manipulator integrating compliant hinges in all joints is termed a compliant parallel micromanipulator (CPM) in the current paper. In the literature, a lot of CPMs have been separately presented to perform the manipulation in micro/nano meter scales with high accuracy, speed, and load capacity [8], [9]. The objective of this paper is to propose the mechanical design considerations in developing an ultrahigh precision CPM for nano scale manipulation. And as an example, the architecture of a new CPM is presented and its versatile configurations for applications are provided as well.
Abstract— As the rapid growing of a wide variety of research and development activities on nanotechnoloty, ultra-high precision nanoposioners are greatly required for nano scale manipulation. In this paper, the design issues of a compliant parallel micromanipulator (CPM) for nanomanipulation is presented from the mechanical design point of view. A CPM is an integration of parallel and compliant mechanisms, the design considerations of which in terms of flexure joints, actuators, materials and fabrications, even modeling methods are proposed, and as an example, a new type of CPM is designed and its applications are presented for nano scale manipulation. The design guidelines outlined in this paper will be valuable for the development of CPMs applicable to nanomanipulation. Index Terms— compliant mechanisms; parallel manipulators; nanomanipulation
I. I NTRODUCTION In recent years, the research and development activities surrounding nanotechnology have been growing explosively worldwide particularly since the discovery of carbon nanotubes (CNTs) with remarkable electrical and mechanical properties [1], which have been shown to be one of the most promising nanomaterials for versatile applications [2]. Nanomachines are devices capable of performing specific functions that are in the size of nanometers built from individual atoms. It is believed that nanodevices will one day be used as assemblers in the construction of new materials and objects from inside out, which also offer humanity with the potential to eliminate poverty, pollution, and disease in the future [3]. One possible approach to develop nanodevices involves the precise manipulation and control of atoms and molecules to create novel structures with remarkable properties. This influential technology requires a new field termed nanomanipulation to deal with how to handle components and structures in nanometer scale [4], [5] by utilizing devices with high positioning accuracy and dexterous motion of the end-effector and controlling external forces with sensory feedback, which has been enabled by the invention of scanning tunneling microscopes (STMs), atomic force microscopes (AFMs), and other types of scanning probe microscopes (SPMs). Therefore,
II. M ECHANICAL D ESIGN RULES
CPM
A CPM relies on the elastic deformation of flexible joints to carry out mechanical tasks of transferring and transforming energy, force, and motion. Generally, exact solutions of compliant mechanisms involve complex elliptic integral solutions, which make the design problems tremendously difficult. On the contrary, the pseudo-rigid-body (PRB) model can facilitate the design of compliant mechanisms intensively [7], since the PRB model allows compliant mechanisms to be modeled as equivalent rigid-link mechanisms and enables the use of traditional mechanism analysis approaches to design compliant mechanisms especially in the initial design stage. Once a CPM is designed, a detailed finite element analysis can be performed or a prototype can be fabricated for testing [10]. Concerning the geometry of a CPM, a symmetric architecture is preferred since it can reduce the effect of temperature gradient and disturbance on the structure. In addition, the
This work was supported by the Research Committee of University of Macau under Grant RG083/04-05S/LYM/FST and Macao Science and Technology Development Fund under Grant 069/2005/A. ∗ Contact author. phone: +853 3974464; fax: +853 838314; e-mail:
[email protected].
1-4244-0140-2/06/$20.00 ©2006 IEEE
OF A
653
(a)
(b) Fig. 1.
(a)
(b) Fig. 2.
(c)
(a)
(b)
Compliant prismatic joints.
(c)
Fig. 3.
(d)
(a)
Compliant revolute joints.
(d)
Compliant universal joints.
(b) Fig. 4.
CPM should be designed to have high stiffness and high natural frequency so as to ensure the well static and dynamic characteristics. Other design considerations are presented as follows.
(c)
(c)
Compliant spherical joints.
other three types have no such problems. However, the first compliant U joint (Fig. 3(a)) is a little difficult to manufacture, and the third type (Fig. 3(c)) does not possess a compact architecture. Thus, the fourth one (Fig. 3(d)) appears to be an ideal alternative, which can also protect the R joints from over bent. The compliant spherical (S) joints with 3-DOF are shown in Fig. 4, where the first type is commonly utilized although it is not strong and not easy to manufacture. The second one is used for its large displacement, although it has a weakness of poor accuracy. In fact, all of the profiles illustrated in Fig. 2 can be adopted as the longitudinal section shapes of the S joints with the corresponding characteristics. The third type of compliant S joints shown in Fig. 4(c) is created by adding another R joint on a compliant U joint described in Fig. 3(d), which has a better stiffness property. Additionally, a new type of compliant R and P joints with large-displacement are proposed in reference [14], and reference [15] presents the flexure hinges integrating several compliant R joints connected in parallel. However, one drawback of these integrated types of compliant joints is their large physical sizes, which may not suitable for the design of a micromanipulator with compact architecture.
A. Compliant Joints 1) 1-DOF Joints: Most of the existing compliant prismatic (P) joints are based upon a parallel four-bar mechanism. Their flexibility is derived from leaf springs or notch joints as illustrated in Figs. 1(a) and 1(b), respectively. Also, the compound four-bar blocks can be used as P joints since they can provide a larger range of straight-line motion. In addition, the compliant P joint shown in Fig. 1(c) is usually adopted into an actuation joint. The compliant revolute (R) joints can also be made from notch and leaf springs, and the profiles of four typical compliant R joints are illustrated in Fig. 2, which stand for the right circular, elliptical, right angle, and corner filleted hinges, respectively. Each style has its advantages and drawbacks. The right circular hinge is the so-called precision-oriented hinge since the motion it provides is quite accurate [11]. Unfortunately, a drawback is the highly localized stress that is experienced upon deflection, thereby limiting its displacement. The elliptical, right angle, and corner filleted hinges are well suitable for large displacement applications [12], [13]. They possess a more favorable stress distribution and allows larger deflections, which however, is as the sacrifice of accuracy. The elliptical profile has an additional drawback of more difficulty to manufacture. 2) Multi-DOF Joints: The usual forms of 2-DOF compliant universal (U) joints made of two perpendicularly arranged R joints are depicted in Fig. 3, where the second one (Fig. 3(b)) has an offset distance between the two R joints, and the
B. Actuators, Materials and Fabrication Piezoelectric (PZT) actuators transfer electrical energy to mechanical energy based upon the property of piezoelectric materials, and PZT actuators are applied more and more widely in precision instruments owning to the well-known advantages they can offer in terms of high accuracy, fast response, and high energy density, etc., which make them much suitable for precision engineering applications. Since most high voltage amplifiers are current limited, the electrical capacitance of
654
w
b1
v
B2
P
B1
u
B3
k1 p
A2
h
C1
C2 y
C3
r
t1
z a1
A1
t
x
O
h
A3 Fig. 5.
A 3-PUU CPM.
Fig. 6.
PRB model of the 3-PUU CPM.
the selected actuator should also be taken into account in selecting a PZT. On the other hand, the major drawback of PZT actuators is their limited stroke. To overcome this limitation, inchworm motors have been proposed [16], which generally consists of three or more PZT actuators mounted within a monolithic frame with its stroke limited only by the length of the guide way. Nevertheless, inchworm motors usually possess a large volume, that restricts their further applications in micro devices. Another efficient approach to enlarge the stroke of PZT actuators once it does not meet the requirement is to use mechanical amplifiers, that are based on the lever mechanism [17]. The elastic deflection limit of the material restricts the mobility of flexure hinges. Because the ratio of yield strength (σy ) to Young’s modulus (E) of the material heavily affects rotary limits of flexure hinges, which partially determine the manipulator workspace, it is necessary to choose materials with high ratio of σy /E in order to achieve a larger workspace. Some materials with high value of σy /E are enumerated in [18]. As far as the fabrication issues are concerned, a CPM is preferred to be manufactured monolithically and therefore avoid assembly errors. The monolithic construction also implies a relatively easy manufacturing process and potentially very compact design, which can be fabricated via a variety of fabrication methods including wire electrical discharge machining (EDM), laser cutting, abrasive water jet cutting, stereo lithography, etc. However, due to the spatial architecture, it is hard to monolithically fabricate many CPMs. Under such cases, the separate parts should be assembled tightly so as to eliminate the relative motion.
Fig. 7.
Parameters of a compliant U joint.
via a microscope, which provides a quite limited field of vision and even a slight rotation of the end-effector will result in the manipulation easily sweeping out of the visual field, the most important motion used in such applications is translational motion. For example, although a dexterous microhand designed in [19] has six DOF, only the translational DOF is utilized in practice. Therefore, a nanopositioner which can provide three DOF translational motion with high precision is greatly required for 3-D nano scale manipulation. In what follows, as an example, a new CPM is designed according to the mechanical design rules outlined above. A. Description and Development of the CPM As shown in Fig. 5, the designed 3-DOF PNP, that employs flexure hinges at all joints, consists of a mobile platform, a fixed base, and three limbs with identical kinematic structure. Each limb connects the fixed base to the mobile platform by one compliant P joint (Fig. 1(c)) and followed by two compliant U joints (Fig. 3(d)) in sequence, where the P joint is fixed at the base and actuated by a PZT actuator. Thus, each limb is a PUU kinematic linkage indeed. It has been shown that a 3-PUU kinematical structure with conventional mechanical joints can be arranged to achieve only translational motions with some certain geometric conditions satisfied [20], i.e., in each kinematic chain, the first revolute (R) joint axis is parallel to the last R joint axis, and the two intermediate R joint axes are parallel to each other. Meeting these conditions, the proposed CPM can provide three translational DOF. Moreover, the CPM is designed to have a symmetric architecture. The compliant P joint shown in Fig. 1(c) is used as the actuation joint, and the adopted compact compliant U joint from Fig. 3(d) consists of two flexure R hinges with right circular profile since its displacement accuracy is the best. To make a compromise between the stroke and resolution, one type of PZT P-239.80 is selected from the Polytec PI, Inc., that has the stoke of 140 μm and resolution of 1.4 nm. The linear actuator of the PNP is implemented with each PZT embedded
III. D ESIGN AND A PPLICATIONS OF A N EW CPM A few of parallel manipulators employing compliant mechanisms have been designed to perform the manipulation in micro/nano meter scales. However, most of the existing micromanipulators can provide only a planar 3-DOF motion, or spatial 3-DOF combined motions of translation and rotation. Since the nanometer-scale manipulation is usually performed
655
in a flexure P hinge as shown in Fig. 5. In view of the elasticity of the material, the titanium alloy Ti-6Al-4V is selected to manufacture the CPM via the EMD fabrication method. B. Kinematic Modeling of the CPM With the mechanism topology identified and each flexure R hinge replaced by a R joint and a torsional spring, the PRB model of the PNP is developed in Fig. 6. For the purpose of analysis, we assign a fixed Cartesian coordinate system O{x, y, z} at the centered point O of the fixed base platform ΔA1 A2 A3 with a circumcircle of radius a, and a moving Cartesian frame P {u, v, w} on the moving platform at the centered point P of triangle ΔB1 B2 B3 with a circumcircle of radius b. For simplification and without the loss of generality, let the x axis and u axis be parallel to one another, −−→ −−→ and the x axis direct along OA1 . Vector OAi (i = 1, 2, 3) is −−→ not necessarily parallel to vector P Bi , and the angle between them is defined as the twist angle θ, i.e., the angle between the mobile platform and the fixed base. The P joints are restricted to move along a direction perpendicular to the base platform so as to obtain a compact architecture. Additionally, in order to generate a symmetric workspace of the manipulator, the twist angle is designed as θ = 0◦ , the three links Ci Bi are designed to possess equal lengths of l, and both the base and mobile platforms are designed into equilateral triangles. Referring to the PRB model shown in Fig. 6, within the ith limb, due to the torsion deformation of the spring with stiffness i , links j and k act on each other by the torsion moment Kjk i i , that is caused by the angular displacement δjk of the of Mjk links and can be expressed as: i i i i i i i0 = Mkj = Kjk δjk = Kjk (θjk − θjk ), Mjk
(a)
(b)
(c) Fig. 8. Applications of a 3-PUU CPM using (a) a single CPM, two CPMs connected (b) in series, and (c) in parallel.
can be solved in closed-forms [22]. For example, referring to Fig. 6, a vector-loop equation can be written for the ith limb: l ki = si − di ti ,
(3)
si = p + bi − ai .
(4)
where
(1)
Then, in view of (3), the inverse kinematics solutions can be derived as follows: di = tTi si − (tTi si )2 − sTi si + l2 . (5)
i can be calculated via the formulation where the stiffness Kjk [21]: 2Eht2.5 , (2) K= 9πr0.5
Furthermore, substituting (4) into (3) and differentiating with respect to time, yields
with E denotes Young’s modulus of the material, and parameters h, t, and r of flexure hinges are depicted in Fig. 7. Let q = [d1 d2 d3 ]T be the vector of the three actuated joint variables. Generally, the position and orientation of the mobile platform with respect to the reference frame can be described by a position vector p = [x y z]T of the reference point P , and a 3×3 rotation matrix R. Since the mobile platform of a 3-PUU parallel manipulator possesses only a translational motion, R becomes an identity matrix. Given the mobile platform position, the objective of the inverse kinematics problem is to solve the actuated values. While given a set of the actuated inputs, the mobile platform position is solved by the forward kinematics. Let ki denote a unit vector along the leg Ci Bi , di represent a linear displacement of the ith actuator, and ti denote the corresponding unit vector pointing along Ai Ci . In addition, −−→ −−→ ai = OAi and bi = P Bi . Using a suitable vector-loop analysis, both the inverse and forward kinematics problems
d˙i ti = p˙ − l ω i × ki ,
(6)
where ω i denotes the vector of angular velocities for link Ci Bi with respect to the fixed frame, and p˙ = [x˙ y˙ z] ˙ T is the vector of linear velocities for the mobile platform. Dot-multiplying both sides of (6) by ki , leads to ˙ kTi ti d˙i = kTi p,
(7)
which can be assembled into the matrix form: ˙ Bq˙ = Ap, where
⎤ ⎡ T⎤ 0 kT1 t1 0 k1 B = ⎣ 0 kT2 t2 0 ⎦ , A = ⎣ kT2 ⎦ , 0 0 kT3 t3 kT3 ⎡
and q˙ = [d˙1 d˙2 d˙3 ]T is the vector of actuated joint rates.
656
(8)
it is reasonable to expect that the CPM could find its way into 3-D nano scale manipulation. The design considerations presented in this paper are helpful in designing various CPMs for nanomanipulation. R EFERENCES
Fig. 9.
[1] S. Iijima, “Helical microtubules of graphitic carbon,” Nature, vol. 354, pp. 56–58, 1991. [2] R. H. Baughman, A. A. Zakhidov, and W. A. de Heer, “Carbon nanotubes—the route toward applications,” Science, vol. 297, pp. 787– 792, 2002. [3] G. S. Chirikjian, K. Kazerounian, and C. Mavroidis, “Analysis and design of protein based nanodevices: Challenges and opportunities in mechanical design,” ASME J. Mech. Des., vol. 127, no. 4, pp. 695–698, 2005. [4] T. Fukuda, F. Arai, and L. Dong, “Assembly of Nanodevices with Carbon Nanotubes through Nanorobotic Manipulations,” Proc. of the IEEE, vol. 91, no. 11, pp. 1803–1818, 2003. [5] M. Sitti, “Survey of Nanomanipulation Systems,” in Proc. of 1st IEEE Conf. on Nanotechnology, 2001, pp. 75–80. [6] J.-P. Merlet, Parallel Robots. London: Kluwer Academic Publishers, 2000. [7] L. L. Howell, Compliant Mechanisms. New York: Wiley, 2001. [8] T. Tanikawa, T. Arai, and N. Koyachi, “Development of small-sized 3 DOF finger module in micro hand for micro manipulation,” in Proc. of IEEE/RSJ Int. Conf. on Intelligent Robots and Systems, 1999, pp. 876–881. [9] Y. Li and Q. Xu, “Design and analysis of a new 3-DOF compliant parallel positioning platform for nanomanipulation,” in Proc. of 5th IEEE Conf. on Nanotechnology, 2005, pp. 126–129. [10] G. K. Ananthasuresh and L. L. Howell, “Mechanical design of compliant microsystems—a perspective and prospects,” ASME J. Mech. Des., vol. 127, no. 4, pp. 736–738, 2005. [11] S. Zhang and E. D. Fasse, “A finite-element-based method to determine the spatial stiffness properties of a notch hinge,” ASME J. Mech. Des., vol. 123, no. 1, pp. 141–147, 2001. [12] S. T. Smith, V. G. Badami, J. S. Dale, and Y. Xu, “Elliptical flexure hinges,” Review of Scientific Instruments, vol. 68, no. 3, pp. 1474–1483, 1997. [13] N. Lobontiu, J. S. N. Paine, E. Garcia, and M. Goldfarb, “Corner-filleted flexure hinges,” ASME J. Mech. Des., vol. 123, no. 3, pp. 346–352, 2001. [14] Y.-M. Moon, B. P. Trease, and S. Kota, “Design of large-displacement compliant joints,” in Proc. of ASME Design Engineering Technical Conf., 2002, DETC2002/MECH-34207. [15] J. Hesselbach, J. Wrege, A. Raatz, and O. Becker, “Aspects on design of high precision parallel robots,” Assembly Automation, vol. 24, no. 1, pp. 49–57, 2004. [16] P. E. Tenzer and R. Ben Mrad, “On amplification in inchworm precision positioners,” Mechatronics, vol. 14, no. 5, pp. 515–531, 2004. [17] J. Yu, S. Bi, G. Zong, and X.-J. Liu, “On the design of compliant-based micro-motion mainpulators with a nanometer range resolution,” in Proc. of IEEE/ASME Int. Conf. on Advanced Intelligent Mechatronics, 2003, pp. 149–154. [18] E. Pernette, S. Henein, I. Magnani, and R. Clavel, “Design of parallel robots in microrobotics,” Robotica, vol. 15, no. 4, pp. 417–420, 1997. [19] T. Tanikawa and T. Arai, “Development of a micro-manipulation system having a two-fingered micro-hand,” IEEE Trans. Robot. Automat., vol. 15, no. 1, pp. 152–162, 1999. [20] R. Di Gregorio and V. Parenti-Castelli, “Mobility analysis of the 3-UPU parallel mechanism assembled for a pure translational motion,” in Proc. of IEEE/ASME Int. Conf. on Advanced Intelligent Mechatronics, 1999, pp. 520–525. [21] J. M. Paros and L. Weisbord, “How to design flexure hinges,” Machine Design, vol. 37, pp. 151–156, 1965. [22] Y. Li and Q. Xu, “Kinematic analysis and dynamic control of a 3-PUU parallel manipulator for cardiopulmonary resuscitation,” in Proc. of 12th Int. Conf. on Advanced Robotics, 2005, pp. 344–351. [23] ——, “Novel Design of a 3-PUU Spatial Compliant Parallel Micromanipulator for Nanomanipulation,” in Proc. of IEEE Int. Conf. on Mechatronics and Automation, 2005, pp. 1575–1580.
An orthogonal 3-PUU CPM.
When the manipulator is away from singularities, in view of (8), we can obtain that
where
˙ q˙ = J p,
(9)
J = B−1 A
(10)
is the Jacobian matrix of a 3-PUU PNP relating output velocities to the actuated joint rates. In addition, the analysis for a traditional 3-PUU translational parallel manipulator involving workspace determination, dexterity evaluation, and architecture optimization, etc., can be applied to the 3-PUU CPM. C. Applications of a 3-PUU CPM The designed 3-PUU CPM can be applied in nano scale manipulation by placing its mobile platform under a specified microscope as an ultra-precision XYZ-stage (Fig. 5), or mounting a suitable end-effector on the mobile platform as shown in Fig. 6(a). Furthermore, in order to enhance the operation dexterity of the end-effector, two 3-PUU CPM can be used in series or in parallel to perform a more complicated task as illustrated in Figs. 6(b) and 6(c), respectively. In addition, the three links of a 3-PUU CPM can also be designed in such an orthogonal way as depicted in Fig. 7, which has been proposed in our previous work [23]. It has been shown that an orthogonal 3-PUU CPM possesses a fairly regular like workspace with a maximum cuboid defined as usable workspace inscribed and one isotropic configuration involved, and the CPM can perform a high dexterous manipulation within the usable workspace. IV. C ONCLUSION The design considerations for a compliant parallel micromanipulator covering the issues of flexure joints, actuators, materials, and fabrication methods are proposed in this paper. In view of the design guidelines, a novel 3-PUU CPM is designed as an example, the architecture of the CPM is presented and its versatile applications are provided as well. Since the designed CPM is composed solely of flexible elements which are known to be competent in high precision applications,
657
