Design of a Partially Decoupled High Precision XYZ Compliant Parallel Micromanipulator

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1 Proceedings of the 3rd IEEE Int. Conf. on Nano/Micro Engineered and Molecular Sstems Januar 6-9, 28, Sana, China Design of a Partiall Decoupled High Precision XYZ Compliant Parallel Micromanipulator Qingsong Xu and Yangmin Li Dept. of Electromechanical Engineering, Facult of Science and Technolog, Universit of Macau Av. Padre Tomás Pereira S.J., Taipa, Macao SAR, P. R. China {a4741 mli}@umac.mo Abstract A newl designed three-degree-of-freedom compliant parallel micromanipulator (CPM) with partiall decoupled characteristics of XYZ translational motion is proposed in this paper. The CPM is driven b the selected pieoelectric actuators (PZTs) whose strokes are amplified b using the amplification lever mechanism. The design procedure of the CPM is presented in detail, and the CPM parasitic motion is studied analticall. Moreover, its motion properties are verified through the finite element analsis conducted with ANSYS software package. The simulation results reveal that the CPM has negligible parasitic rotations and negligible parasitic translation along one direction, and it possesses a good decoupled propert. The CPM is expected to be applied to operate the objects in micro/nano-meter scales with high precision. Limb 1 Mobile platform PZT Limb 3 Kewords flexure hinges; parallel manipulators; decoupled motion; design theor I. INTRODUCTION Recentl, the research and development around the micro/nano technolog have stimulated the activities relating to the design and fabrication of new micromanipulators with ultra-high precision operation [1]. This comes from the reason that the micromanipulators with micro/nano scale accurac offer an alternative approach for the manipulation of micro/nanometer sie components. As an evidence, a great number of micromanipulators have been proposed and investigated in both academ and industr [2] [8]. A surve of the existing micromanipulators reveals that almost all of the manipulators emplo compliant or flexure joints other than the traditional mechanical joints to achieve the ultra-high accurac. Because compliant joints deliver the motion b making use of elastic propert of the material, the constructed manipulators are out of clearance, friction, and backlash properties in consequence, and the are also vacuum compatibilit. In addition, the manipulators are preferred to be designed as parallel kinematic structures so as to further improve the accurac. As is known, parallel mechanism features the important propert that the end-effector is connected to the base b more than one kinematic chain (limb or leg), which This work was supported b the Research Committee of Universit of Macau under Grant RG65/6-7S/LYM/FST and Macao Science and Technolog Development Fund under Grant 69/25/A. Corresponding author: Y. Li is with the Department of Electromechanical Engineering, Facult of Science and Technolog, Universit of Macau, Av. Padre Tomás Pereira S.J., Taipa, Macao SAR, P. R. China (phone: ; fax: ; mli@umac.mo). Fixturing block Fig. 1. Limb 2 The designed XYZ CPM. means that no cumulative errors exist in the end-effector like the case in conventional serial manipulators. Moreover, for a parallel manipulator, it is possible to mount all of the actuators on the base, so that the moving components can be made as light as possible. Hence, parallel manipulators usuall possess a good dnamic propert in terms of high acceleration and fast response, etc. In view of the above merits, compliant parallel manipulators (CPMs) are gaining more and more attentions nowadas [9]. According to the application requirements, various tpes such as XY, XYθ, XYZ, and 6-DOF (degree of freedom) CPMs have been designed and developed. In this paper, we are concentrated on the design of CPM with XYZ motion due to its potential applications in scanning table, bio-cell injector, and nano-positioner, etc. In the literature, man XYZ CPMs have been proposed and investigated. For example, the Delta Cube with three translational DOF was designed for Electro- Discharge Machining (EDM) applications [5]. However, the three DOF of the Delta Cube are coupled, which complicates its control scheme design issue. Besides, an XYZ stage was previousl designed b the authors for the use of nano scale manipulation [1]. Whereas the motion of the stage is also coupled and large parasitic rotations exist in the end-effector (mobile platform). On the other hand, a smart 3-DOF CPM with decoupled kinematic structure has been proposed in [11] /8/$ IEEE. 13

2 b PZT Mobile platform x R joint P joint C joint Actuation direction Fixturing hole x a l l 2 l 1 P joint R joint w t r Fig. 2. Limb parameters of the CPM. q 2 θ d 2 Limb 2 e 2 Fig. 4. Parameters of one actuation prismatic joint. Fig. 3. The adopted PZT actuator with feedback. recentl. Each limb of the CPM is actuall a PPP (prismaticprismatic-prismatic) structure fabricated b assembling three flexure prismatic joints together. Since each limb is not a monolithic architecture, the excessive assembl ma introduce assembl errors which can degrade the CPM accurac. Therefore, it is necessar to design a decoupled CPM with compact structure as monolithic as possible. In the current research, a partiall decoupled compliant parallel manipulator is designed for ultra-high precision applications. The CPM possesses the advantage of partiall decoupled kinematic propert with each limb being a monolithic structure which can be easil fabricated b a piece of material. In what follows, the design procedure of the CPM is presented, and the decoupled characteristics of the CPM are validated via the simulations using the ANSYS software package. II. ARCHITECTURE DESCRIPTION OF THE XYZ CPM The designed CPM is shown in Fig. 1. It emplos flexure hinges at all joints, and consists of a mobile platform, a fixed base, and three limbs with identical kinematic structure. As depicted in Fig. 2, each limb connects the fixed base to the mobile platform in sequence b one flexure prismatic (P) hinge, two flexure revolute (R) hinges, and another passive flexure P joint that is a parallelogram structure consisting of four flexure R hinges. The first P joint within each limb is screwed onto the base through two bolts and actuated b a pieoelectric actuator (PZT). Thus, each limb is actuall a PRRP kinematic linkage. It is observed that the axes of the last R and P joints are parallel to each other, and hence the combined effect of these two joints is similar to a clindrical (C) joint. It follows that the mobile platform can be viewed to be attached to the base b three identical PRC linkages. Regarding an orthogonal 3-PRC parallel manipulator with conventional mechanical joints, it has been shown that such a mechanism can act as a translational parallel manipulator with some certain geometric conditions satisfied [12]: briefl, the axes of the R and C joints within the same limb are parallel to each other. Due to an equivalent kinematic architecture, the proposed CPM possesses three translational DOF as well. Moreover, in order to generate a regular cubic shape workspace of the manipulator, the three limbs are arranged in an orthogonal manner. Mounting a suitable end-effector on the mobile platform or placing the mobile platform under a specified microscope as an XYZ-stage, the CPM can be used in 3-D micro/nano scale positioning manipulation. Concerning the development of the CPM, we select the aluminum allo (Al 775) to fabricate three identical limbs via the wire-edm process, and then assemble the limbs with the mobile platform together. As far as the PZT actuator is concerned, we adopt the PAZ1 (see Fig. 3) with a travel range of 1 μm and a closed-loop resolution of 25 nm from the Thorlabs, Inc. The main parameters of the designed CPM 14

3 1 8 Calculated FEA results Force (N) Fig. 5. Meshed FEM of actuated flexure P joint Displacement (um) Fig. 7. Force-displacement relationship of actuated P joint. 4 Output displacement.1 Output displacement (um) Parasitic displacement (um).5 Parasitic motion Fig. 6. Deflection of the actuated flexure P joint. Fig. 8. Input and output displacement relationship of actuated P joint. are elaborated in Table I. III. PERFORMANCE OF THE AMPLIFICATION PRISMATIC JOINT For the sake of simplification, the pseudo-rigid-bod (PRB) model approach [13] is utilied to facilitate the CPM design. In the PRB model, the CPM is simplified as an equivalent rigid-link mechanism connected b revolute joints with the residence of rotational springs. The prismatic joint with displacement amplification is illustrated in Fig. 4. The theoretical amplification ratio can be TABLE I MAIN PARAMETERS OF THE XYZ CPM Architectural parameters (mm) a b l l 1 l 2 r t w CPM material parameters Young s modulus Yield strength Poisson s ratio 71.7 GPa 53Mpa.33 expressed as: A P = l 1. (1) l 2 B using the amplification mechanism, the stroke of the actuator can be amplified b a factor of A P, whereas the resolution of the actuator will be degraded b A P times as an expense. So, a compromise between the stroke and resolution sies of the PZT needs to be taken for a specified application. Here, we adopt the amplification ratio of A P =4to design the CPM, which results in a workspace sie of μm 3 and a resolution of 1 nm of the CPM in theor. The actuation stiffness of the prismatic joint in its working direction can be calculated as follows. Let the force and displacement created b the PZT be F and q 2, respectivel, which are applied on the input end of the amplification flexure P joint. In addition, assign same dimensions to the five notch hinges of the P joint, then the rotation angles of the hinges around the x-axis (see Fig. 4) are all equal to the same value, namel, θ. Hence, the potential energ of the P joint due to elastic deflections can be expressed b: P p = 1 2 K 2q 2 2 =5 1 2 kθ2 (2) 15

4 d2 β2 Limb 1 l x e 1 e 3 γ 2 a Limb 3 Fig. 9. Parasitic motion of Limbs 1 and 3. where k = 2Ewt2.5 9πr.5 (3) is the rotation stiffness of the right circle flexure hinge around the x-axis [14], and the relationship between the small rotation angle θ and displacement q 2 can be approximatel written as: q 2 = l 2 θ. (4) Substituting (3) and (4) into (2) allows the calculation of the stiffness of the amplification P joint along its working direction: K P = 1Ewt2.5 9πr.5 l2 2. (5) For an amplification P joint with architectural parameters depicted in Table I, the nonlinear statics finite element analsis (FEA) is performed with ANSYS. The finite element model (FEM) of the P joint is created b adopting the 2-node element SOLID186 as illustrated in Fig. 5, and the deformed shape is shown in Fig. 6. Moreover, the force-displacement relationship is plotted in Fig. 7. It can be observed that the simulated and calculated stiffness values are ver close, which validates the accurac of the derived stiffness model in (5). In addition, the relationships between the input and output displacements are shown in Fig. 8. From the plot, one can see that the amplification ratio of the flexure P joint is about 3.84, which is less than the theoretical value A P =4. This comes from the reason that the elements other than notch hinges are not full rigid bodies. Besides, the actuation P joint introduces a parasitic translational motion along the -axis as reflected in Fig. 8. In what follows, we will present the design of a partiall decoupled XYZ CPM b eliminating this parasitic motion. IV. MOTION PROPERTY OF THE PARTIALLY DECOUPLED XYZ CPM In order to design an XYZ CPM with partiall decoupled motion, it is necessar to investigate the motion propert of the CPM firstl. Due to a smmetric architecture of the three limbs as shown in Fig. 1, we can consider the case when the second limb solel is driven b a PZT with an input displacement q 2 while the other two limbs remain unactuated. Under such a case, one parasitic translation motion (e 1 )inthex-axis is caused Fig. 1. Fig. 11. Meshed FEM of the CPM. Deformed shape of the CPM. b limb 1, and two parasitic displacements (e 2, e 3 ) along the -axis can be induced b limb 2 and limb 3, respectivel. In view of Figs. 4 and 9, we can observe that the parasitic displacements due to the three limbs can be calculated b: with e 1 = l [ 1 cos(β 2 ) ] (6) [ e 2 = l 1 1 cos(θ2 ) ] (7) e 3 = a [ 1 cos(γ 2 ) ] (8) β 2 =sin 1 (d 2 /l) d 2 /l (9) θ 2 =sin 1 (d 2 /l 1 ) d 2 /l 1 (1) γ 2 =sin 1 (d 2 /a) d 2 /a (11) where d 2 = A P q 2 is illustrated in Fig. 4. Taking into consideration the directions of parasitic motions, we can see that e 2 is along the positive -axis, while e 3 is along the negative -axis instead. In accordance with the relationship between e 2 and e 3, three cases ma occur. For the sake of eliminating the parasitic motion in direction, the case of e 2 = e 3 should be designed. In view of (7) and (8), one can 16

5 Force (N) Deflection (um) Output displacement (um) Fig. 12. Force-deflection relationship of the CPM. Fig. 13. Input and output displacement relationship of the CPM. deduce that it is the situation when l 1 = a. (12) Therefore, if the CPM is designed with the parameters satisfing (12), its output motion is partiall decoupled. That is, the motion along the -axis alwas keeps ero once the P joint within limb 2 is actuated. Likewise, similar results can be obtained for other two directions due to the smmetr. In addition, considering the length of the selected PZT actuators, the CPM parameters are designed as shown in Table I. V. PERFORMANCE TEST OF THE XYZ CPM VIA FEA In order to demonstrate the merits of the designed XYZ CPM, the nonlinear statics FEA is carried out b using ANSYS software package. To generate a higher accurac calculation and enhance the calculation efficienc, both the 2-node element SOLID186 and 1-node element SOLID187 are adopted to create the finite element model (FEM) of the CPM, which is graphicall shown in Fig. 1. In the simulation, the fixing holes of the CPM are constrained, and then a displacement of 1 μm is assigned as input of the CPM. The corresponding loads can be generated after the solution. At the same time, the output motion for the mobile platform can be monitored as well. The deformed FEM of the CPM is depicted in Fig. 11. And the relationship between the actuation force and resulted deflection of the CPM is described in Fig. 12. The linear relationship reveals the constant stiffness propert of the CPM with the absence of stress stiffening phenomenon. Additionall, the relationship between the input and output displacements is plotted in Fig. 13. It is found that the ratio of output to input displacement is 3.48, which results in a CPM with a workspace sie of μm 3 and a resolution of 25 nm 3.48=87 nm, respectivel. Besides, the parasitic motions versus the input displacement for the CPM are elaborated in Fig. 14, where the parasitic motions along and around the x- and -axes, i.e., u x, u, θ x, and θ, are lined out separatel in the figures. We can observe that the maximum parasitic rotations around the x and directions are degree and.13 degree, respectivel, which can be neglected in practice. Furthermore, we can see that although the adopted amplification P joint possesses a parasitic motion along the -axis, the parasitic translation of the CPM in this direction is onl 32.2 nm which is less than the CPM resolution. When the CPM is actuated to move along the direction, the ratio of the CPM parasitic motion in the direction to the output motion in direction is 32.2 nm/348 μm=.9%, which means that the CPM translation in the direction can be neglected. In addition, the CPM translation u x =12.9μm along the x-axis direction can be controlled b the PZT of the limb 1. Thus the CPM motion can be partiall decoupled. At the same time, the simulation results also verif the efficienc of the decoupled design as performed in Section IV. In addition to the kinematics performance assessment of the designed XYZ CPM, it is also necessar to characterie its statics and dnamics properties for the optimum design purposes. Such a statics and dnamics performance evaluation for the CPM is carried out in another paper of the authors, and the reader can refer to [15] for further details. VI. CONCLUSIONS The design procedure for an XYY CPM with partiall decoupled motion characteristics is presented in this paper. The adopted amplification compliant prismatic joint is investigated in terms of input and output displacement and force-deflection relationships. The parasitic motions of the CPM are derived in analtical forms and a decoupled design is proposed for the CPM. And the decoupled properties of the CPM are validated based on the finite element analsis via the ANSYS software package. It is shown that if the CPM is driven using PZTs with a travel range of 1 μm, the CPM workspace is about μm 3 with a resolution of 87 nm. And the simulation results show that the CPM has negligible parasitic rotations and negligible translation in one direction, which validates the well motion propert of the designed CPM. 17

6 Parasitic motion Ux (um) Parasitic motion θ x (degree) x 1 4 (a) u x (c) θ x. Parasitic motion U (um) Parasitic motion θ (degree) (b) u (d) θ. Fig. 14. Relationships between parasitic motions and input displacement of the CPM. In our research, the hardware development of the designed CPM is in progress, and a suitable control scheme will be designed and the CPM accurac will be verified b experimental studies in our next step work. Moreover, the design procedures presented in this paper can be applied to other tpes of CPMs as well. REFERENCES [1] M. Sitti, Micro- and nano-scale robotics, in Proc. 24 American Control Conference, 24, pp [2] J. W. Ru, D.-G. Gweon, and K. S. Moon, Optimal design of a flexure hinge based XYθ wafer stage, Precision Engineering, vol. 21, no. 1, pp , [3] T. Tanikawa and T. Arai, Development of a micro-manipulation sstem having a two-fingered micro-hand, IEEE Trans. Robot. Automat., vol. 15, no. 1, pp , [4] B.-J. Yi, G. B. Chung, H. Y. Na, W. K. Kim, and I. H. Suh, Design and experiment of a 3-DOF parallel micromechanism utiliing flexure hinges, IEEE Trans. Robot. Automat., vol. 19, no. 4, pp , 23. [5] T.-F. Niaritsir, N. Faenda, and R. Clavel, Stud of the sources of inaccurac of a 3DOF flexure hinge-based parallel manipulator, in Proc. of IEEE Int. Conf. on Robotics and Automation, 24, pp [6] K.-K. Oh, X.-J. Liu, D. S. Kang, and J. Kim, Optimal design of a micro parallel positioning platform. part II: Real machine design, Robotica, vol. 23, no. 1, pp , 25. [7] W. J. Chen, W. Lin, K. H. Low, and G. Yang, A 3-DOF flexure-based fixture for passive assembl of optical switches, in Proc. of IEEE/ASME Int. Conf. on Advanced Intelligent Mechatronics, 25, pp [8] Y. Li and Q. Xu, A novel design and analsis of a 2-DOF compliant parallel micromanipulator for nanomanipulation, IEEE Trans. Automat. Sci. Eng., vol. 3, no. 3, pp , 26. [9] B. H. Kang, J. T. Wen, N. G. Dagalakis, and J. J. Gorman, Analsis and design of parallel mechanisms with flexure joints, in Proc. IEEE Int. Conf. on Robotics and Automation, 24, pp [1] Q. Xu and Y. Li, A novel design of a 3-PRC translational compliant parallel micromanipulator for nanomanipulation, Robotica, vol. 24, no. 4, pp , 26. [11] X. Tang and I.-M. Chen, A large-displacement 3-DOF flexure parallel mechanism with decoupled kinematics structure, in Proc. IEEE/RSJ Int. Conf. on Intelligent Robots and Sstems, 26, pp [12] Q. Xu and Y. Li, Design and analsis of a new singularit-free threeprismatic-revolute-clindrical translational parallel manipulator, Proc. Inst. Mech. Eng. Part C-J. Mech. Eng. Sci., vol. 221, no. 5, pp , 27. [13] L. L. Howell and A. Midha, A method for the design of compliant mechanisms with small-length flexural pivots, ASME J. Mech. Des., vol. 116, no. 1, pp , [14] J. M. Paros and L. Weisbord, How to design flexure hinges, Machine Design, vol. 37, pp , [15] Q. Xu and Y. Li, Statics and dnamics performance evaluation for a high precision XYZ compliant parallel micromanipulator, in Proc. of IEEE Int. Conf. on Robotics and Biomimetics (ROBIO), Sana, China, 27, (accepted). 18