Design and Analysis of a Single Notch Parallelogram Flexure Mechanism Based X-Y Nanopositioning Stage

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1 Design and Analysis of a Single Notch Parallelogram Flexure Mechanism Based X-Y Nanopositioning Stage Vithun S N *, Narendra Reddy T 1, Prakash Vinod 2, P V Shashikumar 3 Central Manufacturing Technology Institute, Bangalore , *vithun.sn@cmti-india.net, 1 narendrareddy t@cmti-india.net, 2 prakash.vinod@cmti-india.net, 3 pvs@cmti-india.net Abstract The main requirement of a for nanopositioning stage used in varieties of nanotechnology equipments is to have minimum cross axis motion, high bandwidth and large range. This paper presents the design and analysis of 2-DOF flexure for a nanopositioning stage. Improved compliance is used to have minimum parasitic motion and higher bandwidth, unlike the lumped-compliance circular hinge is used only on the drive end of the. The behaviour of is analysed theoretically for its range and stiffness and further the designed flexure having range of 650 µm range, with high resonant frequency and negligible cross axis motion is validated with a detailed study of dynamic and static behaviour of using FEA. Both the theoretical and FEA results confirm the meeting the requirement for nanopositioning stage. Keywords:Flexure, parallel kinematic, nanopositioning stage, finite element analysis. 1. Introduction The nanopositioning system is gaining more importance and finds its application in various areas of nanotechnology. Many state-of-the-art nanopositioning systems are using flexure for guiding the required motion due to their advantages like low friction and backlash that helps in obtaining a high repeatable motion. The need for higher resonant frequency nanopositioning stage is growing in many fields like fabrication, nanometrology and in cell-biology. In order to obtain the high resonant frequency many research work have been carried out [2]. To obtain required degree of motion the flexure are generally arranged in two configurations, namely serial and parallel kinematics. A serial-kinematics obtains the required degree of motion by stacking single axis system in series with another axis system, whereas parallel kinematics connects the each axis system to the sample platform independently with respect to the ground. Generally, parallel kinematics is used in the design of flexure due to various advantages over serial kinematics.many flexure used in nanopositioning stage have a cross axis motion which is an undesirable requirement for nanopositioning stage. 2. Literature Review Shorya Awtar and Alexander H. Slocum[2] have designed parallel kinematic XY flexure based on constraint patterns for large range of motion without over-constraint. Non-linear analysis is carried to predict the beam-based flexure performance. It is also shown that the design with higher degree of symmetry, exhibits improved actuator isolation, less parasitic rotations, and also a higher degree of robustness against manufacturing and assembly errors. The designed stage has range of 5mm x 5mm, cross-axis coupling, lost motion and actuator isolation better than 1%, and a motion stage rotation of less than 1 arc sec. Yangmin Li and QingsongXu[10] have designed XY parallel stage with decoupled motion. They have incorporated double parallelogram flexures and a compact displacement amplifier with high transverse stiffness. Kinematic and dynamic modelling of the stage is been done based on compliance and stiffness matrix which are validated by finite-element analysis. The designed stage has low cross axis motion (1.8%) and first natural frequency of 110 Hz and a range of 117µm. Sebastian Polit and Jingyan Dong[5] have developed XY nanopositioning stage which has a doubly clamped beam and a parallelogram hybrid flexure with compliant beams and circular flexure hinges. The design decouples the motion in the X-Ydirections and restricts parasitic rotations in the XY plane while allowing for an increased bandwidth. The stage has motion of 15 µm along each axis with a resolution of about 1 nm and natural frequency of over 8 khz. Similarly there are many efforts made to develop a nanopositioning stage having high motion range, resonant frequency and minimum parasitic motion.however, a with higher resonant 670-1

Design and Analysis of a Single Notch Parallelogram Flexure Mechanism Based X-Y Nanopositioning Stage frequency, range with minimum parasitic motion is still a challenge.

2 Design and Analysis of a Single Notch Parallelogram Flexure Mechanism Based X-Y Nanopositioning Stage frequency, range with minimum parasitic motion is still a challenge. In this paper,design of a flexure that meets the above requirements is presented. 3. Design and Analysis The main objectives of current work is to design flexure that have minimum parasitic motion (cross-axis motion), large range of motion and higher resonant frequency. The methodology followed for design of the is as shown in figure1 Need or Requirement Actuator Sample Platform Mechanism No Kinematic Design Material Selection Theoretical calculation Satisfied Yes Finite element analysis Satisfied No Figure 2Kinematic representation of flexure The link is replaced by beam fixed at both end and a symmetrical parallelogram. Parallelogram has flexure beam and circular hinge notch at one end of the beam that is connected to the sample platform. The flexure beams provide high structural stiffness and also have high natural frequency, while circular hinge absorbs the rotary motion and also reduces the stress and increasing the motion range.when compared to s that have beam flexure with circular hinges at both ends and the having only flexure beams, the with circular hinge at one end (near to sample platform) gives the reduced parasitic motion, higher bandwidth and range. Symmetrical design further reduces the parasitic motion and actuator isolation. The solid model of the is as shown in figure 3. Yes Prototype fabrication and Testing Figure 1Methodology followed in design 3.1 Design The kinematic design of the flexure is as shown in figure 2. This kinematic design as a four individual kinematic chain connected to the sample platform in a parallel configuration. The kinematic chains consist of a prismatic joint and parallelogram. When the is displaced in one direction, the resulting motion of the sample platform is accommodated by the other kinematic chains i.e. by an angular displacement at the parallelogram compliant s. Figure 3Solid model of for XY stage The overall stiffness of the is calculated by considering the stiffness of each components i.e. beam fixed at ends, flexure beam and circular flexure hinge. The stiffness of the beams fixed at ends is given by [5] 670-2

3 (1) Where, E is the young s modulus of the material, T, w e, l e is the thickness, width and length of beam fixed at ends. The overall stiffness is K e = nk e, n= number of beam in a same direction In parallelogram, the circular flexure hinges absorb the rotary motion at end of the beams,therefore the beam is simplified as cantilever beam subjected to end load for calculation. The stiffness of cantilever beam subjected to end load is given by [5] (2) Where, T, W c, l is the thickness, width and length of cantilever beam. The overall stiffness is K c = nk c, n=number of flexure beam in a parallelogram The rotary stiffness of the 1-D circular hinge for small deflections and for ratio near unity is given by [6] (3) Where, t is minimum thickness of the circular hinge, b is maximum thickness, r is semi-circular notch radius as shown in figure 4. In the parallelogram, when the sample platform is actuated, all the circular hinges undergo the same deflection, the rotary stiffness of the circular hinge is K z = nk z contributes to stiffness more than the flexure beam and circular flexure hinge. The maximum displacement that can be obtained by this is also calculated, as the flexure works on the principle of compliant. Considering maximum allowable stress should be within elastic limit of the material, the maximum displacement of is the least displacement that is achieved from either of three components when the stress reaches maximum allowable stress. Table 1 Architecture parameter of XY stage Parameter Value (mm) Parameter Value (mm) T t 0.30 W e 2.10 l l e r 1.00 W c 2.30 b The maximum allowable rotation of the hinge will be given by [6] (4) Where, σ max is the maximum allowable stress, k is the correction factor for notch curvature, K t is the stress concentration factor. The value of k and K t is calculated by the formulas given below. (5) (6) The maximum deflection of the notch corresponding to maximum rotary motion of the hinge is calculated by [5] (7) Figure 4 Isometric view of circular hinge The overall stiffness of the structure is calculated on basis of principle of virtual work and it is found to be K=K e +K c +K z (4) It is observed from above equations that the stiffness is directly proportional to the young s modulus and hence a material with higher young s modulus is suitable. As the density of the material will have inverse effect on the resonant frequency of the material the material with higher stiffness to density ratio is selected for. In this work, Titanium alloy grade 5 has been selected because of its high stiffness to density ratio and also relatively low thermal coefficient of expansion. Substituting the values shown in the Table 1 to the equations 1 to 4 the overall stiffness of the structure is 1.44N/µm, beam fixed at both ends The maximum displacement of the flexure beam subjected to end load is given by (8) The maximum displacement of the beam fixed at both ends and subjected to load at center is given by (9) The maximum achievable displacement of the is minimum of ( d max-h, d max-c, d max-e ), by solving the above equation the displacement of each members are evaluated.the minimum achievable motion of the three components namely, circular flexure hinge, beam fixed at both ends, flexure beam are 651µm, 2304µm and 1173µm respectively. Therefore the maximum achievable displacement of the is 651µm

Design and Analysis of a Single Notch Parallelogram Flexure Mechanism Based X-Y Nanopositioning Stage 3.

Ansys software is used for finite element analysis, the maximum displacement corresponding stress distribution and cross axis effect of the is studied using linear static analysis.

The boundary conditions during the linear static analysis are applied similar to the actual boundary condition and the load is applied at the center of the beam fixed at both ends and the maximum

4 Design and Analysis of a Single Notch Parallelogram Flexure Mechanism Based X-Y Nanopositioning Stage 3.2 Finite element analysis In this section finite element analysis is carried out to verify design objective of the XY nanopositioning stage. Ansys software is used for finite element analysis, the maximum displacement corresponding stress distribution and cross axis effect of the is studied using linear static analysis. The dynamic behaviour of the such as natural frequency, mode shape of the is studied using dynamic analysis. The boundary conditions during the linear static analysis are applied similar to the actual boundary condition and the load is applied at the center of the beam fixed at both ends and the maximum achievable displacement and stress is shown in figure 5 and figure6 respectively. value from FEM is 1.55N/μm which is close to theoretical calculation. It can also be observed that there is a good linearity between the load and displacement of stage. Figure 7Load Vs displacement Figure 5 Maximum displacement of deformed Figure 5 shows the maximum displacement of the, when a load of 1020N is applied in either of one direction (either in X or Y) it was observed that stage undergoes the displacement of 657μm in the actuation direction. The vibrational modes and frequencies are evaluated using FEA figure 8 shows the natural frequency and corresponding mode shape of the. It is seen that the first resonant frequency occurs at Hz and having translational mode shape. Mode 1: Hz Figure 8 Mode shape and corresponding frequency Figure 6 Maximum stress of deformed During same loading condition as mentioned above the maximum von Mises stress was observed and stress distribution pattern is as shown in figure 6 the maximum stress of N/mm 2 was observed in circular flexure hinge. It is observed that the maximum displacement of stage was almost near to the theoretical calculation and also the maximum stress was observed in the circular flexure hinge, hence the displacement of was limited by the circular flexure as it reaches maximum allowable stress limit. Figure 7 shows the load vs. displacement plot of both theoretical and FEM, the stiffness values of obtained from theoretical calculation and FEM are very close to each. Stiffness Table 2 shows the comparison of theoretical and FEA results. The FEA values of stiffness and working range have deviation of 7.09% and 0.92% from theoretically calculated values respectively. Table 2. Comparison of Theoretical and FEA results Sl. No. Parameter Theoretical FEM Deviation (%) 1 Stiffness (N/µm) 2 Working range(µm)

5 The cross axis effect of the the transverse and perpendicular direction displacement to the applied load was evaluated. The maximum cross axis displacement were within 0.76% and 0.247% of total motion. The designed also has less cross axis motion which is a desirable requirement of nanopositioning stage. 4. Conclusion This paper presents design and analysis of a decoupled, long range translational nanopositioning stage. The designed is monolithic and has symmetrical parallelogram with beam fixed at both ends at the end of parallelogram. The designed has high working range (651µm), high resonant frequency (1005.6Hz) and also the minimum cross axis motion (0.76%). FEA has been carried out to evaluate the performance of the. FEA results and theoretically calculated stiffness and working range are in good agreement, with deviation in values of 7.09% and 0.92% respectively as indicated in table 2. The designed stage meets the requirement for nanometrology application. 5. References 1. Hui Tang, Yangmin Li and Jiming Huang (2012), Design and analysis of a dual-mode driven parallel XY micromanipulator for micro/ nanomanipulations, J Mechanical Engineering Science, pp S. Awtar and A. H. Slocum (2007), Constraintbased design of parallel kinematic XY flexure s, J. Mech. Des., vol. 129, no. 8, pp Kam K. Leang and Andrew J. Fleming (2009), High-Speed Serial-Kinematic SPM Scanner: Design and Drive Considerations, Asian Journal of Control, Vol. 11, No. 2, pp Shorya Awtar, John Ustick, ShiladityaSen (2013), An XYZ Parallel-Kinematic Flexure Mechanism With Geometrically Decoupled Degrees of Freedom, ASME, Journal of Mechanisms and Robotics, Vol Sebastian Polit and Jingyan Dong (2010), Development of a High-Bandwidth XY Nanopositioning Stage for High-Rate Micro- /Nanomanufacturing, IEEE/ASME Transactions on Mechatronics. 6. S T Smith and D G Chetwynd (1992), Foundation of Ultra precision Mechanism Design, Development of Nanotechnology, Gordon and Breach Science Publishers, Vol Yao, J. Dong and P.M. Ferreira (2008), A Novel Parallel Kinematics for Integrated, Multi-axis Nano-positioning. Part1: Kinematics and Design for Fabrications, Precision Engineering, Elsevier, Vol Yangmin Li, and Qingsong Xu (2011), A Totally Decoupled Piezo-Driven XYZ Flexure Parallel Micropositioning Stage for Micro/ Nanomanipulation, IEEE Transactions on Automation Science and Engineering, VOL Yuen Kuan Yong, Sumeet S. Aphale, and S. O. Reza Moheimani (2009), Design, Identification, and Control of a Flexure-Based XY Stage for Fast Nanoscale Positioning, IEEE Transactions on Nanotechnology, Vol Yangmin Li and Qingsong Xu (2009), Design and analysis of a totally decoupled flexure-based XY parallel micromanipulator. IEEE Transactions and Robotics, Vol Yuen Kuan Yong and S. O. Reza Moheimani (2010), A Compact XYZ Scanner for Fast Atomic Force Microscopy in Constant Force Contact Mode, IEEE/ASME, International Conference on Advanced Intelligent Mechatronics, Montreal, Canada

Novel Design of a Totally Decoupled Flexure-Based XYZ Parallel Micropositioning Stage

2010 IEEE/ASME International Conference on Advanced Intelligent Mechatronics Montréal, Canada, July 6-9, 2010 Novel Design of a Totally Decoupled Flexure-Based XYZ Parallel Micropositioning Stage Qingsong