Kinematic design of large displacement precision XY positioning stageusing cross strip flexure joints and overconstrained mechanism

Kinematic design of large displacement precision XY positioning stage by using cross strip flexure joints and over-constrained mechanismYeong-jun Choi *, S.V. Sreenivasan, Byung Jin ChoiDepartment of Mechanical Engineering, University of Texas at Austin, Austin, TX 78712, USAAbstractFlexures are widely used in precision machines since they offer frictionless, particle-free, and low maintenance operation, and they provide extremely high resolution. A large displacement precision XY positioning stage is designed by using cross strip flexure joints. An over-constrained mechanism is used to incorporate symmetry to cancel out the effects of center shifting in large-motion flexures. Advanced kinematic techniques such as screw system theory are used to achieve a good kinematic design. Existing flexure-based translation stages usually have motion range to size ratios of less than 0.01 as compared to 0.25 or higher in this research. It is believed that large-motion flexure-based XY stages can be a cost-effective solution for semiconductor applications, particularly the ones that operate in vacuum.Keywords: Flexure; Motion stage; Screw system theory; Over-constrained mechanism1. IntroductionAs an effort to eliminate undesirable characteristics such as friction and backlash in traditional joints, a flexure joint was proposed in the 1960s 6. Flexure joints do not have stickslip friction or backlash. Additional advantages of flexure joints are that they are wear-free and can be made as a monolithic element. If the forcedisplacement curves are known, then the displacements that are continuous at all ranges can be calculated from the external force. However, these flexures have disadvantages such as the limited range of motion.Some researchers have developed high precision positioning systems using flexure joints. Rong and Zhu 8 designed and analyzed a flexure-hinge mechanism that has a motion range of 100 lm and a positioning accuracy of 0.1 lm. Single-axis flexures and piezoelectric actuators were used in the motion stage. Yang et al. 13. developed a micro-positioning stage that was actuated by piezo actuator and guided by structure based on flexure joints. The motion range of that stage was only 200 (im. The comparison of static and dynamic characteristics between analytical model and FEM model was completed in that research. Ryu et al. 9 developed a flexure hinge based XY9 stage which has the total range of 41.5 x 47.8 (im. They presented an optimal design method. Tajbakhsh et al. 11 used flexures to make a three D.O.F. optic mount with the motion limit of 100 (im. Commercially Physik Instrumente 7 are selling P-731 Series XY Piezo Flexure Nano Positioners which can travel in ranges of 100 x 100 (im. It uses low voltage PZTs (0-100 V) and flexures are used as the drive and guiding system. Integrated capacitive position feedback sensors provide sub-nanometer resolution. The flexures provide zero sticktion/friction, ultra-high resolution and exceptional guiding precision. All positioning stages developed so far can give a few hundreds of micrometer motion range, because notch type flexure joints are adequate for small motion range.In order to use flexure joints in large-motion range, some researchers made dual servomechanism that has a fine motion stage mounted on a coarse motion stage. They incorporated flexure joints in fine motion stages. Lee and Kim 3 presented an ultra precision three D.O.F. stage for alignment of wafers in micro lithography. For high precision, they adopted a dual servo system and used flexures and piezoelectric actuators in the fine motion stage. The working range was 200 x 200 mm. Lee et al. 4 developed an ultra precision positioning system using a dual servomechanism that consists of the global stage and the micro stage. The global stage can travel 40 cm and include a ball screw that has the position accuracy of 5 (im. Piezoelectric actuator actuates the micro stage connected by flexures. Dual servo stages make the whole stage complex, and errors associated with coarse motion stage degrade the performance of the whole stage.Fig. 1 depicts a crossed strip type flexure joint that provides large rotation. The flexural pivot made by Lucas Aerospace 5 is a commercially available large deformation revolute flexure joint. This flexure does not have friction or backlash, and provides a large rotation of 60. The kinematic and dynamic characteristics of crossed strip type flexure joint are described in 1,12 well. These flexure joints do not provide exact rotary motion over the entire 60 motion range. They can however, used in conjunction with symmetric kinematic designs, yield exact linear motion stages.Since linear motors are completely non-contact devices, there is no friction, no cogging, and no parts to wear. As a linear-motor-based system can provide high speeds and accelerations, linear motors are becoming the best actuators for ultra-high precision applications. A large displacement flexure-based precision XY stage for vacuum-based semiconductor equipment is developed in this research. The weight support mechanism of this motion stage is made of links and flexure joints, and a linear motor is used as the actuator. Until now, no researches have been done on positioning system that can move large displacement only with flexure joints without using dual servo stages. This research is, to our knowledge, the first work for developing a macro motion stage that can support the weight of the stage and guide the motion by a mechanism based purely on flexure joints. 2. Design conceptFig. 2 shows a double compound notch type small motion rectilinear spring that is used as the basic configuration for the new XY stage design. Since semi-circular notch type flexures are ideal only for small motion range, large-motion flexural pivots such as the one in Fig. 1 are used here. The flexural pivot has many advantages such as no rolling or Coulomb friction, no backlash, no lubrication, and applicability in vacuum. However, center shift may introduce inaccuracies in the positioning of a mechanical system using flexural joints. For the case of complex loading, since the center shift is a function of the deflection angle and the proposed motion stage has a symmetrical structure, it is assumed that the center shift does not make any significant error in the direction perpendicular to the moving direction of the motion stage. An over-constrained mechanism can make no benefit when there is sticktion or friction. Since purely compliant system is employed in the current design, there is no sticktion or friction. Temperature variation can cause thermal expansions, but temperature controlled environment such as within 0.01 C is available in semiconductor industry. However, there is a lack of analysis methods to understand and predict such over-constrained mechanisms performances.The moving body in Fig. 2 has one degree-of-freedom in its nominal configuration and has been used for small motion applications 10. The nominal configuration as shown in Fig. 2 is defined as the configuration with minimum strain energy. However, a mobility analysis based on screw system theory 2 shows that the moving body has two degrees-of-freedom in its off-nominal configurations (see Fig. 3). This mobility analysis. is described in Section 3. Therefore, the undesirable degree-of-freedom must be eliminated for a large-motion application.3. Mobility analysisThe mobility of a double compound notch type rectilinear spring shown in Fig. 2 is expressed aswhere Mis the mobility, n is the number of links, and/is the number of joints. This is only applicable when the stage is in its nominal configuration.The actual mobility of the mechanism in its off-nominal position can be found by using screw system theory. More detailed descriptions related to screw system theory can be found in 2. A brief introduction of screw theory is included in this paragraph. The advantage one can achieve by using screw theory in the field of robotics has been repeatedly emphasized. It has been known to provide geometric insight into the kinematics and static force analyses and syntheses of spatial mechanisms. An instantaneous screw axis $ can be represented by a vector pair, or motor: $=(o)T;T)T, where co represents three angular velocity components and fi represents three linear velocity components of the point on the rigid body instantaneously coincident with the origin of the reference frame.Fig. 4 shows the schematic for the mobility analysis. Points A, B, C, and D are located in the center of link 2 or the edge of the moving body.The motor of point A of link 2, va, can be obtained simultaneously starting at joint 1 or joint 3. The resultant motors from the two starting points should be same.The screw of point A by joint 1, $1, can be represented as 4. Calculation of design parametersThe Side Links shown in Fig. 5 eliminate the undesirable degree-of-freedom, which makes this stage one degree-of-freedom. However, when two stages are stacked orthogonal to each other to result in the XY stage, the actuation of one stage causes undesirable orthogonal excitations to the moving body. It is necessary to use additional linkages to eliminate the undesirable motion and constrain the moving body along the linear motion direction. Therefore, side links are installed at both sides of the moving body. Assuming that constraining linkages exist, the mechanism in Fig. 5 can be optimized to lead to the smallest footprint for a 300 mm motion range. Fig. 6 shows a schematic of the basic linkage in Fig. 5. Links 1 and 3 are of the same length. When the moving body moves along X direction, all the joints in Fig. 6 rotate by the same absolute angle. It should be noted that the motion range is independent of the length of link 2. Due to kinematic constraints, link 2 remains parallel to the line connecting joints 1 and 4. The range of motion, xm, is expressed as The minimum link length for a 300 mm motion range is 150 mm when abs(0max) is 30. Fig. 7 shows the three-dimensional model of the proposed XY stage.5. Design revisionIncorporation of symmetry can lead to undesirable singularities in mechanisms 2. From preliminary assembly of the proposed motion stage, an unexpected independent mode vibration problem was noticed. As shown in Fig. 8, link 2 can vibrate independently in the nominal position, even when the moving plate is fixed at the nominal position. Since the flexure joints are installed at the nominal position, the nominal position corresponds to the center of the stage motion range. The screw system analysis presented earlier did not account for this singularity because the analysis only studied the mobility of the moving plate.In order to prevent this independent vibration mode, the flexure joints are installed in the off-nominal configuration (X = 135 mm). This makes the nominal position (X=0mm) of the entire linkage outside the motion range. Fig. 9 depicts the new linkage structure with the modified design. Total travel range was reduced to 200 mm because of interference between linkages. The motion stage moves from 150 mm to 150 mm for the motion range of 300 mm. The modified design uses from 10 mm to 210 mm for the reduced motion range of 200 mm. Fig. 10 shows the schematic of the modified side linkage to prevent independent vibration of the side linkage. These side linkages are oriented orthogonal to the XY plane and move in the XZ plane. Fig. 11 shows a modified 3D model of the resulting XY stage design.6. Experimental resultsA single-axis motion stage which can move kinematically up to 200 mm was fabricated as shown in Fig. 12. Majority of the fabricated parts was made with aluminum alloy while others such as links and flexure joints were made with stainless steel. It is actuated by a high-resolution linear motor with a laser interferometer providing real-time position feedback. The BLM-203-A linear motor manufactured by Aerotech Inc. is used as an actuator to move the stage. The BA20-160 amplifier produced by the same company generates input power into the linear motor. The Agilent 10889B servo axis board is employed as the motion controller to send the control signal to the amplifier. A digital PID control algorithm is employed to control the position of the stage. The fabricated motion operated with minimum resolution of 1 lm without any problem. Fig. 13 shows position control test result with 10 lm stepwise input. The control resolution of the fabricated motion stage is limited by microscopic vibration which is originated from low damping of the stage. The horizontal straightness, yaw, and their repeatability are observed experimentally by using the laser interferometer. If these undesirable motions are repeatable, a lookup table can eliminate such errors. If not, it is necessary to do a complicated coordinated control of the two stages which is more difficult to be implemented in real-time at high bandwidths. Fig. 14 depicts the schematic of the laser interferometer setup for the horizontal straightness, yaw, and their repeatability tests and Fig. 15 shows the corresponding photograph of the test setup. The Agilent 5517C laser head generates a coherent, collimated, light beam consisting of two orthogonally polarized frequency components. The wavelength of light from the laser head is used as the length standard for the laser interferometer measurement system. Three beam splitters and one beam bender are implemented to distribute light into the appropriate directions. Two Agilent 10706A plane mirror interferometers are utilized to measure the Y-axis movement. One Agilent 10706B high stability plane mirror interferometer is used to measure the X-axis position for control purposes. Three laser receivers are used: one for the X-axis control and two for the Y-axis measurements. The signal from the X-axis receiver is sent to the Agilent 10889B servo axis board installed in the host computer. The 10889B board measures the X-axis position and send a control signal to the amplifier to reposition the linear motor. The other two receivers are connected to two Agilent 10885A PC axis boards that only read the Y-axis positions.As the stage is moved step-by-step at the increment of 10 mm for a distance of 100 mm, for three runs, the lateral displacements at each step are measured using the laser interferometer. Fig. 16 shows the straightness error test result. Fig. 17 shows the measured values of the yaw of the stage. The straightness error and yaw test results show very repeatable behavior. The repeatability of the horizontal straightness and yaw of the stage is also examined. Moving the stage forward and backward 20 times, the Y-axis displacements at 50 mm from the home position are measured. Figs. 18 and 19 shows the repeatability test results of the horizontal straightness and yaw. The repeatability (3r) of the horizontal straightness of the stage is about 3.9 lm, but the stage shows a very excellent yaw repeatability of 0.0045 mrad. The major reason for relatively large straightness repeatability error is low lateral stiffness of the current flexure stage.7. ConclusionsA large displacement precision XY positioning stage was designed by using cross strip flexure joints and over-constrained mechanism. The weight support mechanism of the motion stage was made of links and flexure joints, and a linear motor was used as the actuator. Crossed strip type flexure joints that provide large rotation were used. This stage is not a dual servo stage, but it can provide large-motion range of greater than 200 mm 200 mm to support a substrate during semiconductor manufacturing. An over-constrained mechanism was used to incorporate symmetry to cancel out the effects of center shifting in large-motion flexures. Advanced kinematic techniques such as screw system theory were used to achieve a good kinematic design. A single-axis motion stage actuated by a high-resolution linear motor with a laser interferometer providing real-time position feedback has been fabricated. The horizontal straightness, yaw, and their repeatability tests are performed.Future work will focus on further improving damping and lateral stiffness for better resolution and straight-ness since the current stage has relatively low damping and lateral stiffness.