- Email: [email protected]
Comments on the XY stage design in paper “Modular kinematics and statics modeling for precision positioning stage”
Mechanism and Machine Theory 121 (2018) 148–150
Contents lists available at ScienceDirect
Mechanism and Machine Theory journal homepage: www.elsevier.com/locate/mechmachtheory
Letter to the editor
Comments on the XY stage design in paper “Modular kinematics and statics modeling for precision positioning stage” We would like to congratulate Ling et al on their published paper [1] about the modular kinematics and statics modeling for precision positioning stage. However, there is a technical design issue of the XY motion stage in [1], which we would like to bring to the readers’ attention. The proposed design in Fig. 3(a) in [1] (shown in Fig. 1(a) in this letter) has been claimed to be an XY motion stage as a case study to demonstrate the proposed modelling method, which is not correct. The problem is that the in-plane rotations of the mechanism’s output platform and of the two amplifying mechanisms’ output stages are not constrained at all, and therefore remain as the degree of freedom (DOF). The non-constrained rotation appears due to the fact that there is a common intersection point between the line along beam 5 (or 6) and the line along beam 7 (or 8) in the two guiding modules [2]. The resulting rotation of the amplifying mechanism’s output stage can even damage the piezoelectric actuator due to the undesired transverse motion/load imposed on the actuator. The proof to verify our above argument is provided in Fig. 1(b) and (c), which are the first two planar modal analysis results based on finite element analysis (under the geometric linear assumption). It can be observed that the first-order modal shape is the rotational mode (about Z-axis) while the second-order modal shape is the translational mode (along X/Y-axis). The natural frequency values (proportional to stiffness) of the two modes are very close (14% difference in the simulation). Both modes correspond to low stiffness (i.e., high compliance) in their directions, which is usually two orders of magnitude smaller than that in other directions [3]. Therefore, the in-plane rotation is a DOF that is not constrained in [1]. In order to confirm the modal analysis findings, static loading was applied to detect the significant in-plane rotation as shown in Fig. 2. It is found that the single-axis actuation and non-identical two-axis actuations can both result in apparent/large rotations (Fig. 2(a) and (c)). One approach to remedy the design issue in [1] is to use the full mirror-symmetry strategy to effectively constrain the undesired rotations, as shown in Fig. 3. Such a constraint arrangement has been previously reported in [4] where no common intersection point mentioned above exists. Another approach rectifying Ref. [1] is to replace the single beam (beam 5, 6, 7 or 8) in Fig. 1 with a parallelogram mechanism, as employed in [5]. Even though the unwanted in-plane rotation is effectively constrained by mirror symmetry (Fig. 3), it always unavoidably exists when dissimilar input motions/forces are applied along the X and Y directions. However, the magnitude of the rotations is significantly lower (negligible/trivial) than that of the case without constrained rotation (Fig. 1), as seen when comparing Figs. 2(c) and 3(b) with the same actuation conditions. Note that the focus of the commented article [1] lies not in the description of a new design for XY motion stages, but the verification of the modelling theory is demonstrated by the XY motion stage in Sections 3 in [1]. The questionable design in [1] and other literatures can mislead potential readers to design/use the similar XY motion stages, and may prove the limitation of the modelling theory. Actually, the theoretical modelling method in [1] is ordinary, and cannot capture any parasitic motion and cross-axis coupling that are inherent in compliant mechanisms [4]. It should be also pointed out that although the geometric linear assumption was used in the above simulation, geometrical nonlinearity can be taken into account in the finite element analysis of this letter, which produces the same finding on the non-constrained rotations in [1]. Figure 4 in [1], under the geometric linear assumption, shows no parasitic rotation when an axial force on the one end port of the rhombic structure was excited, because the other end port was held fixed. This constraint scheme on the XY stage in [1] does not reflect the actual constraint in work, which is different from that in Fig. 2. This may lead to that the non-constrained rotations in [1] were not detected.
https://doi.org/10.1016/j.mechmachtheory.2017.10.021 0094-114X/© 2017 Elsevier Ltd. All rights reserved.
Letter to the editor / Mechanism and Machine Theory 121 (2018) 148–150
149
Fig. 1. The XY compliant motion stage design presented in [1] and its modal analysis. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Fig. 2. Static analysis of the design presented in [1]: Simulations in amplified scale; Colour in simulation denoting resultant displacement, with red being the largest and blue being the lowest. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Fig. 3. An improved XY stage: Simulation in amplified scale; Colour in simulation denoting resultant displacement, with red being the largest and blue being the lowest; Force in simulation (denoted by solid arrow) in Y-axis is 5 times larger than that in the X-axis. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
150
Letter to the editor / Mechanism and Machine Theory 121 (2018) 148–150
References [1] M. Ling, J. Cao, Z. Jiang, J. Lin, Modular kinematics and statics modeling for precision positioning stage, Mech. Mach. Theory 107 (2017) 274–282. [2] L.C. Hale, Principles and Techniques for Designing Precision Machines PhD Thesis, Lawrence Livermore National Lab., CA (US), 1999. [3] G. Hao, X. Kong, A normalization-based approach to the mobility analysis of spatial compliant multi-beam modules, Mech. Mach. Theory 59 (2013) 1–19. [4] Y.K. Yong, S.S. Aphale, S.O. Moheimani, Design, identification, and control of a flexure-based XY stage for fast nanoscale positioning, IEEE Trans. Nanotechnol. 8 (2009) 46–54. [5] G. Hao, J. Yu, Design, modelling and analysis of a completely-decoupled XY compliant parallel manipulator, Mech. Mach. Theory 102 (2016) 179–195.
Guangbo Hao School of Engineering, -Electrical and Electronic Engineering, University College Cork, Cork, Ireland E-mail address: [email protected] Received 5 October 2017 Revised 23 October 2017 Accepted 24 October 2017
Contents lists available at ScienceDirect
Mechanism and Machine Theory journal homepage: www.elsevier.com/locate/mechmachtheory
Letter to the editor
Comments on the XY stage design in paper “Modular kinematics and statics modeling for precision positioning stage” We would like to congratulate Ling et al on their published paper [1] about the modular kinematics and statics modeling for precision positioning stage. However, there is a technical design issue of the XY motion stage in [1], which we would like to bring to the readers’ attention. The proposed design in Fig. 3(a) in [1] (shown in Fig. 1(a) in this letter) has been claimed to be an XY motion stage as a case study to demonstrate the proposed modelling method, which is not correct. The problem is that the in-plane rotations of the mechanism’s output platform and of the two amplifying mechanisms’ output stages are not constrained at all, and therefore remain as the degree of freedom (DOF). The non-constrained rotation appears due to the fact that there is a common intersection point between the line along beam 5 (or 6) and the line along beam 7 (or 8) in the two guiding modules [2]. The resulting rotation of the amplifying mechanism’s output stage can even damage the piezoelectric actuator due to the undesired transverse motion/load imposed on the actuator. The proof to verify our above argument is provided in Fig. 1(b) and (c), which are the first two planar modal analysis results based on finite element analysis (under the geometric linear assumption). It can be observed that the first-order modal shape is the rotational mode (about Z-axis) while the second-order modal shape is the translational mode (along X/Y-axis). The natural frequency values (proportional to stiffness) of the two modes are very close (14% difference in the simulation). Both modes correspond to low stiffness (i.e., high compliance) in their directions, which is usually two orders of magnitude smaller than that in other directions [3]. Therefore, the in-plane rotation is a DOF that is not constrained in [1]. In order to confirm the modal analysis findings, static loading was applied to detect the significant in-plane rotation as shown in Fig. 2. It is found that the single-axis actuation and non-identical two-axis actuations can both result in apparent/large rotations (Fig. 2(a) and (c)). One approach to remedy the design issue in [1] is to use the full mirror-symmetry strategy to effectively constrain the undesired rotations, as shown in Fig. 3. Such a constraint arrangement has been previously reported in [4] where no common intersection point mentioned above exists. Another approach rectifying Ref. [1] is to replace the single beam (beam 5, 6, 7 or 8) in Fig. 1 with a parallelogram mechanism, as employed in [5]. Even though the unwanted in-plane rotation is effectively constrained by mirror symmetry (Fig. 3), it always unavoidably exists when dissimilar input motions/forces are applied along the X and Y directions. However, the magnitude of the rotations is significantly lower (negligible/trivial) than that of the case without constrained rotation (Fig. 1), as seen when comparing Figs. 2(c) and 3(b) with the same actuation conditions. Note that the focus of the commented article [1] lies not in the description of a new design for XY motion stages, but the verification of the modelling theory is demonstrated by the XY motion stage in Sections 3 in [1]. The questionable design in [1] and other literatures can mislead potential readers to design/use the similar XY motion stages, and may prove the limitation of the modelling theory. Actually, the theoretical modelling method in [1] is ordinary, and cannot capture any parasitic motion and cross-axis coupling that are inherent in compliant mechanisms [4]. It should be also pointed out that although the geometric linear assumption was used in the above simulation, geometrical nonlinearity can be taken into account in the finite element analysis of this letter, which produces the same finding on the non-constrained rotations in [1]. Figure 4 in [1], under the geometric linear assumption, shows no parasitic rotation when an axial force on the one end port of the rhombic structure was excited, because the other end port was held fixed. This constraint scheme on the XY stage in [1] does not reflect the actual constraint in work, which is different from that in Fig. 2. This may lead to that the non-constrained rotations in [1] were not detected.
https://doi.org/10.1016/j.mechmachtheory.2017.10.021 0094-114X/© 2017 Elsevier Ltd. All rights reserved.
Letter to the editor / Mechanism and Machine Theory 121 (2018) 148–150
149
Fig. 1. The XY compliant motion stage design presented in [1] and its modal analysis. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Fig. 2. Static analysis of the design presented in [1]: Simulations in amplified scale; Colour in simulation denoting resultant displacement, with red being the largest and blue being the lowest. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Fig. 3. An improved XY stage: Simulation in amplified scale; Colour in simulation denoting resultant displacement, with red being the largest and blue being the lowest; Force in simulation (denoted by solid arrow) in Y-axis is 5 times larger than that in the X-axis. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
150
Letter to the editor / Mechanism and Machine Theory 121 (2018) 148–150
References [1] M. Ling, J. Cao, Z. Jiang, J. Lin, Modular kinematics and statics modeling for precision positioning stage, Mech. Mach. Theory 107 (2017) 274–282. [2] L.C. Hale, Principles and Techniques for Designing Precision Machines PhD Thesis, Lawrence Livermore National Lab., CA (US), 1999. [3] G. Hao, X. Kong, A normalization-based approach to the mobility analysis of spatial compliant multi-beam modules, Mech. Mach. Theory 59 (2013) 1–19. [4] Y.K. Yong, S.S. Aphale, S.O. Moheimani, Design, identification, and control of a flexure-based XY stage for fast nanoscale positioning, IEEE Trans. Nanotechnol. 8 (2009) 46–54. [5] G. Hao, J. Yu, Design, modelling and analysis of a completely-decoupled XY compliant parallel manipulator, Mech. Mach. Theory 102 (2016) 179–195.
Guangbo Hao School of Engineering, -Electrical and Electronic Engineering, University College Cork, Cork, Ireland E-mail address: [email protected] Received 5 October 2017 Revised 23 October 2017 Accepted 24 October 2017