DESIGN AND 3D PRINTING OF COMPLIANT MECHANISMS PHAM MINH TUAN SCHOOL OF MECHANICAL & AEROSPACE ENGINEERING A thesis submitted to Nanyang Technological University in fulfillment of the requirement for the degree of Doctor of Philosophy January 2019 Statement of Originality I hereby certify that the work embodied in this thesis is the result of original research, is free of plagiarised materials, and has not been submitted for a higher degree to any other University or Institution. 09 January 2019 Date Pham Minh Tuan Supervisor Declaration Statement I have reviewed the content and presentation style of this thesis and declare it is free of plagiarism and of sufficient grammatical clarity to be examined. To the best of my knowledge, the research and writing are those of the candidate except as acknowledged in the Author Attribution Statement. I confirm that the investigations were conducted in accord with the ethics policies and integrity standards of Nanyang Technological University and that the research data are presented honestly and without prejudice.
09 January 2019 Date Yeo Song Huat Authorship Attribution Statement This thesis contains material from 2 papers published in the following peer-reviewed journals where I was the first author. Chapter 3 is published as M. Yeo, "Synthesis of multiple degrees-of-freedom spatial-motion compliant parallel mechanisms with desired stiffness and dynamics characteristics," Precision Engineering, vol. DOI: http://dx.014 The contributions of the co-authors are as follows: Prof Yeo suggested the initial project direction.
I prepared the manuscript drafts. The manuscript was revised by Dr. Teo and Prof Yeo. I co-designed the study with Dr.
Teo and performed all the laboratory work at the School of Mechanical and Aerospace Engineering and the Singapore Institute of Manufacturing Technology. I also analyzed the data. Chapter 4 is published as M. Nai, "A 3D-printed Ti-6Al-4V 3-DOF compliant parallel mechanism for high precision manipulation," IEEE/ASME Transactions on Mechatronics, vol.2726692 The contributions of the co-authors are as follows: Prof Yeo suggested the initial project direction.
I prepared the manuscript drafts. The manuscript was revised by Dr. Teo and Prof Yeo. The 3D printed prototype was built by Dr.
Wang and Dr. Nai at the Singapore Institute of Manufacturing Technology. I co-designed the study with Dr. Teo and performed all the laboratory work at the School of Mechanical and Aerospace Engineering and the Singapore Institute of Manufacturing Technology.
I also analyzed the data. Wang verified the experimental data on the mechanical properties of thin beams fabricated by Electron Beam Melting method. 09 January 2019 Date Pham Minh Tuan Abstract Compliant mechanism has been a popular solution for developing precise motion systems. This is because the working principle of compliant mechanism is based on elastic deformation of flexure elements, which is capable of providing highly repeatable motions that conventional bearing-based counterparts fail to deliver.
In positioning applications, compliant parallel mechanism (CPM) is preferred because its closed-form architecture has high payload allowance and can better reject external mechanical disturbances. However, the performance of CPMs is often constrained by the limitations of synthesis techniques and fabrication methods. At present, it is still a challenge to synthesize multiple degrees-of-freedom (DOF) CPMs with spatial motions, optimized stiffness and dynamic properties. In addition, using conventional machining methods to fabricate the structure of CPMs by sub-parts will incur assembly errors.
To address the limitations, this research focuses on the development of a new synthesis method for multi-DOF CPMs and the investigation on the mechanical characteristics of CPMs that are monolithically fabricated by 3D printing technology. A novel structural optimization method, termed as beam-based structural optimization method, is proposed to synthesize CPMs with multi-DOF, optimized stiffness and desired dynamic properties. A well-defined objective function for the optimization process is also presented where the different units of components within the stiffness matrix of CPMs are normalized. It is shown that the desired motions of CPMs can be obtained by determining specific geometries of the curved-and-twisted beams.
The effectiveness of the beam-based method is demonstrated by synthesizing a 3-DOF spatial-motion (θX – θY – Z) CPM with high stiffness ratios of more than 200 for the rotations and 4000 for the translations, a large workspace of 8° × 8° × 5.5 mm and a targeted dynamic response of 100 Hz. A monolithic prototype of the synthesized CPM is fabricated by electron beam melting (EBM) technology and the characteristics of the 3D-printed CPM are experimentally investigated. By introducing a coefficient factor to compensate the difference between the designed thickness and effective thickness, the mechanical properties of 3D-printed CPMs can be well predicted. Experimental results show that EBM technology can be used to fabricate compliant devices for high- precision positioning systems.
CPMs with motion-decoupling capability are desirable to eliminate parasitic motions. Several design criteria are analytically derived for synthesizing 3-legged CPMs with any DOF and fully-decoupled motions. A design of 3-DOF (θX – θY – Z) CPM with decoupled output motions is presented and experimentally evaluated. To demonstrate the versatility of the beam- based method and the decoupled-motion criteria, a new CPM with 6-DOF is synthesized.
Its end effector is built by cellular structure to exploit the benefit of 3D printing technology. Experimental investigations show that the EBM-printed prototype of the 6-DOF CPM has motion-decoupling capability and is able to produce a large workspace of more than 6 mm for the translations and 12° the for the rotations. It is envisaged that results of this research can help engineers to develop a variety of high-precision machines with optimal performances. i Acknowledgment First, I would like to express my deeply gratitude to my main supervisor, Professor Yeo Song Huat, from the School of Mechanical and Aerospace Engineering (MAE), Nanyang Technological University (NTU).
From the very first day of my PhD study, he always shows his kindness and enthusiasm to help me in my life and support me in research. Second, I am deeply grateful to my co-supervisor, Dr. Daniel Teo Tat Joo, from A*STAR. He is willing to help me with any issue, and always shares his academic and practical knowledge to help me in developing the theoretical approaches as well as conducting experiments.
I would like to express my special thanks to my Thesis Advisory Committee, and also acknowledge the ASEAN University Network/Southeast Asia Engineering Education Development Network (AUN/SEED-Net) and the Singapore Centre for 3D Printing (SC3DP) for giving me the opportunity to pursue PhD study. I sincerely thank Dr. Wang Pan and Dr. Nai Mui Ling Sharon from Singapore Institute of Manufacturing Technology (SIMTech) for their support in 3D printing.
I want to express my special thanks to Dr. Wang Pan, who always gives me helpful advises on fabrication issues. I would like to thank Dr. Zhu Haiyue from SIMTech for helping me to setup the experiments and my senior, Dr.
Lum Guo Zhan, for sharing his valuable experience on this research topic. I also want to extend my appreciation to the staff from Robotics Research Centre (RRC), Mr. Lim Eng Cheng, Ms. Agnes Tan Siok Kuan and Mr.
You Kim San, for their kindness. Finally, I would like to thank all my family and especially my wife, for the continuous support and encouragement that they have given to me during the time I have been studying at NTU. ii Contents Abstract. ii List of Figures.
vii List of Tables. xi List of Abbreviations. xii List of Notations. xiii Chapter 1 Introduction .1 Background and Motivation .2 Objectives and Scope .3 Organization of the Thesis.
9 Chapter 2 Literature Review .1 Rigid body replacement approach .2 Constraint-based approach.2 Solid Isotropic Microstructure with Penalization (SIMP) method .3 Evolutionary Structural Optimization (ESO) method .4 Level set method .5 Ground structure method .6 Morphological representation method.7 Mechanism integrated method .2 3-Legged CPMs for Motion Systems .1 Fundamentals and benefits.2 3-DOF planar-motion (X – Y – θZ) CPM .3 3-DOF spatial-motion (θX – θY – Z) CPM. 42 Chapter 3 Beam-based Method .5 Synthesis and Evaluation of a 3-DOF Spatial-Motion (θX – θY – Z) CPM .4 Experimental investigations and results. 66 Chapter 4 Investigation on the Mechanical Characteristics of 3D-Printed CPM .1 3D-Printed Prototype of the Synthesized 3-DOF (θX – θY – Z) CPM .2 Effective Thickness of 3D-Printed Flexures .3 Evaluation on the Stiffness and Dynamic Properties of the 3D-Printed CPM .4 Precision Manipulator based on 3D-Printed CPM. 83 Chapter 5 Design Criteria for 3-Legged CPM with Fully-Decoupled Motion Characteristics .2 Stiffness Modeling of CPMs Containing a Single Serial Flexure Chain in a Limb .3 Characteristics of Flexure Elements in Decoupled-Motion CPMs .4 Stiffness Modeling of CPMs Containing Two Reflecting Serial Flexure Chains in a Limb.
108 Chapter 6 Synthesis and Evaluation of a 6-DOF CPM with Decoupled Motions .2 Improvement of Dynamic Property by Employing Cellular Structure .3 Experimental Investigation and Results .2 Evaluation of compliance .3 Evaluation of decoupled-motion capability .4 Evaluation of dynamic behavior. 129 Chapter 7 Conclusion and Future Works. 133 List of Author’s Publications. 136 The Equivalent PRB Model for Over-Constrained CPMs.
146 EBM Printing Process. 148 Effective Thickness of EBM-Printed Flexures Regarding to Different Designed Thickness and Building Directions. 151 Stiffness Characteristics of Some Popular Flexure Elements. 153 Conditions of the Compliance Matrix of a Limb for Achieving Decoupled- Motion CPM.
154 Inversion of the Compliance Matrix of a Limb in a Decoupled-Motion CPM. 158 v vi List of Figures Figure 1.1: Flow of rigid body replacement approach [33].2: Fundamentals of constraint-based approach [33].3: Synthesis process of optimization approach [55].4: A flexure hinge with large elastic deformation fabricated by EBM method [80].2: PRB models of compliant joint (a) beam-type and (b) notch-type [1].3: Complex beam-type compliant joints (a) revolute joint [82], (b) universal joint [77] and (c) spherical joint [83].5: Flexure elements provided by FACT [51].6: FACT library showing the relation between freedom- and constraint-space [51].7: Synthesis process of a 3-DOF (θX – θY – θZ) CPM using FACT [1, 86].9: Details of a microstructure used in homogenization method [73].10: A compliant clamp synthesized by homogenization method [73].11: Three states of element in SIMP method [1].12: A compliant displacement inverter synthesized by SIMP method [98].13: A compliant gripper synthesized by BESO method [59].14: Demonstration of level set method [109].15: A compliant gripper synthesized by level set method [107].16: Demonstration of ground structure method (a) design domain, (b) optimized result and (c) final design [113].17: Disconnected structures generated in ground structure method [55].18: Synthesis process of morphological representation method [71].19: A compliant gripper synthesized by morphological representation method [118].20: Concept of mechanism integrated method [120].21: Synthesis process of a prismatic compliant joint [75].24: 3-DOF planar-motion (X – Y – θZ) CPMs used in (a) precise motion system [42] and (b) MEMS device [128].25: Large-workspace 3-DOF (X – Y – θZ) CPMs with optimized stiffness and dynamic properties [74].26: Manipulators developed based on 3-DOF (θX – θY – Z) CPMs used in (a) micro- finger module [132] and (b) nanoimprint lithography process [129].27: 6-DOF CPM synthesized by rigid body replacement approach [49].28: 6-DOF CPM synthesized by constraint-based approach [135].29: EBM-printed 2-DOF pointing CPM (a) physical prototype built by Ti6Al4V material and (b) integrated with a thruster for positioning application [79].30: EBM-printed 2-DOF (X – Y) nano-positioner [138].31: Compliant joints with lattice flexures fabricated by EBM method [139].32: Lattice structures fabricated by EBM method [141].1: Model of CPM used in beam-based method.2: Structure of (a) C-T beam and (b) compliant limb.3: Flow of the beam-based method.4: Corresponding displacements of the CPM under a general load.5: Design variables of the dynamic optimization process defined by (a) the C-T beam and (b) the end effector.6: Structure of (a) one compliant limb and (b) the entire CPM after the stiffness optimization process.7: (a) Synthesized CPM and (b) the first resonant mode simulated via ANSYS.8: Prototype of the synthesized CPM fabricated by milling method.9: Experimental setup for evaluating the compliance along the Z axis.10: Compliance along the Z axis with the experimental results plotted against the predicted, FEA and PRB model.