Mechanical and geometric advantages in compliant mechanism optimization

doi:10.1007/s11465-009-0066-1

Front Mech Eng Chin

2009, Vol. 4

Issue (3) : 229-241 https://doi.org/10.1007/s11465-009-0066-1

RESEARCH ARTICLE

Mechanical and geometric advantages in compliant mechanism optimization

Michael Yu WANG(

)

Department of Mechanical & Automation Engineering, The Chinese University of Hong Kong, Hong Kong, China

Download: PDF(363 KB) HTML
Export: BibTeX | EndNote | Reference Manager | ProCite | RefWorks

Abstract

This paper presents a focused examination of the mechanical and geometric advantages in compliant mechanisms and their ramifications in the design formulations of compliant mechanisms posed as a topology optimization problem. With a linear elastic structural analysis, we quantify mechanical (and geometric) advantage in terms of the stiffness elements of the mechanism's structure. We then analyze the common formulations of compliant mechanism optimization and the role of the external springs added in the formulations. It is shown that the common formulations using mechanical (or geometric) advantage would directly emulate at best a rigid-body linkage to the true optimum design. As a result, the topology optimization generates point flexures in the resulting optimal mechanisms. A case study is investigated to demonstrate the resulting trends in the current formulations.

Keywords compliant mechanisms topology optimization mechanical advantage pseudo rigid-body mechanisms

Corresponding Author(s): WANG Michael Yu,Email:yuwang@mae.cuhk.edu.hk

Issue Date: 05 September 2009

Cite this article:

Michael Yu WANG. Mechanical and geometric advantages in compliant mechanism optimization[J]. Front Mech Eng Chin, 2009, 4(3): 229-241.

URL:

https://academic.hep.com.cn/fme/EN/10.1007/s11465-009-0066-1
https://academic.hep.com.cn/fme/EN/Y2009/V4/I3/229

Fig.1 Schematic of monolithic compliant mechanism

Fig.2 (a) Compliant gripper with its boundary and loading conditions; (b) stress contours with concentrated stress in the hinge areas

Fig.3 Input-output stiffness diagram of continuum compliant mechanism

Fig.4 Schematic illustration of optimal solutions. (a) , : non-singular structure without material connection between input and output ports; (b) , : singular structure with a rigid-body displacement mode and without material connection between input and output ports; (c) , : positive semi-definite structure with material connection between input and output ports, and with a rigid-body displacement mode; (d) , : positive definite structure as a proper design solution with material connection between input and output ports, and without any rigid-body displacement mode

Fig.5 Design domain of compliant force inverter

Fig.6 Optimal force inverters for four different volume ratios: (a) volume ratio of 0.4 and M of 0.75, (b) volume ratio of 0.25 and M of 0.77, (c) volume ratio of 0.2 and M of 0.79, and (d) volume ratio of 0.1 and M of 0.80. In (a), the analogous rigid-body linkage is also shown

Fig.7 Iterations of force inverter design (top-half only)

Fig.8 Objective function during iterations

1	Salamon B A, Midha A. An introduction to mechanical advantage in compliant mechanisms. J Mech Des , 1998, 120(2): 311–316 doi: 10.1115/1.2826974
2	Howell L L. Compliant Mechanisms. New York: John Wiley & Sons, 2001
3	Ananthasuresh G K, Kota S, Kikuchi N. Strategies for Systematic Synthesis of Compliant MEMS. Chicago: ASME Winter Annual Meeting, Dynamic Systems and Control Division , 1994: 677–686
4	Paros J M, Weisbord L. How to design flexure hinges. Machine Design , 1965, 37: 151–156
5	Burns R H, Crossley F R E. Kinetostatic Synthesis of Flexible Link Mechanisms. ASME Paper No. 68–Mech–36 , 1968
6	Howell L L, Midha A. A loop-closure theory for the analysis and synthesis of compliant mechanisms. Journal of Mechanical Design, Transactions of the ASME , 1996, 118: 121–125 doi: 10.1115/1.2826842
7	Midha, Norton T W, Howell L L. On the nomenclature, classification, and abstractions of compliant mechanisms. J Mech Des , 1994, 116(1): 270–280 doi: 10.1115/1.2919358
8	Sigmund O. On the design of compliant mechanisms using topology optimization. Mechanics of Structures and Machines , 1997, 25(4): 495–526
9	Frecker M I, Ananthasuresh G K, Nishiwaki S, Kikuchi N, Kota S. Topological synthesis of compliant mechanisms using multi-criteria optimization. Journal of Mechanical Design , 1997, 19(2): 238–245 doi: 10.1115/1.2826242
10	Yin L, Ananthasuresh G K. Design of distributed compliant mechanisms. Mechanics Based Design of Structures and Machines , 2003, 31(2): 151–179 doi: 10.1081/SME-120020289
11	Saxena A, Ananthasuresh G K. On an optimal property of compliant topologies. Structural and Multidisciplinary Optimization , 2000, 19: 36–49 doi: 10.1007/s001580050084
12	Hetrick J, Kota S. An energy efficiency formulation for parametric size and shape optimization of compliant mechanism. ASME Journal of Mechanical Design , 1999, 121: 229–234 doi: 10.1115/1.2829448
13	Chen S K, Wang M Y. Designing distributed compliant mechanisms with characteristic stiffness. The ASME 2007 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference IDETC/CIE 2007, Las Vegas, Nevada, USA, 2007. Paper No. DETC2007–34437
14	Wang M Y, Chen S K. Compliant mechanism optimization: analysis and design with intrinsic characteristic stiffness. Mechanics Based Design of Structures and Machines , 2009 (in press)
15	Rahmatalla S, Swan C C. Sparse monolithic compliant mechanisms using continuum structural topology optimization. International Journal for Numerical Methods in Engineering , 2005, 62: 1579–1605 doi: 10.1002/nme.1224
16	Deepak S R, Dinesh M, Sahu D, Ananthasuresh G K. A comparative study of the formulations and benchmark problems for topology optimization of compliant mechanisms. Journal of Mechanisms and Robotics , 2009, 1: 011003 doi: 10.1115/1.2959094
17	Wang M Y, Chen S K, Wang X M, Mei Y L. Design of multimaterial compliant mechanisms using level set methods. ASME Journal of Mechanical Design , 2005, 127: 941–956 doi: 10.1115/1.1909206
18	Bends ? e M P, Sigmund O. Topology Optimization: Theory, Methods and Applications. Springer–Verlag, Berlin, 2003
19	Chen S K. Compliant Mechanisms with Distributed Compliance and Characteristic Stiffness: A Level Set Approach. Hong Kong: PhD Thesis, The Chinese University of Hong Kong, 2006
20	Pedersen C B, Buhl T, Sigmund O. Topology synthesis of large-displacement compliant mechanisms. International Journal for Numerical Methods in Engineering , 2001, 50: 2683–2750 doi: 10.1002/nme.148
21	Yin L, Ananthasuresh G K. A novel topology design scheme for the multi-physics problems of electro-thermally actuated compliant micromechanisms. Sensors and Actuators, Series A: physical , 2002, 97-98: 599–609
22	Yin L, Ananthasuresh G K. Topology optimization of compliant mechanisms with multiple materials using a peak function material interpolation scheme. Structural and Multidisciplinary Optimization , 2001, 23(1): 49–62 doi: 10.1007/s00158-001-0165-z
23	Joo J, Kota S, Kikuchi N. Topological synthesis of compliant mechanisms using linear beam elements. Mechanics and Structures of Machines , 2000, 28: 245–280 doi: 10.1081/SME-100102022
24	Kim C J, Kota S, Moon Y M. An instant center approach towards the conceptual design of compliant mechanisms. ASME Journal of Mechanical Design , 2006, 128: 542–550 doi: 10.1115/1.2181992
25	Wang M Y. A Kinetoelastic approach to continuum compliant mechanism optimization. USA: ASME 2008 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference IDETC/CIE 2008, Paper No. DETC2008–49426
26	Luo Z, Wang M Y, Tong L Y, Wang S Y. Shape and topology optimization of compliant mechanisms using a parameterization level set method. Journal of Computational Physics , 2008, 227: 5561–5581 doi: 10.1016/j.jcp.2008.02.003
27	Wang M Y. A kinetoelastic formulation of compliant mechanism optimization. ASME Journal of Mechanisms and Robotics , 2009, 1(2): 021011 doi: 10.1115/1.3056476

[1]	Peng WEI, Wenwen WANG, Yang YANG, Michael Yu WANG. Level set band method: A combination of density-based and level set methods for the topology optimization of continuums[J]. Front. Mech. Eng., 2020, 15(3): 390-405.
[2]	Emmanuel TROMME, Atsushi KAWAMOTO, James K. GUEST. Topology optimization based on reduction methods with applications to multiscale design and additive manufacturing[J]. Front. Mech. Eng., 2020, 15(1): 151-165.
[3]	Xianda XIE, Shuting WANG, Ming YE, Zhaohui XIA, Wei ZHAO, Ning JIANG, Manman XU. Isogeometric topology optimization based on energy penalization for symmetric structure[J]. Front. Mech. Eng., 2020, 15(1): 100-122.
[4]	Manman XU, Shuting WANG, Xianda XIE. Level set-based isogeometric topology optimization for maximizing fundamental eigenfrequency[J]. Front. Mech. Eng., 2019, 14(2): 222-234.
[5]	Jikai LIU, Qian CHEN, Xuan LIANG, Albert C. TO. Manufacturing cost constrained topology optimization for additive manufacturing[J]. Front. Mech. Eng., 2019, 14(2): 213-221.
[6]	Mariana MORETTI, Emílio C. N. SILVA. Topology optimization of piezoelectric bi-material actuators with velocity feedback control[J]. Front. Mech. Eng., 2019, 14(2): 190-200.
[7]	Junjie ZHAN, Yangjun LUO. Robust topology optimization of hinge-free compliant mechanisms with material uncertainties based on a non-probabilistic field model[J]. Front. Mech. Eng., 2019, 14(2): 201-212.
[8]	Long JIANG, Yang GUO, Shikui CHEN, Peng WEI, Na LEI, Xianfeng David GU. Concurrent optimization of structural topology and infill properties with a CBF-based level set method[J]. Front. Mech. Eng., 2019, 14(2): 171-189.
[9]	Markus J. GEISS, Jorge L. BARRERA, Narasimha BODDETI, Kurt MAUTE. A regularization scheme for explicit level-set XFEM topology optimization[J]. Front. Mech. Eng., 2019, 14(2): 153-170.
[10]	Yu-Chin CHAN, Kohei SHINTANI, Wei CHEN. Robust topology optimization of multi-material lattice structures under material and load uncertainties[J]. Front. Mech. Eng., 2019, 14(2): 141-152.
[11]	Jiadong DENG, Claus B. W. PEDERSEN, Wei CHEN. Connected morphable components-based multiscale topology optimization[J]. Front. Mech. Eng., 2019, 14(2): 129-140.
[12]	Yingjun WANG,David J. BENSON. Geometrically constrained isogeometric parameterized level-set based topology optimization via trimmed elements[J]. Front. Mech. Eng., 2016, 11(4): 328-343.
[13]	Guangbo HAO,Haiyang LI,Suzen KEMALCAN,Guimin CHEN,Jingjun YU. Understanding coupled factors that affect the modelling accuracy of typical planar compliant mechanisms[J]. Front. Mech. Eng., 2016, 11(2): 129-134.
[14]	Guangbo HAO,Jingjun YU,Haiyang LI. A brief review on nonlinear modeling methods and applications of compliant mechanisms[J]. Front. Mech. Eng., 2016, 11(2): 119-128.
[15]	Shutian LIU,Quhao LI,Wenjiong CHEN,Liyong TONG,Gengdong CHENG. An identification method for enclosed voids restriction in manufacturability design for additive manufacturing structures[J]. Front. Mech. Eng., 2015, 10(2): 126-137.

Viewed

Full text

Abstract

Cited

Shared

Discussed