Abstract
A unified procedure for the synthesis of planar linkages that may take the form of rigid body, fully compliant or partially compliant mechanisms is presented. The procedure automates the selection of mechanism topology as characterized by the number and connectivity of the links as well as the nature of the connections between them, the mechanism shape as characterized by the shapes of the individual links, and the mechanism dimensions which include the locations of the joints and the cross-sectional dimensions of the links. The synthesis task is posed as a constrained optimization problem and is solved by a hybrid, elite-preserving genetic algorithm. Three examples of compact mechanisms that trace different non-smooth paths in response to a single, monotonic and bounded force input are used to illustrate the synthesis capability of the procedure. Prototypes of the designs are built and tested to verify their performance. It is observed that in all three examples, partially compliant mechanism designs offer better conformance with design intent than either rigid body or fully compliant mechanisms.
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References
Ananthasuresh GK, Kota S (1995) Designing compliant mechanisms. Mechanical Engineering, Magazine of the ASME 117(11):93–96
Artobolevskii II (1964) Mechanisms for the generation of plane curves. Pergammon and Macmillan, Oxford
Bannerjee A, Bhattacharya B, Mallik AK (2009) Forward and inverse analyses of smart compliant mechanisms for path generation. Mech Mach Theory 44(2):369–381
Crisfield MA (1991) Nonlinear finite element analysis of solids and structures, vol 1. Wiley, New York
Gao X-S, Zhu C-C, Chou S-C, Ge J-X (2001) Automated generation of kempe linkages for algebraic curves and surfaces. Mech Mach Theory 36:1019–1033
Hetrick JA, Kota S (1999) An energy formulation for parametric size and shape optimization of compliant mechanisms. Trans ASME J Mech Des 121(2):229–234
Howell LL (2001) Compliant mechanisms. Wiley Interscience, Wiley, New York
Hrones JA, Nelson GL (1951) Analysis of the four-bar linkage. Technology Press of MIT and Wiley, New York
Huey CO Jr, Dixon MW (1974) The cam-link mechanism for structural error-free path and function generation. Mech Mach Theory 9:367–384
Hunt KH (1978) Kinematic geometry of mechanisms. Oxford University Press, Oxford
Kawamoto A, Bendsøe MP, Sigmund O (2004) Articulated mechanism design with a degree of freedom constraint. Int J Numer Methods Eng 61:1520–1545
Kempe AB (1876) On a general method of describing planar curves of the n th degree by linkwork. Proc Lond Math Soc 7:213–216
Mankame ND (2004) Investigations on contact-aided compliant mechanisms. PhD thesis, University of Pennsylvania, Philadelphia, PA. Advisor: G. K. Ananthasuresh
Mankame ND, Ananthasuresh GK (2004) Topology optimization for synthesis of contact-aided compliant mechanisms using regularized contact modeling. Comput Struct 82:1267–1290
Mankame ND, Ananthasuresh GK (2007) Synthesis of contact-aided compliant mechanisms for non-smooth path generation. Int J Numer Methods Eng 69:2564–2605
Mettlach GA (1996) Analysis and design of compliant mechanisms using analytical and graphical techiniques. PhD thesis, Purdue University, West Lafayette, IN
Midha A (1993) In: Erdman AG (ed) Modern kinematics—the developments in the last forty years, chapter 9: elastic mechanisms. Wiley, New York
Pedersen CBW, Buhl T, Sigmund O (2001) Topology synthesis of large displacement compliant mechanisms. Int J Numer Methods Eng 50(2):2683–2705
Rai AK, Saxena A, Mankame ND (2007) Synthesis of path generating compliant mechanisms using initially curved frame elements. J Mech Des 129:1056–1063
Ramrakhyani DS, Frecker MI, Lesiutre GA (2006) Hinged beam elements for the topology design of compliant mechanisms using the ground structure approach. In: Proc. 2006 ASME design engineering technical conferences, DETC2006-99439
Saxena A, Ananthasuresh GK (2001) Topology synthesis of compliant mechanisms for non-linear force-deflection and curved path specifications. Trans ASME, J Mech Des 123:1–10
Saxena A, Ananthasuresh GK (2003) A computational approach to the number synthesis of linkages. J Mech Des 125:1–10
Sigmund O (2001) Design of multiphysics actuators using topology optimization—parts I and II. Comput Methods Appl Mech Eng 190:6577–6627
Sriram BR, Mruthyunjaya TS (1995) Synthesis of path generating flexible-link mechanisms. Comput Struct 56(4):657–666
Streinu I (2003) A crash course in rigidity theory, lectures 1 and 2. World Wide Web, mhtml:http://maven.smith.edu/ streinu/Talks/StanfordRigid/lecture1.mht!lecture1_files/frame.htm. Accessed 22 Sept 2008
Swan CC, Rahmatalla SF (2004) Design and control of path following compliant mechanisms. In: Proc. of the 2004 ASME design engineering technical conferences, DETC2004–57441
Ullah I, Kota S (1997) Optimal synthesis of mechanisms for path generation using fourier descriptors and global search methods. Trans ASME J Mech Des 119:504–510
Winter SJ, Shoup TE (1973) The displacement analysis of path-generating flexible-link mechanisms. Mech Mach Theory 7:443–451
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Rai, A.K., Saxena, A. & Mankame, N.D. Unified synthesis of compact planar path-generating linkages with rigid and deformable members. Struct Multidisc Optim 41, 863–879 (2010). https://doi.org/10.1007/s00158-009-0458-1
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DOI: https://doi.org/10.1007/s00158-009-0458-1