Structural optimization of typical rigid links in a parallel kinematic machine

Abstract

The motion dynamics and accuracy of parallel kinematic machines largely depend on the weights and rigidity of typical rigid links. Therefore, these parts should be designed in such a way that they are light but rigid. This work employs the techniques of topology and size optimization to design two typical rigid links of a parallel kinematic machine (PKM) and subsequently obtains applicable structures for them. The calculation models are established, and a new algorithm called the Guide-Weight method is introduced to solve topology optimization problems. The commercial software Ansys is used to perform size optimization.

Keywords

topology optimization / size optimization / parallel kinematic machine (PKM)

References

[1] Fassi I, Wiens G J. Multiaxis machining: PKMs and traditional machining centers. Journal of Manufacturing Processes, 2000, 2(1): 1–14

[2] Weck M, Staimer D. Parallel kinematic machines-current state and future potentials. CIRP Annals- Manufacturing Technology, 2002, 51(2): 671–683

[3] Bonnemains T, Chanal H, Bouzgarrou B, Ray P. Stiffness computation and identification of parallel kinematic machine tools. Journal of Manufacturing Science and Engineering, 2009, 131(4): 041013.1–041013.7

[4] Li Y, Xu Q. Stiffness analysis for a 3-PUU parallel kinematic machine. Mechanism and Machine Theory, 2008, 43(2): 186–200

[5] Zhang D, Wang L, Lang S Y T. Parallel kinematic machines: design, analysis and simulation in an integrated virtual environment. Journal of Mechanical Design, 2005, 127(4): 580–588

[6] Li Y, Xu Q. Dynamic modeling and robust control of a 3-PRC translational parallel kinematic machine. Robotics and Computer-Integrated Manufacturing, 2009, 25: 630–640

[7] Bendsoe M P, Sigmund O. Topology Optimization: Theory, Methods and Applications. Berlin: Springer, 2003

[8] Eschenauer H A, Olhoff N. Topology optimization of continuum structure: a review. Applied Mechanics Reviews, 2001, 54(4): 331–390

[9] Hull P V, Canfield S. Optimal synthesis of compliant mechanisms using subdivision and commercial FEA. Journal of Mechanical Design, 2006, 128(2): 337–348

[10] Wang M Y. Mechanical and geometric advantages in compliant mechanism optimization. Frontiers of Mechanical Engineering in China, 2009, 4(3): 229–241

[11] Patel N M, Kang B S, Renaud J E, Tovar A. Crashworthiness design using topology optimization. Journal of Mechanical Design, 2009, 131(6): 061013.1–061013.12

[12] Albert A, Jens O.Integrated structural and controller optimization in dynamic mechatronic systems. Journal of Mechanical Design, 2010, 132(4): 041008.1–041008.8

[13] Krog L, Tucker A, Rollema G. Application of topology, sizing and shape optimization methods to optimal design of aircraft components. In: Proceedings of the 3rd Altair UK HyperWorks Users Conference, 2002

[14] Hassani B, Hinton E. A review of homogenization and topology optimization I: homogenization theory for media and periodic structure. Computers & Structures, 1998, 69(6): 707–717

[15] Hassani B, Hinton E. A review of homogenization and topology optimization II: analytical and numerical solution of homogenization equations. Computers & Structures, 1998, 69(6): 719–738

[16] Hassani B, Hinton E. A review of homogenization and topology optimization III: topology optimization using optimality criteria. Computers & Structures, 1998, 69(6): 739–756

[17] Bendsøe M P, Sigmund O. Material interpolation schemes in topology optimization. Archive of Applied Mechanics, 1999, 69(9–10): 635–654

[18] Rozvany G I N. A critical review of established methods of structural topology optimization. Structural and Multidisciplinary Optimization, 2009, 37(3): 217–237

[19] Rozvany G I N, Zhou M. The COC algorithm, part I: cross-section optimization or sizing. Computer Methods in Applied Mechanics and Engineering, 1991, 89(1–3): 281–308

[20] Rozvany G I N, Zhou M. The COC algorithm, part II: topological, geometrical and generalized shape optimization. Computer Methods in Applied Mechanics and Engineering, 1991, 89(1–3): 309–336

[21] Zhou M, Rozvany G I N. DCOC: an optimality criteria method for large systems part I: theory. Structural Optimization, 1992, 5(1): 12–25

[22] Zhou M, Rozvany G I N. DCOC: An optimality criteria method for large systems part II: Algorithm. Structural Optimization, 1992, 6(3): 250–262

[23] Bruyneel M, Duysinx P, Fleury C. A family of MMA approximations for structural optimization. Structural and Multidisciplinary Optimization, 2002, 24(4): 263–276

[24] Zhou M, Pagaldipti N, Thomas H L, Shyy Y K. An integrated approach to topology, sizing, and shape optimization. Structural and Multidisciplinary Optimization, 2004, 26(5): 308–317

[25] Chen S, Ye S A. Guide-Weight criterion method for the optimal design of antenna structures. Engineering Optimization, 1986, 10(3): 199–216

[26] Chen S. Analysis, synthesis and optimization of engineering structural systems. Hongkong: China Science Culture Publishing House, 2008

[27] Chen S, Torterelli D A. Three-dimensional shape optimization with variational geometry. Structural Optimization, 1997, 13(2–3): 81–94

[28] Hetrick J A, Kota S. An energy formulation for parametric size and shape optimization of compliant mechanisms. Journal of Mechanical Design, 1999, 121(2): 229–234

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