Skip to main content
SpringerLink
Log in

Worst case identification based topology optimization of a 2-DoF hybrid robotic arm

  • Regular Paper
  • Published:
International Journal of Intelligent Robotics and Applications Aims and scope Submit manuscript

Abstract

In the design of robotic arms, structural topology optimization considering variable configurations with high computational efficiency is still a challenging issue. In this paper, the worst case identification based topology optimization of a 2-DoF hybrid robotic arm is accomplished, and the presented work mainly covers: (1) efficient worst case identification; (2) optimization problem construction and (3) iterative criterion and filtering method with fast convergence. The forward kinematics are investigated to identify the workspace. Thereafter, the equivalent external load is proposed to unify the effect of axial load and shear by force analysis and compliance calculation. The worst case is the load case with maximum compliance and can be located efficiently by searching for the maximum equivalent external load. The optimization problem is constructed based on the solid isotropic material with penalization (SIMP) interpolation scheme. For links with multiple worst cases, the objective function is constructed as the weighted sum of compliance under each worst case. For better computational efficiency, the modified guide-weight method is used to solve the optimization problem. To eliminate the mesh dependence and checkerboard problem, a guide weight filtering method is proposed. Under the guidance of derived optimal topology, the CAD model of the hybrid robotic arm is presented. The effect of the optimization is testified through performance comparison in finite element analysis. The optimization method can derive the optimal topology with global validity within allowable computational time and the optimization approach can be applied to other hybrid robotic arms as well.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

Similar content being viewed by others

References

  • Bendsøe, M.P.: Optimal shape design as a material distribution problem. Struct. Optim. 1(4), 193–202 (1989)

    Google Scholar 

  • Bendsøe, M.P., Kikuchi, N.: Generating optimal topologies in structural design using a homogenization method. Comput. Methods Appl. Mech. Eng. 71(2), 197–224 (1988)

    MathSciNet  MATH  Google Scholar 

  • Ben-Tal, A., Nemirovski, A.: Robust truss topology design via semidefinite programming. SIAM J. Optim. 7(4), 991–1016 (1997)

    MathSciNet  MATH  Google Scholar 

  • Bi, W.Y., Xie, F.G., Liu, X.J., Luo, X.: Optimal design of a novel 4-degree-of-freedom parallel mechanism with flexible orientation capability. Proc. Inst. Mech. Eng. Part B J. Eng. Manuf. 233(2), 632–642 (2019)

    Google Scholar 

  • Bruyneel, M., Duysinx, P., Fleury, C.: A family of MMA approximations for structural optimization. Struct. Multidiscip. Optim. 24(4), 263–276 (2002)

    Google Scholar 

  • Chen, S. X., Ye, S. H.: Criterion method for the optimal design of antenna structure. Acta Mech. Sol. Sinica 5(4), 482–498 (1984)

  • Chen, S.X., Ye, S.H.: A guide-weight criterion method for the optimal design of antenna structures. Eng. Optim. 10(3), 199–216 (1986)

    Google Scholar 

  • Chen X., Liu X. J., & Xie F. G.: Screw theory based singularity analysis of Lower-Mobility parallel robots considering the Motion/Force transmissibility and constrainability. Math. Prob. Eng. 2015, 487956 (2015)

  • Da Silva Smith, O.: Topology optimization of trusses with local stability constraints and multiple loading conditions—a heuristic approach. Struct. Optim. 13(2–3), 155–166 (1997)

    Google Scholar 

  • Diaz, A., Sigmund, O.: Checkerboard patterns in layout optimization. Struct. Optim 10(1), 40–45 (1995)

    Google Scholar 

  • Essiet, I.O., Sun, Y., Wang, Z.: Improved genetic algorithm based on particle swarm optimization-inspired reference point placement. Eng. Optim. 51(7), 1097–1114 (2019)

    MathSciNet  Google Scholar 

  • Fleury, C., Braibant, V.: Structural optimization: a new dual method using mixed variables. Int. J. Numer. Meth. Eng. 23(3), 409–428 (1986)

    MathSciNet  MATH  Google Scholar 

  • Fujii, D., Kikuchi, N.: Improvement of numerical instabilities in topology optimization using the SLP method. Struct. Multidiscip. Optim. 19(2), 113–121 (2000)

    Google Scholar 

  • Haber, R.B., Jog, C.S., Bendsøe, M.P.: A new approach to variable-topology shape design using a constraint on perimeter. Struct. Optim 11(1–2), 1–12 (1996)

    Google Scholar 

  • Jin, X., Li, G.X., Zhang, M.: Design and optimization of nonuniform cellular structures. Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci. 232(7), 1280–1293 (2018)

    Google Scholar 

  • Kharmanda, G., Olhoff, N., Mohamed, A., Lemaire, M.: Reliability-based topology optimization. Struct. Multidiscip Optim. 26(5), 295–307 (2004)

    Google Scholar 

  • Liu, X.J., Li, Z.D., Chen, X.: A new solution for topology optimization problems with multiple loads: the guide-weight method. Sci. China Technol. Sci. 54(6), 1505–1514 (2011)

    MATH  Google Scholar 

  • Liu, X.J., Wang, C., Zhou, Y.H.: Topology optimization of thermoelastic structures using the guide-weight method. Sci. China Technol. Sci. 57(5), 968–979 (2014)

    Google Scholar 

  • Liu, X.J., Li, J., Zhou, Y.H.: Kinematic optimal design of a 2-degree-of-freedom 3-parallelogram planar parallel manipulator. Mech. Mach. Theory 87, 1–17 (2015)

    Google Scholar 

  • Lombardi, M., Haftka, R.T.: Anti-optimization technique for structural design under load uncertainties. Comput. Methods Appl. Mech. Eng. 157(1–2), 19–31 (1998)

    MATH  Google Scholar 

  • Luh, G.C., Lin, C.Y.: Optimal design of truss-structures using particle swarm optimization. Comput. Struct. 89(23–24), 2221–2232 (2011)

    Google Scholar 

  • Luo, Y., Kang, Z., Luo, Z., Li, A.: Continuum topology optimization with non-probabilistic reliability constraints based on multi-ellipsoid convex model. Struct. Multidiscip. Optim. 39(3), 297–310 (2009)

    MathSciNet  MATH  Google Scholar 

  • Luo, X., Xie, F.G., Liu, X.J., Li, J.: Error modeling and sensitivity analysis of a novel 5-degree-of-freedom parallel kinematic machine tool. Proc. Inst. Mech. Eng. Part B J. Eng. Manuf. 233(6), 1637–1652 (2019)

    Google Scholar 

  • Matsui, K., Terada, K.: Continuous approximation of material distribution for topology optimization. Int. J. Numer. Meth. Eng. 59(14), 1925–1944 (2004)

    MathSciNet  MATH  Google Scholar 

  • Panagant, N., Bureerat, S.: Truss topology, shape and sizing optimization by fully stressed design based on hybrid grey wolf optimization and adaptive differential evolution. Eng. Optim. 50(10), 1645–1661 (2018)

    MathSciNet  Google Scholar 

  • Rozvany, G.I.N., Zhou, M.: The COC algorithm, part I: cross-section optimization or sizing. Comput. Methods Appl. Mech. Eng. 89(1–3), 281–308 (1991)

    Google Scholar 

  • Sedaghati, R., Tabarrok, B., Suleman, A., Dost, S.: Optimization of adaptive truss structures using the finite element force method based on complementary energy. Trans. Can. Soc. Mech. Eng. 24(1B), 263–271 (2000)

    Google Scholar 

  • Sethian, J.A., Wiegmann, A.: Structural boundary design via level set and immersed interface methods. J. Comput. Phys. 163(2), 489–528 (2000)

    MathSciNet  MATH  Google Scholar 

  • Sigmund, O.: Morphology-based black and white filters for topology optimization. Struct. Multidiscip. Optim. 33(4–5), 401–424 (2007)

    Google Scholar 

  • Smyl, D.: An inverse method for optimizing elastic properties considering multiple loading conditions and displacement criteria. J. Mech. Des. 140(11), 111411 (2018)

    Google Scholar 

  • Stolpe, M., Svanberg, K.: An alternative interpolation scheme for minimum compliance topology optimization. Struct. Multidiscip. Optim. 22(2), 116–124 (2001)

    Google Scholar 

  • Sui, Y.K., Yang, D.Q., Sun, H.C.: Uniform ICM theory and method on optimization of structural topology for skeleton and continuum structures. Chin. J. Comput. Mech. 17(1), 28–33 (2000)

    Google Scholar 

  • Svanberg, K.: The method of moving asymptotes—a new method for structural optimization. Int. J. Numer. Meth. Eng. 24(2), 359–373 (1987)

    MathSciNet  MATH  Google Scholar 

  • Wang, X., Zhang, D., Zhao, C., Zhang, P., Zhang, Y., Cai, Y.: Optimal design of lightweight serial robots by integrating topology optimization and parametric system optimization. Mech. Mach. Theory 132, 48–65 (2019)

    Google Scholar 

  • Xie, Y.M., Steven, G.P.: A simple evolutionary procedure for structural optimization. Comput. Struct. 49(5), 885–896 (1993)

    Google Scholar 

  • Xie, F.G., Liu, X.J., Wu, C., Zhang, P.: A novel spray painting robotic device for the coating process in automotive industry. Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci. 229(11), 2081–2093 (2015)

    Google Scholar 

  • Xu, H.Y., Guan, L.W., Chen, X., Wang, L.P.: Guide-weight method for topology optimization of continuum structures including body forces. Finite Elem. Anal. Des. 75, 38–49 (2013)

    MathSciNet  MATH  Google Scholar 

  • Zillober, C., Schittkowski, K., Moritzen, K.: Very large scale optimization by sequential convex programming. Optim. Methods Softw 19(1), 103–120 (2004)

    MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

This work is supported by the National Key Scientific and Technological Project of China under Grant No. 2018ZX04018001, National Natural Science Foundation of China under Grant No. 91948301, and Beijing Municipal Science and Technology Commission under Grant No. Z181100003118003.

Author information

Authors and Affiliations

  1. The State Key Laboratory of Tribology and Tsinghua University (DME)-Siemens Joint Research Center for Advanced Robotics, Department of Mechanical Engineering (DME), Tsinghua University, Beijing, 100084, China

    Zenghui Chong, Fugui Xie, Xin-Jun Liu, Jinsong Wang & Peng Li

  2. Beijing Key Lab of Precision/Ultra-Precision Manufacturing Equipments and Control, Tsinghua University, Beijing, 100084, China

    Fugui Xie & Xin-Jun Liu

Authors
  1. Zenghui Chong
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Fugui Xie
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Xin-Jun Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Jinsong Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Peng Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Fugui Xie or Xin-Jun Liu.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Chong, Z., Xie, F., Liu, XJ. et al. Worst case identification based topology optimization of a 2-DoF hybrid robotic arm. Int J Intell Robot Appl 4, 136–148 (2020). https://doi.org/10.1007/s41315-020-00133-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s41315-020-00133-4

Keywords

Search

Navigation