Abstract
We present an evolution-based method for optimal mechanism {synthesis}. It is based on the embedding of the Euclidean motion group in the space of affine displacements upon which an object-oriented Euclidean metric is imposed. This Euclidean structure allows the use of curve and surface evolution techniques from computer aided design and image processing. We demonstrate the algorithm by synthesizing planar four-bar mechanisms and we show how to modify it so that the resulting four-bar is free of circuit defects.
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References
Aigner, M. Jüttler, B. (2007), “Approximation Flows in Shape Manifolds”, in: Curve and Surface Design, Avignon 2006, ed. by Chenin, P., Lyche, T. and Schumaker, L. L., Nashboro Press, pp. 1–10.
Aigner, M. and Jüttler, B. (2008), Gauss-Newton-type Techniques for Robustly Fitting Implicitly Defined Curves and Surfaces to Unorganized Data Points, FSP Report Industrial geomentry 65, To appear in Proc. Shape Modelling International 2008, IEEE; available at http://www.ig.jku.at, University Linz.
Ainger, M., Šír, Z. and Jüttler, B. (2007), “Evolution-Based Least-Squares Fitting Using Pythagorean Hodograph Spline Curves”, Comput. Aided Geom. Design 24:6, pp. 310–322.
Angeles, J. (2006), “Is There a Characteristic Length of Rigid-Body Displacements?”, Mech. Machine Theory 41:8, pp. 884–896.
Belta, C. and Kumar, V. (2002), “An SVD-Based Projection Method for Interpolation on SE(3)”, IEEE Trans. Robotics Automation18:3, pp. 334–345.
Cabrera, J. A., Simon, A. and Prado, M. (2002), “Optimal Synthesis of Mechanisms with Genetic Algorithms”, Mech. Machine Theory 37:10, pp. 1165–1177.
Chase, T. R. and Mirth, J. A. (1993), “Circuits and Branches of Single-Degree-of-Freedom Planer Linkages”, ASME J. Mechanical Design 115:2, pp. 223–230.
Chen, C. and Angeles, J. (2007), “Kinematic Synthesis of an Eight-Bar Linkage to Visit Eleven Poses Exactly”, in: Proc. CDEN/C2E2 2007 Conference, Winnipeg, Alberta.
Chirikjian, G. S. and Zhou, S. (1998), “Metrics on Motion and Deformation of Solid Models”, ASME J. Mechanical Design 120:2, pp. 252–261.
Hayes, M. J. D., Luu, T. and Chang, X.-W. (2004), “Kinematic Mapping Application to Approximate Type and Dimension Synthesis of Planar Mechanisms”, in: Advances in Robot Kinematics, ed. by Lenarˇiˇ, J. and Galletti, C., Kluwer Academic Publishers.
Hofer, M. and Pottmann, H. (2004), “Energy-Minimizing Splines in Manifolds”, Transactions on Graphics 23:3, Proc. of ACM SIGGRAPH 2004, pp. 284–293.
Hofer, M., Pottmann, H. and Ravani, B. (2004), “From curve design algorithms to the design of rigid body motions”, The Visual Computer 20:5, pp. 279–297.
Kunjur, A. and Krishnamurty, S. (1995), “Genetic Algorithms in Mechanism Synthesis”, in: Fourth Applied Mechanisms and Robotics Conference AMR 95-068, Cincinnati, Ohio, pp. 1–7.
Larochelle, P. M., Murray, A. P. and Angeles, J. (2004), “SVD and PD Based Projection Metrics on SE(n)”,in: On Advances in Robot Kinematics, ed. by Lenarˇiˇ, J. and Galetti, C., Dordrecht, Boston and London: Kluwer Academic Publishers, pp. 13–22.
Nawratil, G. (2007), “New Performance Indices for 6R Robots”, Mech. Machine Theory 42:11, pp. 1499–1511.
Nawratil, G., Pottmann, H. and Ravani, B. (2007), Generalized Penetration Depth Computation Based on Kinematical Geometry, Geometry Preprint Series 172, Vienna University of Technology.
Shiakolas, P. S., Koladiya, D. and Kebrle, J. (2002), “On the Optimum Synthesis of Four-Bar Linkages Using Differential Evolution and the Geometric Centroid of Precision Positions”, J. Inversive Problems Engineering 10:6, pp. 485–502.
Shiakolas, P. S., Koladiya, D. and Kebrle, J. (2005), “On the Optimum Synthesis of Six-Bar Linkages Using Differential Evolution and the Geometric Centroid of Precision Positions Technique”, Mech. Machine Theory 4:3, pp. 319–335.
Smaili, A. A. and Diab, N. A. (2005), “Optimum Synthesis of Mechanisms Using Tabu-Gradient Search Algorithm”, ASME J. Mechanical Design 127:5, pp. 917–923.
Yao, J. and Angeles, J. (2000), “Computation of All Optimum Dyads in the Approximate Synthesis of Planar Linkages for Rigid-Body Guidance”, Mech. Machine Theory 35:8, pp. 1065–1078.
Zhang, X., Zhou, J. and Ye, Y. (2000), “Optimal Mechanism Design Using Interior-point Methods”, Mech. Machine Theory 35:1, pp. 83–98.
Zhou, H. and Cheung Edmund, H. M (2001), “Optimal Synthesis of Crank-Rocker Linkages for Path Generation Using the Orientation Structural Error of the Fixed Link”, Mech. Machine Theory 36:8, pp. 973–982.
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Schröcker, HP., Jüttler, B., Aigner, M. (2009). Evolving Four-Bars for Optimal Synthesis. In: Ceccarelli, M. (eds) Proceedings of EUCOMES 08. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-8915-2_14
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DOI: https://doi.org/10.1007/978-1-4020-8915-2_14
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