Optimization of the Kinematic Sensitivity and the Greatest Continuous Circle in the Constant-orientation Workspace of Planar Parallel Mechanisms

Authors

1 Colorado School of Mines

2 University of Tehran

3 University of Tartu

Abstract

This paper presents the results of a comprehensive study on the efficiency of planar parallel mechanisms, considering their kinetostatic performance and also, their workspace. This aim is approached upon proceeding single- and multi-objective optimization procedures. Kinetostatic performances of ten different planar parallel mechanisms are analyzed by resorting to a recent index, kinematic sensitivity. Moreover, the greatest possible continuous circle in the constant-orientation workspace of the latter mechanisms is considered as another objective for the optimization procedures. Seeking the set of design parameters which compromises simultaneous optimal values for the two aforementioned objectives, i.e., kinematic sensitivity and workspace, necessitates launching a multi-objective optimization process. The mathematical framework adopted for the optimization problem is based on genetic algorithm. The results of multi-objective optimization are based on the sets of Pareto points, offering the most reliable decisions to reconciliate between some conï‌‚icting objectives. To this end, the ten planar parallel mechanisms are sorted into two sets based on their type of actuator, some of them with prismatic actuators and the other ones with revolute actuators. Finally, a comparison between performances of these mechanisms, according to the obtained results, is carried out.

Keywords


J. Angeles, Fundamentals of Robotic Mechanical Systems: Theory, Methods, and Algorithms, Springer, (2006).
J., Angeles, Is there a Characteristic Length of a Rigidbody Displacement?, Mechanism and Machine Theory, Vol. 41(8), (2006), 884–896.
S. Bai, M. R. Hansen and T. O. Andersen, Modeling of a Special Class of Spherical Parallel Manipulators with Euler Parameters, Robotica, Vol. 27(2), (2009),161.
S. Bai, M. R. Hansen and J. Angeles, A Robust Forwarddisplacement Analysis of Spherical Parallel Robots Mechanism and Machine Theory, Vol. 44(12), (2009), 2204–2216.
N. Binaud, S. Caro and P. Wenger, Sensitivity Comparison of Planar Parallel Manipulators, Mechanism and Machine Theory, Vol. 45(11), (2010), 1477–1490.
I. A. Bonev, D. Chablat, P. Wenger, Working and Assembly Modes of the Agile Eye, IEEE International Conference on Robotics and Automation (ICRA), (2006), 2317–2322.
I. A. Bonev, Geometric Analysis of Parallel Mechanisms, Ph.D. Thesis, Laval University, Quebec, Canada, (2002).
I. A. Bonev, D. Zlatanov and C. Gosselin, Singularity Analysis of 3-DOF Planar Parallel Mechanisms via Screw Theory, Journal of Mechanical Design, Vol. 1 25(3), (2003), 573 – 581.
S. Briot and I. A. Bonev, Are Parallel Robots More Accurate than Serial Robots?, Transactions of the Canadian Society for Mechanical Engineering, Vol. 31(4), (2007), 445–456.
P. Cardou, S. Bouchard and C. Gosselin, Kinematicsensitivity Indices for Dimensionally Nonhomogeneous Jacobian Matrices, IEEE Transactions on Robotics, Vol. 26(1), (2010), 166–173.
S. Caro, F. Bennis, P. Wenger, et al., Tolerance Synthesis of Mechanisms: a Robust Design Approach, Journal of Mechanical Design, Vol. 127, (2005), 86–94.
M. Daneshmand, M. H. Saadatzi, M. Tale Masouleh, M. B. Menhaj, Optimization of Kinematic Sensitivity and Workspace of Planar Parallel Mechanisms, Multibody Dynamics Thematic Conference, Zagreb, Croatia, (2013), 391 -392.
M. Daneshmand, M. Tale Masouleh, M. H. Saadatzi, M. B. Menhaj, On the Optimum Design of Planar Parallel Mechanisms Based on Kinematic Sensitivity and Workspace, CCToMM Symposium, IFToMM, Montreal, Quebec, Canada, (2013).
B. Dasgupta and T. Mruthyunjaya, The Stewart Platform Manipulator: A Review, Mechanism and Machine Theory, Vol. 35(1), (2000), 15–40.
A. Engelbrecht, A., Computational Intelligence: An Introduction, Wiley, 2007.
E. Faghih, M. Daneshmand, M. H. Saadatzi, M. Tale Masouleh, A Benchmark Study on the Kinematic Sensitivity of Planar Parallel Mechanisms, CCToMM Symposium, IFToMM, Montreal, Quebec, Canada, (2013).
M. H. Farzaneh Kaloorazi, S. Esfahani, M. Tale Masouleh, M. Daneshmand, Dimensional Synthesis of Planar Cable-driven Parallel Robots via Interval Analysis, CCToMM Symposium, IFToMM, Montreal, Quebec, Canada, (2013).
C. Gosselin and J. Angeles, The Optimum Kinematic Design of a Spherical Three-degree-of-freedom Parallel Manipulator. Journal of Mechanisms, Transmissions, and Automation in Design, Vol. 111(2), (1989), 202–207.
C. M. Gosselin, J. F. Hamel, The Agile Eye: a Highperformance Three-degree-of-freedom Camera-orienting Device, IEEE International Conference on Robotics and Automation (ICRA), (1994), 781–786.
W. Khan and J. Angeles, The Kinetostatic Optimization of Robotic Manipulators: The Inverse and the Direct Problems, Journal of Mechanical Design, Vol. 128(1), (2006), 168–178.
X. Kong, C. Gosselin, Type Synthesis of Parallel Mechanisms, Springer, Heidelberg, 2007.
Y. Li, Q. Xu, Design and Analysis of a New 3-DOF Compliant Parallel Positioning Platform for Nanomanipulation, 5th IEEE Conference on Nanotechnology, (2005), 861 –864.
J. Merlet, Jacobian, Manipulability, Condition Number, and Accuracy of Parallel Robots, Journal of Mechanical Design, Vol. 128, (2006), 199–206.
K. Price, R. M. Storn, J. A. Lampinen, Differential Evolution: A Practical Approach to Global Optimization, first ed., Springer-Verlag, New York, 2005.
M. H. Saadatzi, M. Tale Masouleh, H. Taghirad, C. Gosselin, P. Cardou, On the Optimum Design of 3-RPR Parallel Mechanisms, 19th Iranian IEEE Conference on Electrical Engineering (ICEE), (2011), 1 –6.
M. H. Saadatzi, Workspace and Singularity Analysis of 5DOF Symmetrical Parallel Robots with Linear Actuators, Master’s Thesis, Faculty of Electrical and Computer Engineering, K.N. Toosi University of Technology, Tehran, Iran, (2011).
M. H. Saadatzi, M. Tale Masouleh, H. D. Taghirad, C. Gosselin and P. Cardou, Geometric Analysis of the Kinematic Sensitivity of Planar Parallel Mechanisms, Transactions of the Canadian Society for Mechanical Engineering, Vol. 35(4), (2011), 477–490.
M. H. Saadatzi, M. Tale Masouleh, H. D. Taghirad, C. Gosselin, M. Teshnehlab, Multi-Objective Scale Independent Optimization of 3-RPR Parallel Mechanisms, 13th World Congress in Mechanism and Machine Science, Guanajuato, Mexico, (2011).
L. J. Stocco, S. Salcudean and F. Sassani, On the Use of Scaling Matrices for Task-specific Robot Design, IEEE Transactions on Robotics and Automation, Vol. 15(5), (1999), 958–965.
R. Storn and K. Price, Differential Evolution - A Simple and Efficient Heuristic for Global Optimization over Continuous Spaces, Journal of Global Optimization, Vol. 11 , (1997), 341 – 359.
Y. Takeda, H. Funabashi and Y. Sasaki, Development of a Spherical in-parallel Actuated Mechanism with Three Degrees of Freedom with Large Working Space and High Motion Transmissibility: Evaluation of Motion Transmissibility and Analysis of Working Space, JSME International Journal. Ser. C, Dynamics, Control, Robotics, Design and Manufacturing, Vol. 39(3), (1996), 541–548.
P. Wenger, C. Gosselin, B. Maill, B., A Comparative Study of Serial and Parallel Mechanism Topologies for Machine Tools, Parallel Kinematic Machine, (1999), 23- 32.
B. J. Yi, G. B. Chung, H. Y. Na, W. K. Kim and I. H. Suh, Design and Experiment of a 3-DOF Parallel Micromechanism Utilizing Flexure Hinges, IEEE Transactions on Robotics and Automation, Vol. 19(4), 604–612.
T, Yoshikawa, Manipulability of Robotic Mechanisms. The International Journal of Robotics Research, Vol. 4(2), (1985), 3–9.