Kinetostatic Performance Comparison of Spherical Parallel Mechanisms Extracted from Type Synthesis with Modeling Clearance in Passive Joints

Document Type : Research Article

Authors

1 Researcher, Human and Robot Interaction Laboratory, University of Tehran, Tehran, Iran

2 Human and Robot Interaction Laboratory, School of Electrical and Computer Engineering, University of Tehran,

3 Department of Mechanical Engineering, Malek Ashtar University of Technology, Tehran, Iran

Abstract

A spherical parallel mechanism is used to rotate a body around a fixed point. Different kinematic arrangements can be obtained for the robot with three degrees of rotational freedom. The most commonly used structure for this robot is the 3-RRR kinematic architecture which is an overconstrained parallel mechanism and causes several problems of mounting the mechanism. In this paper two non[1]overconstrained architectures 3-RRS and 3-RSR are compared with overconstrained one from the accuracy point of view based on the joint clearance. First, a method to obtain a model of moving platform pose (position and orientation) error based on the joint clearance is introduced which leads to a standard convex optimization problem. Then maximum values of six components of the pose error are computed in more than 1000 different configurations within their workspace. It is shown that this displacement is configuration dependent. The obtained results revealed that the 3-RRR spherical parallel mechanism has better position accuracy while in the case of orientation, the 3-RRS SPM has the lowest maximum error between spherical parallel mechanisms under study in the prescribed workspace. It can be concluded that non-overconstrained structures can be used instead of the overconstrained structure. Finally, a comparison was made between the performance indices and the presented method.

Keywords

Main Subjects

References

[1] C.M. Gosselin, J.-F. Hamel, The agile eye: a highperformance three-degree-of-freedom cameraorienting device, in:  Robotics and Automation, 1994. Proceedings., 1994 IEEE International Conference on, IEEE, 1994, pp. 781-786.
[2]   A. Safaryazdi, M. Zarei, O. Abolghasemi, M. Tale Masouleh, Experimental study on the modelbased control of a 2-degree-of-freedom spherical parallel robot camera stabilizer based on multithread programming concept, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 232(10) (2018) .7981-2881
[3]  A. Chaker, A. Mlika, M.A. Laribi, L. Romdhane, S. Zeghloul, Synthesis of spherical parallel manipulator for dexterous medical task, Frontiers of Mechanical Engineering, 7(2) (2012) 150-162.
[4]   M.T. Masouleh, M.H. Saadatzi, C.m. Gosselin, H.D. Taghirad, A geometric constructive approach for the workspace analysis of symmetrical 5-PRUR parallel mechanisms (3T2R), in:  ASME 2010 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, American Society of Mechanical Engineers, 2010, pp. 1335-1344.
[5]   C. Gosselin, J. Angeles, The optimum kinematic design of a spherical three-degree-of-freedom parallel manipulator, Journal of mechanisms, transmissions, and automation in design, 111(2) (1989) 202-207.
[6] C.M. Gosselin, É. St-Pierre, Development and experimentation of a fast 3-DOF camera-orienting  device, The International Journal of Robotics Research, 16(5) (1997) 619-630.
[7]    S. Bai, Optimum design of spherical parallel manipulators for a prescribed workspace, Mechanism and Machine Theory, 45(2) (2010) 200-211.
[8]  M. Daneshmand, M.H. Saadatzi, M.H.F. Kaloorazi, M.T. Masouleh, G. Anbarjafari, Optimal design of a spherical parallel manipulator based on kinetostatic performance using evolutionary techniques, Journal of Mechanical Science and Technology, 30(3) (2016) 1323-1331.
[9] R. Di Gregorio, A new parallel wrist using only revolute pairs: the 3-RUU wrist, Robotica, 19(3) (2001) 305-309.
[10]  K. Al-Widyan, X.Q. Ma, J. Angeles, The robust design of parallel spherical robots, Mechanism and Machine Theory, 46(3) (2011) 335-343.
[11] M. Karouia, J.M. Hervé, An orientational 3-dof parallel mechanism, in:  Proceedings of the 3rd Chemnitz Parallel Kinematics Seminar, Chemnitz, Germany, April, 2002, pp. 23-25.
[12]  R. Di Gregorio, The 3-RRS wrist: a new, simple and non-overconstrained spherical parallel manipulator, Journal of Mechanical Design, 126(5) (2004) 850855.
[13]  X. Kong, C.M. Gosselin, Type synthesis of threedegree-of-freedom spherical parallel manipulators, The International Journal of Robotics Research, 23(3) (2004) 237-245.
[14]  A. Chaker, A. Mlika, M. Laribi, L. Romdhane, S. Zeghloul, Accuracy analysis of non-overconstrained spherical parallel manipulators, European Journal of Mechanics-A/Solids, 47 (2014) 362-372.
[15]  A. Chaker, A. Mlika, M. Laribi, L. Romdhane, S. Zeghloul, Clearance and manufacturing errors’ effects on the accuracy of the 3-RCC Spherical Parallel Manipulator, European Journal of Mechanics-A/ Solids, 37 (2013) 86-95.
[16]  S. Venanzi, V. Parenti-Castelli, A new technique for clearance influence analysis in spatial mechanisms, Journal of Mechanical Design, 127(3) (2005) 446-455.
[17]  J. Meng, D. Zhang, Z. Li, Accuracy analysis of parallel manipulators with joint clearance, Journal of Mechanical Design, 131(1) (2009) 011013.
[18]  N. Binaud, P. Cardou, S.p. Caro, P. Wenger, The kinematic sensitivity of robotic manipulators to joint clearances, in:  ASME 2010 International Design engineering Technical Conferences and Computers and Information in Engineering Conference, American Society of Mechanical Engineers, 2010, pp. 1371.0831
[19]  S. Mojtaba, S. Mousavi, A. Khoogar, M.T. Masouleh, Accuracy Comparison of Spherical Parallel Manipulators Based on Joint Clearance, in:  2017 5th RSI International Conference on Robotics and Mechatronics (ICRoM), IEEE, 2017, pp. 570-575.
[20]  G. Wu, S. Bai, S. Caro, Transmission Quality Evaluation for a Class of Four-limb Parallel Schönfliesmotion Generators with Articulated Platforms, in: Computational Kinematics, Springer, 2018, pp. 282.092
[21] M. Gallant, C. Gosselin, Singularities of a planar 3-RPR parallel manipulator with joint clearance, Robotica,  (2018) 1-12.
[22] J. Zhu, K.-L. Ting, Uncertainty analysis of planar and spatial robots with joint clearances, Mechanism and Machine Theory, 35(9) (2000) 1239-1256.
[23]  C. Innocenti, Kinematic clearance sensitivity analysis of spatial structures with revolute joints, Journal of mechanical design, 124(1) (2002) 52-57.
[24]  M.-J. Tsai, T.-H. Lai, Accuracy analysis of a multiloop linkage with joint clearances, Mechanism and machine theory, 43(9) (2008) 1141-1157.
[25] P. Voglewede, I. Ebert-Uphoff, Application of workspace generation techniques to determine the unconstrained motion of parallel manipulators,  Journal of Mechanical Design, 126(2) (2004) 283-290.
[26]  P.D. Lin, J.F. Chen, Accuracy analysis of planar linkages by the matrix method, Mechanism and Machine Theory, 27(5) (1992) 507-516.
[27]   P. Cardou, S. Bouchard, C. Gosselin, Kinematicsensitivity indices for dimensionally nonhomogeneous jacobian matrices, IEEE Transactions on Robotics, 26(1) (2010) 166-173.
[28]   M. Daneshmand, M.H. Saadatzi, M.T. Masouleh, Kinematic sensitivity and workspace optimization of planar parallel mechanisms using evolutionary techniques, in:  Robotics and Mechatronics (ICRoM), 2013 First RSI/ISM International Conference on, IEEE, 2013, pp. 384-389.
[29]  M. Saadatzi, M.T. Masouleh, H. Taghirad, C. Gosselin, M. Teshnehlab, Multi-objective Scale Independent Optimization of 3-RPR Parallel Mechanisms, Proceedings of the IFToMM,  (2011).
[30]  A.G. Hoevenaars, C. Gosselin, P. Lambert, J.L. Herder, Experimental validation of Jacobian-based stiffness analysis method for parallel manipulators with nonredundant legs, Journal of Mechanisms and Robotics, 8(4) (2016) 041002.
[31]  A. Hoevenaars, C. Gosselin, P. Lambert, J. Herder, Consistent modeling resolves asymmetry in stiffness matrices, Mechanism and Machine Theory, 105 (2016) 80-90.
[32]  M.H. Saadatzi, M.T. Masouleh, H.D. Taghirad, C. Gosselin, P. Cardou, Geometric analysis of the kinematic sensitivity of planar parallel mechanisms, Transactions of the Canadian Society for Mechanical Engineering, 35(4) (2011) 477-490.
[33]  J.-P. Merlet, Jacobian, manipulability, condition number, and accuracy of parallel robots, Journal of Mechanical Design, 128(1) (2006) 199-206.
[34] C.M. Gosselin, E.S. Pierre, M. Gagne, On the development of the agile eye, IEEE Robotics & Automation Magazine, 3(4) (1996) 29-37.
[35]  M.C. Grant, S.P. Boyd, Graph implementations for nonsmooth convex programs, in:  Recent advances in learning and control, Springer, 2008, pp. 95-110.
[36] M. Grant, S. Boyd, Y. Ye, CVX: Matlab software for disciplined convex programming, in, 2008.
[37] T. Yoshikawa, Analysis and control of robot manipulators with redundancy, in:  Robotics research: the first international symposium, MIT press Cambridge, MA, USA, 1984, pp. 735-747.
Amirkabir Journal of Mechanical Engineering
Volume 52, Issue 5
August 2020
Pages 1301-1318

Files

Share

How to cite

Statistics