Kinematic Modeling, Dexterity and Performance Analysis of Planar Parallel Manipulators

Document Type : Original Article

Authors

Department of Industrial Electronics and Control Engineering, Faculty of Electronic Engineering at Menouf, Menofia University, Egypt

Abstract

This research work is concerned with the Planar Parallel
Manipulator (PPM). This investigation leads to a comparative study
between the 2-RRR PPM which is a non-redundant PPM and 3-RRR
PPM which is a redundant PPM. The main objective is to compare
one type of PPM with another one that has one step of
construction’s upgrading with respect to the other PPM. An
important issue for optimal design of these manipulators is related
to their performance characterizations. These two PPMs are
introduced with their mechanism construction. Investigation of
characteristics of PPMs goes through the complexity of the direct
and inverse kinematics problems, which are solved using the
suggested and proper geometrical equations. The dexterous
workspace is geometrically obtained where the End-Effector (EE)
can reach and illustrate some of its properties. In order to complete
the study for these PPMs, the virtual work is determined, obtained
and used, to get the PPM characteristics using the dynamic model.
Jacobian matrix has been determined and used. This research work
is terminated not only by two kinematic characteristics maps
dexterity and manipulability - indices, but also with a dynamic
characteristics map called dynamic index.

Keywords

References

[1] Y. D. Patel, P. M. George: Parallel Manipulators ApplicationsA Survey,
http://dx.doi.org/10.4236/mme.2012.23008.
[2] Merlet, Jean-Pierre. Parallel robots. Vol. 128. Springer Science and
Business Media, 2006.
[3] Carretero, Juan A., Iman Ebrahimi, and Roger Boudreau. "Overall Motion
Planning for Kinematically Redundant Parallel Manipulators." Journal of
Mechanisms and Robotics 4.2 (2012): 024502.
[4] Park, F. C., and Jin Wook Kim. "Singularity analysis of closed kinematic
chains." TRANSACTIONS-AMERICAN SOCIETY OF MECHANICAL
ENGINEERS JOURNAL OF MECHANICAL DESIGN 121 (1999): 32-
38.
[5] Kock, Snke, and Walter Schumacher. "A parallel xy manipulator with
actuation redundancy for high-speed and active-stiffness applications."
Robotics and Automation, 1998. Proceedings. 1998 IEEE International
Conference on. Vol. 3. IEEE, 1998.
[6] Gosselin, Clment M., and Jean-Pierre Merlet. "The direct kinematics of
planar parallel manipulators: special architectures and number of
solutions." Mechanism and Machine Theory 29.8 (1994): 1083-1097.
[7] Gao, Feng, Xinjun Liu, and William A. Gruver. "Performance evaluation
of twodegree-of freedom planar parallel robots." Mechanism and Machine
Theory 33.6 (1998): 661-668.
[8] Shin, Hyunpyo, et al. "Kinematic optimization of a redundantly actuated
parallel mechanism for maximizing stiffness and workspace using Taguchi
method." Journal of Computational and Nonlinear Dynamics 6.1 (2011):
011017.
[9] Ebrahimi, Iman, Juan A. Carretero, and Roger Boudreau. "3-PRRR
redundant planar parallel manipulator: Inverse displacement, workspace
and singularity analyses." Mechanism and Machine Theory 42.8 (2007):
1007-1016.
[10] Garg, Venus, Scott B. Nokleby, and Juan A. Carretero. "Wrench capability
analysis of redundantly actuated spatial parallel manipulators." Mechanism
and machine theory 44.5 (2009): 1070-1081.
[11] Wu, Jun, et al. "Stiffness and natural frequency of a 3-DOF parallel
manipulator with consideration of additional leg candidates." Robotics and
Autonomous Systems 61.8 (2013): 868-875.
[12] Hrones, John Anthony, and George Larsen Nelson. Analysis of the fourbar linkage: its application to the synthesis of mechanisms. Published
jointly by the Technology Press of the Massachusetts Institute of
Technology, and Wiley, New York, 1951.
[13] Modeling, performance analysis and control of robot manipulators/edited
by Etienne Dombre, Wisama Khalil. p. cm. Includes index. ISBN-13: 978-
1-905209-10-1 ISBN-10: 1-905209-10-X 1. Robotics. 2. Manipulators
(Mechanism) I. Dombre, E. (Etienne) II. Khalil, W. (Wisama) TJ211.M626
2006 629.8’933-dc22
[14] A. K. Dash, I. M. Chen, S. H. Yeo, G. Yang: Task-oriented configuration
design for reconfigurable parallel manipulator systems, International
 
Journal of Computer Integrated Manufacturing, Vol. 18, No. 7, pp. 615-
634, 2005.
[15] L. W. Tsai, Robot Analysis: The Mechanics of Serial and Parallel
Manipulators, USA: John Wiley and Sons, 1999.
[16] Zoran PANDILOV,Vladimir DUKOVSKI: Comparison of The
Characteristics Between Serial and Parallel Robots, ISSN: 2067 3809.
[17] Balan R., V. Maties, S. Stan, C. Lapusan: On the Control of a 3-RRR
Planar Parallel Minirobot, Journal Mecatronica, Journal of Romanian
Society of Mechatronics, no. 4/2005 , pp. 20-23, December, 2005.
[18] A. A. Maciejewski and C. A. Klein: Obstacle avoidance for kinematically
redundant manipulators in dynamically varying environments, Int. J.
Robot. Res. 4(3), 109117 (1985).
[19] Y. Nakamura, H. Hanafusa and T. Yoshikawa: Task-priority based
redundancy control of robot manipulators, Int. J. Robot. Res. 6(2), 315
(1987).
[20] J. Wang and C. M. Gosselin: Kinematic analysis and design of
kinematically redundant parallel mechanisms.J. Mech. Des. 126(1),
109118 (2004).
[21] V. Garg, S. B. Nokleby and J. A. Carretero: Determining the Force and
Moment Workspaces of Redundantly-Actuated Spatial Parallel
Manipulators. Proceedings of the 2007 ASME DETC, Las Vegas, Nevada,
USA.
[22] Weiwei Shang, Shuang Cong.: Dexterity and Adaptive Control of Planar
Parallel Manipulators With and Without Redundant Actuation. Contributed
by the Design Engineering Division of ASME for publication in Journal of
Computational and Nonlinear Dynamics.
[23] http://www.mecademic.com/DexTAR.html, signed in 2/2017.
[24] T. Yoshikawa: Manipulability of robotic mechanisms, The International
Journal of Robotics Research, vol. 4, no. 2, pp. 39, 1985.
[25] Pu Zhang, Zhenqiang Yao, Zhengchun Du.: Global Performance Index
System for Kinematic Optimization of Robotic Mechanism. Contributed by
the Mechanisms and Robotics Committee of ASME for publication in the
Journal of Mechanical Design.
[26] Gosselin, Clement, and Jorge Angeles. "Singularity analysis of closed-loop
kinematic chains." IEEE transactions on robotics and automation 6.3
(1990): 281-290.
[27] Sefrioui, Jaouad, and Clment M. Gosselin. "Singularity analysis and
representation of planar parallel manipulators." Robotics and Autonomous
Systems 10.4 (1992): 209-224.
[28] Hubert, J., and J-P. Merlet. "Static of parallel manipulators and closeness
to singularity." Journal of Mechanisms and Robotics 1.1 (2009): 011011.
[29] Rubbert, Lennart, et al. "Using singularities of parallel manipulators to
enhance the rigid-body replacement design method of compliant
mechanisms." Journal of Mechanical Design 136.5 (2014): 051010.
[30] Liu, Guanfeng, Yunjiang Lou, and Zexiang Li. "Singularities of parallel
manipulators: A geometric treatment." IEEE Transactions on Robotics and
Automation 19.4 (2003): 579-594.
[31] Tsai, Lung-Wen. Robot analysis: the mechanics of serial and parallel
manipulators. John Wiley, Sons, 1999.
[32] Briot, Sbastien, and Vigen Arakelian. "Optimal force generation in parallel
manipulators for passing through the singular positions." The International
Journal of Robotics Research 27.8 (2008): 967-983.
[33] He, J. F., et al. "A survey on control of parallel manipulator." Key
Engineering Materials. Vol. 339. Trans Tech Publications, 2007.
[34] Nakamura, Yoshihiko, and Hideo Hanafusa. "Inverse kinematic solutions
with singularity robustness for robot manipulator control." ASME,
Transactions, Journal of Dynamic Systems, Measurement, and Control 108
(1986): 163-171.
[35] Tan, Jindong, and Ning Xi. "Hybrid system design for singularityless task
level robot controllers." Robotics and Automation, 2000. Proceedings.
ICRA’00. IEEE International Conference on. Vol. 3. IEEE, 2000.
[36] Mohamed, Maher G., and Clment M. Gosselin. "Design and analysis of
kinematically redundant parallel manipulators with configurable
platforms." IEEE Transactions on Robotics 21.3 (2005): 277-287.
[37] Dasgupta, Bhaskar, and T. S. Mruthyunjaya. "Force redundancy in parallel
manipulators: theoretical and practical issues." Mechanism and Machine
Theory 33.6 (1998): 727-742.
[38] Cheng, Hui, et al. "Advantages and dynamics of parallel manipulators with
redundant actuation." Intelligent Robots and Systems, 2001. Proceedings.
2001 IEEE/RSJ International Conference on. Vol. 1. IEEE, 2001.
[39] Slotine, Siciliano B. "A general framework for managing multiple tasks in
highly redundant robotic systems." proceeding of 5th International
Conference on Advanced Robotics. Vol. 2. 1991.
[40] Park, Frank C., and Jin Wook Kim. "Manipulability and singularity
analysis of multiple robot systems: A geometric approach." Robotics and
Automation, 1998. Proceedings. 1998 IEEE International Conference on.
Vol. 2. IEEE, 1998.
[41] Quennouelle, Cyril, and C. M. Gosselin. "Stiffness matrix of compliant
parallel mechanisms." Advances in Robot Kinematics: Analysis and
Design (2008): 331-341.
[42] Alici, Grsel, and Bijan Shirinzadeh. "Enhanced stiffness modeling,
identification and characterization for robot manipulators." IEEE
transactions on robotics 21.4 (2005): 554-564.
[43] Baruh, Haim. Analytical dynamics. Boston: WCB/McGraw-Hill, 1999.

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