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Research Papers

Modeling and Analysis of Parallel Mechanisms With Both Kinematic and Actuation Redundancies Via Screw Theory

[+] Author and Article Information
Long Kang

Department of Electronic Systems Engineering,
Hanyang University,
Ansan 15588, Gyeonggi-do, South Korea
e-mail: hitjakie@gmail.com

Wheekuk Kim

Professor
Department of Electro-Mechanical System
Engineering,
Korea University,
2511, Sejong-ro,
Sejong 339-700, South Korea
e-mail: wheekuk@korea.ac.kr

Byung-Ju Yi

Professor
Department of Electronic Systems Engineering,
Hanyang University,
Ansan 15588, Gyeonggi-do, South Korea
e-mail: bj@hanyang.ac.kr

1Corresponding author.

Manuscript received April 13, 2017; final manuscript received August 22, 2017; published online September 20, 2017. Assoc. Editor: Clement Gosselin.

J. Mechanisms Robotics 9(6), 061007 (Sep 20, 2017) (12 pages) Paper No: JMR-17-1108; doi: 10.1115/1.4037805 History: Received April 13, 2017; Revised August 22, 2017

Two kinds of mechanical redundancies, namely kinematic redundancy and actuation redundancy, have been extensively studied due to their advantageous features in autonomous industry. Screw theory has been successfully applied to develop an analytical Jacobian of nonredundant parallel manipulators (PMs). However, to the best of our knowledge, screw theory has not been attempted for modeling of PMs with kinematic redundancies. Thus, first, through the mobility analysis of a simple nonredundant planar PM and its variations, this paper reviews kinematic and actuation redundancy systematically. Then, we demonstrated how to derive analytical Jacobian and also static force relationship for a PM with both kinematic and actuation redundancies by using the screw theory. Finally, simulations were performed to demonstrate the advantageous features of kinematic and actuation redundancies.

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References

Maciejewski, A. A. , and Klein, C. A. , 1985, “ Obstacle Avoidance for Kinematically Redundant Manipulators in Dynamically Varying Environments,” Int. J. Rob. Res., 4(3), pp. 109–117. [CrossRef]
Wang, J. , and Gosselin, C. M. , 2004, “ Kinematic Analysis and Design of Kinematically Redundant Parallel Mechanisms,” ASME J. Mech. Des., 126(1), pp. 109–118. [CrossRef]
Ebrahimi, I. , Carretero, J. A. , and Boudreau, R. , 2007, “ 3-PRRR Redundant Planar Parallel Manipulator: Inverse Displacement, Workspace and Singularity Analyses,” Mech. Mach. Theory, 42(8), pp. 1007–1016. [CrossRef]
Gosselin, C. M. , Laliberté, T. , and Veillette, A. , 2015, “ Singularity-Free Kinematically Redundant Planar Parallel Mechanisms With Unlimited Rotational Capability,” IEEE Trans. Rob., 31(2), pp. 457–467. [CrossRef]
Shimizu, M. , Yoon, W. K. , and Kitagaki, K. , “ A Practical Redundancy Resolution for 7 DOF Redundant Manipulators With Joint Limits,” IEEE International Conference on Robotics and Automation (ICRA), Rome, Italy, Apr. 10–14, pp. 4510–4516.
Flacco, F. , Luca, A. D. , and Khatib, O. , “ Motion Control of Redundant Robots Under Joint Constraints: Saturation in the Null Space,” IEEE International Conference on Robotics and Automation (ICRA), Saint Paul, MN, May 14–18, pp. 285–292.
Hollerbach, J. , and Ki, S. , 1987, “ Redundancy Resolution of Manipulators Through Torque Optimization,” IEEE J. Rob. Autom., 3(4), pp. 308–316. [CrossRef]
Chiaverini, S. , 1997, “ Singularity-Robust Task-Priority Redundancy Resolution for Real-Time Kinematic Control of Robot Manipulators,” IEEE Trans. Rob. Autom., 13(3), pp. 398–410. [CrossRef]
Klein, C. A. , and Blaho, B. E. , 1987, “ Dexterity Measures for the Design and Control of Kinematically Redundant Manipulators,” Int. J. Rob. Res., 6(2), pp. 72–83. [CrossRef]
Nakamura, Y. , 1991, Advanced Robotics: Redundancy and Optimization, Addison-Wesley, Boston, MA.
Yi, B.-J. , Na, H. Y. , Lee, J. H. , Hong, Y.-S. , Oh, S.-R. , Suh, I. H. , and Kim, W. K. , 2002, “ Design of a Parallel-Type Gripper Mechanism,” Int. J. Rob. Res., 21(7), pp. 661–676. [CrossRef]
Mohamed, M. G. , and Gosselin, C. M. , 2005, “ Design and Analysis of Kinematically Redundant Parallel Manipulators With Configurable Platforms,” IEEE Trans. Rob., 21(3), pp. 277–287. [CrossRef]
Isaksson, M. , Gosselin, C. , and Marlow, K. , 2016, “ An Introduction to Utilising the Redundancy of a Kinematically Redundant Parallel Manipulator to Operate a Gripper,” Mech. Mach. Theory, 101, pp. 50–59. [CrossRef]
Saglia, J. A. , Dai, J. S. , and Caldwell, D. G. , 2008, “ Geometry and Kinematic Analysis of a Redundantly Actuated Parallel Mechanism That Eliminates Singularities and Improves Dexterity,” ASME J. Mech. Des., 130(12), p. 124501. [CrossRef]
Shayya, S. , Krut, S. , Company, O. , Baradat, C. , and Pierrot, F. , 2013, “ A Novel (3T-1R) Redundant Parallel Mechanism With Large Operational Workspace and Rotational Capability,” IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Tokyo, Japan, Nov. 3–7, pp. 436–443.
Shin, H. , Lee, S. , Jeong, J. I. , and Kim, J. , 2013, “ Antagonistic Stiffness Optimization of Redundantly Actuated Parallel Manipulators in a Predefined Workspace,” IEEE/ASME Trans. Mechatronics, 18(3), pp. 1161–1169. [CrossRef]
Wang, C. , Fang, Y. , Guo, S. , and Chen, Y. , 2013, “ Design and Kinematical Performance Analysis of a 3-RUS/RRR Redundantly Actuated Parallel Mechanism for Ankle Rehabilitation,” ASME J. Mech. Rob., 5(4), p. 041003. [CrossRef]
Corbel, D. , Gouttefarde, M. , Company, O. , and Pierrot, F. , 2010, “ Actuation Redundancy as a Way to Improve the Acceleration Capabilities of 3T and 3T1R Pick-and-Place Parallel Manipulators,” ASME J. Mech. Rob., 2(4), p. 041002. [CrossRef]
Li, Q. , Zhang, N. , and Wang, F. , 2016, “ New Indices for Optimal Design of Redundantly Actuated Parallel Manipulators,” ASME J. Mech. Rob., 9(1), p. 011007. [CrossRef]
Kang, L. , Kim, W. , and Yi, B. J. , 2016, “ Kinematic Modeling, Analysis, and Load Distribution Algorithm for a Redundantly Actuated 4-DOF Parallel Mechanism,” IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Daejeon, South Korea, Oct. 9–14, pp. 356–361.
Yung, T. , Tosunoglu, S. , and Freeman, R. , 1993, “ Actuator Saturation Avoidance for Fault-Tolerant Robots,” 32nd IEEE Conference on Decision and Control (CDC), San Antonio, TX, Dec. 15–17, pp. 2125–2130.
Gouttefarde, M. , Daney, D. , and Merlet, J. P. , 2011, “ Interval-Analysis-Based Determination of the Wrench-Feasible Workspace of Parallel Cable-Driven Robots,” IEEE Trans. Rob., 27(1), pp. 1–13. [CrossRef]
Gosselin, C. , and Grenier, M. , 2011, “ On the Determination of the Force Distribution in Overconstrained Cable-Driven Parallel Mechanisms,” Meccanica, 46(1), pp. 3–15. [CrossRef]
Bouchard, S. , Gosselin, C. , and Moore, B. , 2009, “ On the Ability of a Cable-Driven Robot to Generate a Prescribed Set of Wrenches,” ASME J. Mech. Rob., 2(1), p. 011010. [CrossRef]
Hassan, M. , and Khajepour, A. , 2008, “ Optimization of Actuator Forces in Cable-Based Parallel Manipulators Using Convex Analysis,” IEEE Trans. Rob., 24(3), pp. 736–740. [CrossRef]
Yuan, H. , Courteille, E. , and Deblaise, D. , 2016, “ Force Distribution With Pose-Dependent Force Boundaries for Redundantly Actuated Cable-Driven Parallel Robots,” ASME J. Mech. Rob., 8(4), p. 041004. [CrossRef]
Davies, T. H. , 1981, “ Kirchhoff's Circulation Law Applied to Multi-Loop Kinematic Chains,” Mech. Mach. Theory, 16(3), pp. 171–183. [CrossRef]
Mohamed, M. G. , and Duffy, J. , 1985, “ A Direct Determination of the Instantaneous Kinematics of Fully Parallel Robot Manipulators,” ASME. J. Mech., Transm., Autom. Des., 107(2), pp. 226–229. [CrossRef]
Joshi, S. A. , and Tsai, L.-W. , 2002, “ Jacobian Analysis of Limited-DOF Parallel Manipulators,” ASME J. Mech. Des., 124(2), pp. 254–258. [CrossRef]
Cox, D. J. , 1981, “ The Dynamic Modeling and Command Signal Formulation for Parallel Multi-Parameter Robotic Devices,” Master's thesis, University of Florida, Gainesville, FL.
Cox, D. J. , and Tesar, D. , 1989, “ The Dynamic Model of a Three Degree of Freedom Parallel Robotic Shoulder Module,” Advanced Robotics: Proceedings of the 4th International Conference on Advanced Robotics, K. J. Waldron , ed., Springer, Berlin, pp. 475–487. [CrossRef]
Yi, B.-J. , Kim, S. M. , Kwak, H. K. , and Kim, W. , 2013, “ Multi-Task Oriented Design of an Asymmetric 3T1R Type 4-DOF Parallel Mechanism,” Proc. Inst Mech Eng. Part C, 227(10), pp. 2236–2255. [CrossRef]
Kang, L. , and Yi, B. J. , 2016, “ Design of Two Foldable Mechanisms Without Parasitic Motion,” IEEE Robot. Autom. Lett., 1(2), pp. 930–937. [CrossRef]
Isaksson, M. , Gosselin, C. , and Marlow, K. , 2017, “ Singularity Analysis of a Class of Kinematically Redundant Parallel Schönflies Motion Generators,” Mech. Mach. Theory, 112, pp. 172–191. [CrossRef]
Isaksson, M. , 2017, “ Kinematically Redundant Planar Parallel Mechanisms for Optimal Singularity Avoidance,” ASME J. Mech. Des., 139(4), p. 042302. [CrossRef]
Gogu, G. , 2005, “ Mobility of Mechanisms: A Critical Review,” Mech. Mach. Theory, 40(9), pp. 1068–1097. [CrossRef]
Li, Q. C. , and Huang, Z. , 2004, “ Mobility Analysis of a Novel 3-5R Parallel Mechanism Family,” ASME J. Mech. Des., 126(1), pp. 79–82. [CrossRef]
Dai, J. S. , Huang, Z. , and Lipkin, H. , 2004, “ Mobility of Overconstrained Parallel Mechanisms,” ASME J. Mech. Des., 128(1), pp. 220–229. [CrossRef]
Zanchettin, A. M. , Rocco, P. , Robertsson, A. , and Johansson, R. , 2011, “ Exploiting Task Redundancy in Industrial Manipulators During Drilling Operations,” IEEE International Conference on Robotics and Automation (ICRA), Shanghai, China, May 9–13, pp. 128–133.
Nokleby, S. B. , Fisher, R. , Podhorodeski, R. P. , and Firmani, F. , 2005, “ Force Capabilities of Redundantly-Actuated Parallel Manipulators,” Mech. Mach. Theory, 40(5), pp. 578–599. [CrossRef]
Gosselin, C. , and Angeles, J. , 1988, “ The Optimum Kinematic Design of a Planar Three-Degree-of-Freedom Parallel Manipulator,” ASME. J. Mech., Transm., Autom. Des., 110(1), pp. 35–41. [CrossRef]
Bonev, I. A. , Zlatanov, D. , and Gosselin, C. M. M. , 2003, “ Singularity Analysis of 3-DOF Planar Parallel Mechanisms Via Screw Theory,” ASME J. Mech. Des., 125(3), pp. 573–581. [CrossRef]
Huang, T. , Liu, H. T. , and Chetwynd, D. G. , 2011, “ Generalized Jacobian Analysis of Lower Mobility Manipulators,” Mech. Mach. Theory, 46(6), pp. 831–844. [CrossRef]
Cha, S. H. , Lasky, T. A. , and Velinsky, S. A. , 2007, “ Singularity Avoidance for the 3-RRR Mechanism Using Kinematic Redundancy,” IEEE International Conference on Robotics and Automation (ICRA), Rome, Italy, Apr. 10–14, pp. 1195–1200.
Chen, X. , Chen, C. , and Liu, X.-J. , 2015, “ Evaluation of Force/Torque Transmission Quality for Parallel Manipulators,” ASME J. Mech. Rob., 7(4), p. 041013. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

Schematic diagram of the 3-RRR nonredundant manipulator

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Fig. 2

Schematic diagram of the 3-RPRR kinematically redundant manipulator

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Fig. 3

Schematic diagram of the RRR-RPRR-RPRRR kinematically redundant manipulator

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Fig. 4

Schematic diagram of the 4-RRR redundantly actuated manipulator

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Fig. 5

Flowchart of the hybrid resolution algorithm

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Fig. 6

Desired trajectory and initial configuration

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Fig. 7

Joint configurations during the trajectory: case of minimum norm solution

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Fig. 8

Link length variations of the three redundant prismatic joints: case of minimum norm solution

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Fig. 10

Link length variations of the three redundant prismatic joints: case of optimized null-space solution

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Fig. 11

Variations of det(AAT) for two different inverse kinematic solutions of 3-RPRR PM

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Fig. 9

Joint configurations during the trajectory: case of optimized null-space solution

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Fig. 12

Comparison of 2-norm of the actuation torque/force of the 3-RPRR PM with that of the 3-RPRR PM

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