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Review Article

Redundancy in Parallel Mechanisms: A Review

[+] Author and Article Information
Clément Gosselin

Professor
Fellow ASME
Laboratoire de robotique,
Département de génie mécanique,
Université Laval,
Québec, QC G1V 0A6, Canada
e-mail: Clement.Gosselin@gmc.ulaval.ca

Louis-Thomas Schreiber

Laboratoire de robotique,
Département de génie mécanique,
Université Laval,
Québec, QC G1V 0A6, Canada
e-mail: louis-thomas.schreiber.1@ulaval.ca

Manuscript received September 15, 2016; final manuscript received August 15, 2017; published online January 31, 2018. Editor: Harry Dankowicz.

Appl. Mech. Rev 70(1), 010802 (Jan 31, 2018) (15 pages) Paper No: AMR-16-1071; doi: 10.1115/1.4038931 History: Received September 15, 2016; Revised August 15, 2017

This paper presents a review of the literature related to the use of redundancy in parallel mechanisms. Two types of redundancies are considered, namely, actuation redundancy and kinematic redundancy. The use of these concepts in the literature is highlighted. Each of the concepts is then formulated mathematically in order to clearly expose their characteristics and their properties. Two subclasses of kinematically redundant parallel mechanisms are defined, namely, those with serial redundant legs and those with parallel redundant legs. The force transmission in redundant parallel mechanisms is then discussed. Finally, a summary of the different approaches that can be used to implement redundancy in parallel mechanisms is given in order to identify the most promising synthesis avenues and to provide insight into their potential fields of application.

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References

Sugimoto, K. , Duffy, J. , and Hunt, K. , 1982, “Special Configurations of Spatial Mechanisms and Robot Arms,” Mech. Mach. Theory, 17(2), pp. 119–132. [CrossRef]
Hunt, K. H. , 1986, “Special Configurations of Robot-Arms Via Screw Theory,” Robotica, 4(3), pp. 171–179. [CrossRef]
Liegeois, A. , 1977, “Automatic Supervisory Control of the Configuration and Behavior of Multibody Mechanisms,” IEEE Trans. Syst. Man Cybern., 7(12), pp. 868–871. [CrossRef]
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]
Kirćanski, M. , and Vukobratović, M. , 1986, “Contribution to Control of Redundant Robotic Manipulators in an Environment With Obstacles,” Int. J. Rob. Res., 5(4), pp. 112–119. [CrossRef]
Chiaverini, S. , Oriolo, G. , and Maciejewski, A. A. , 2016, “Redundant Robots,” Springer Handbook of Robotics, Springer, New York, pp. 221–242.
Nakamura, Y. , Hanafusa, H. , and Yoshikawa, T. , 1987, “Task-Priority Based Redundancy Control of Robot Manipulators,” Int. J. Rob. Res., 6(2), pp. 3–15. [CrossRef]
Nakamura, Y. , 1990, Advanced Robotics: Redundancy and Optimization, Addison-Wesley Longman, Boston, MA.
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]
Khatib, O. , 1987, “A Unified Approach for Motion and Force Control of Robot Manipulators: The Operational Space Formulation,” IEEE J. Rob. Autom., 3(1), pp. 43–53. [CrossRef]
Hollerbach, J. , and Suh, K. , 1987, “Redundancy Resolution of Manipulators Through Torque Optimization,” IEEE J. Rob. Autom., 3(4), pp. 308–316. [CrossRef]
Notash, L. , and Huang, L. , 2003, “On the Design of Fault Tolerant Parallel Manipulators,” Mech. Mach. Theory, 38(1), pp. 85–101. [CrossRef]
Tosi, D. , Legnani, G. , Pedrocchi, N. , Righettini, P. , and Giberti, H. , 2010, “Cheope: A New Reconfigurable Redundant Manipulator,” Mech. Mach. Theory, 45(4), pp. 611–626. [CrossRef]
Tanev, T. K. , 2000, “Kinematics of a Hybrid (Parallel-Serial) Robot Manipulator,” Mech. Mach. Theory, 35(9), pp. 1183–1196. [CrossRef]
Cheng, H. H. , 1994, “Real-Time Manipulation of a Hybrid Serial-and-Parallel-Driven Redundant Industrial Manipulator,” ASME J. Dyn. Syst. Meas. Control, 116(4), pp. 687–701. [CrossRef]
Hamlin, G. J. , and Sanderson, A. C. , 1997, “Tetrobot: A Modular Approach to Parallel Robotics,” IEEE Rob. Autom. Mag., 4(1), pp. 42–50. [CrossRef]
Waldron, K. J. , Raghavan, M. , and Roth, B. , 1989, “Kinematics of a Hybrid Series-Parallel Manipulation System,” ASME J. Dyn. Syst., Meas. Control, 111(2), pp. 211–221. [CrossRef]
Gosselin, C. , and Angeles, J. , 1990, “Singularity Analysis of Closed-Loop Kinematic Chains,” IEEE Trans. Rob. Autom., 6(3), pp. 281–290. [CrossRef]
Bonev, I. , 2003, “The True Origins of Parallel Robots,” Parallemic, Montreal, QC, Canada, accessed Jan. 17, 2018, http://www.parallemic.org/Reviews/Review007.html
Gough, V. , and Whitehall, S. , 1962, “Universal Tyre Test Machine,” FISITA Ninth International Technical Congress, London, Apr. 30–May 5, pp. 117–137.
Stewart, D. , 1965, “A Platform With Six Degrees of Freedom,” Proc. Inst. Mech. Eng., 180(1), pp. 371–386. [CrossRef]
Cappel, K. L. , 1967, “Motion Simulator,” Franklin Institute, Philadelphia, PA, U.S. Patent No. 3,295,224. http://www.google.co.in/patents/US3295224
Wang, J. , and Gosselin, C. , 2002, “Singularity Analysis and Design of Kinematically Redundant of Parallel Mechanisms,” ASME Paper No. DETC2002/MECH-34312.
Firmani, F. , and Podhorodeski, R. P. , 2004, “Force-Unconstrained Poses for a Redundantly-Actuated Planar Parallel Manipulator,” Mech. Mach. Theory, 39(5), pp. 459–476. [CrossRef]
Liu, G. , Lou, Y. , and Li, Z. , 2003, “Singularities of Parallel Manipulators: A Geometric Treatment,” IEEE Trans. Rob. Autom., 19(4), pp. 579–594. [CrossRef]
Xie, F. , Liu, X.-J. , and Wang, J. , 2011, “Performance Evaluation of Redundant Parallel Manipulators Assimilating Motion/Force Transmissibility,” Int. J. Adv. Rob. Syst., 8(5), pp. 113–124.
Isaksson, M. , Marlow, K. , Maciejewski, A. , and Eriksson, A. , 2017, “Novel Fault-Tolerance Indices for Redundantly Actuated Parallel Robots,” ASME J. Mech. Rob., 139(4), p. 042301. [CrossRef]
Luces, M. , Mills, J. K. , and Benhabib, B. , 2017, “A Review of Redundant Parallel Kinematic Mechanisms,” J. Intell. Rob. Syst., 86(2), pp. 175–198.
Zhao, Y. , and Gao, F. , 2009, “Dynamic Performance Comparison of the 8 PSS Redundant Parallel Manipulator and Its Non-Redundant Counterpart: The 6 PSS Parallel Manipulator,” Mech. Mach. Theory, 44(5), pp. 991–1008. [CrossRef]
Cheng, H. , Yiu, Y.-K. , and Li, Z. , 2003, “Dynamics and Control of Redundantly Actuated Parallel Manipulators,” IEEE/ASME Trans. Mechatronics, 8(4), pp. 483–491. [CrossRef]
Kim, S. , 1997, “Operational Quality Analysis of Parallel Manipulators With Actuation Redundancy,” IEEE International Conference on Robotics and Automation (ICRA), Albuquerque, NM, Apr. 20–25, pp. 2651–2656.
Harada, T. , and Nagase, M. , 2010, “Impedance Control of a Redundantly Actuated 3-DOF Planar Parallel Link Mechanism Using Direct Drive Linear Motors,” IEEE International Conference on Robotics and Biomimetics (ROBIO), Tianjin, China, Dec. 14–18, pp. 501–506.
Harada, T. , 2015, “Mode Changes of Redundantly Actuated Asymmetric Parallel Mechanism,” Proc. Inst. Mech. Eng., Part C, 230(3), pp. 454–462.
Harada, T. , and Liu, P. , 2013, “Internal and External Forces Measurement of Planar 3-DOF Redundantly Actuated Parallel Mechanism by Axial Force Sensors,” ISRN Rob., 2013, p. 593606.
Kurtz, R. , and Hayward, V. , 1992, “Multiple-Goal Kinematic Optimization of a Parallel Spherical Mechanism With Actuator Redundancy,” IEEE Trans. Rob. Autom., 8(5), pp. 644–651. [CrossRef]
Leguay-Durand, S. , and Reboulet, C. , 1997, “Optimal Design of a Redundant Spherical Parallel Manipulator,” Robotica, 15(4), pp. 399–405. [CrossRef]
Merlet, J.-P. , 1996, “Redundant Parallel Manipulators,” Lab. Rob. Autom., 8(1), pp. 17–24. [CrossRef]
Zhao, Y. , and Gao, F. , 2009, “Dynamic Formulation and Performance Evaluation of the Redundant Parallel Manipulator,” Rob. Comput. Integr. Manuf., 25(4), pp. 770–781. [CrossRef]
Zhao, Y. , Gao, F. , Li, W. , Liu, W. , and Zhao, X. , 2009, “Development of 6-Dof Parallel Seismic Simulator With Novel Redundant Actuation,” Mechatronics, 19(3), pp. 422–427. [CrossRef]
Jeong, J. , Kang, D. , Cho, Y. M. , and Kim, J. , 2004, “Kinematic Calibration for Redundantly Actuated Parallel Mechanisms,” ASME J. Mech. Des., 126(2), pp. 307–318. [CrossRef]
Nahvi, A. , Hollerbach, J. M. , and Hayward, V. , 1994, “Calibration of a Parallel Robot Using Multiple Kinematic Closed Loops,” IEEE International Conference Robotics and Automation (ICRA), San Diego, CA, May 8–13, pp. 407–412.
Ecorchard, G. , Neugebauer, R. , and Maurine, P. , 2010, “Elasto-Geometrical Modeling and Calibration of Redundantly Actuated PKMs,” Mech. Mach. Theory, 45(5), pp. 795–810. [CrossRef]
Feng, C. , Cong, S. , and Shang, W. , 2009, “Integrated Kinematic Calibration for All the Parameters of a Planar 2DOF Redundantly Actuated Parallel Manipulator,” ASME J. Mech. Rob., 1(3), p. 031003. [CrossRef]
Liu, W. , Gao, F. , Qi, K. , and Zhang, J. , 2008, “Accuracy of a Novel Parallel Robot With Orthogonal Chains,” International Conference on Intelligent Robotics and Applications (ICIRA), Wuhan, China, Oct. 15–17, pp. 1212–1222.
Müller, A. , and Ruggiu, M. , 2014, “Self-Calibration of Redundantly Actuated PKM Exploiting Kinematic Landmarks,” Computational Kinematics, Springer, New York, pp. 93–102. [CrossRef]
Do Thanh, T. , Kotlarski, J. , Heimann, B. , and Ortmaier, T. , 2012, “Dynamics Identification of Kinematically Redundant Parallel Robots Using the Direct Search Method,” Mech. Mach. Theory, 52, pp. 277–295. [CrossRef]
Briot, S. , Gautier, M. , and Krut, S. , 2013, “Dynamic Parameter Identification of Actuation Redundant Parallel Robots: Application to the DualV,” IEEE/ASME International Conference on Advanced Intelligent Mechatronics (AIM), Wollongong, Australia, July 9–12, pp. 637–643.
Yun, Y. , and Li, Y. , 2010, “Design and Analysis of a Novel 6-DOF Redundant Actuated Parallel Robot With Compliant Hinges for High Precision Positioning,” Nonlinear Dyn., 61(4), pp. 829–845. [CrossRef]
Dasgupta, B. , and Mruthyunjaya, T. , 2000, “The Stewart Platform Manipulator: A Review,” Mech. Mach. Theory, 35(1), pp. 15–40. [CrossRef]
Krut, S. , Company, O. , and Pierrot, F. , 2004, “Force Performance Indexes for Parallel Mechanisms With Actuation Redundancy, Especially for Parallel Wire-Driven Manipulators,” IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2004), Sendai, Japan, Sept. 28–Oct. 2, pp. 3936–3941.
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]
Garg, V. , Nokleby, S. B. , and Carretero, J. A. , 2009, “Wrench Capability Analysis of Redundantly Actuated Spatial Parallel Manipulators,” Mech. Mach. Theory, 44(5), pp. 1070–1081. [CrossRef]
Bouchard, S. , Gosselin, C. , and Moore, B. , 2010, “On the Ability of a Cable-Driven Robot to Generate a Prescribed Set of Wrenches,” ASME J. Mech. Rob., 2(1), p. 011010. [CrossRef]
Müller, A. , and Hufnagel, T. , 2012, “Model-Based Control of Redundantly Actuated Parallel Manipulators in Redundant Coordinates,” Rob. Auton. Syst., 60(4), pp. 563–571. [CrossRef]
Muller, A. , 2005, “Internal Preload Control of Redundantly Actuated Parallel Manipulators: Its Application to Backlash Avoiding Control,” IEEE Trans. Rob., 21(4), pp. 668–677. [CrossRef]
Valášek, M. , Bauma, V. , Sika, Z. , and Vampola, T. , 2002, “Redundantly Actuated Parallel Structures-Principle, Examples, Advantages,” Third Parallel Kinematics Seminar (PKS), Chemnitz, Germany, Apr. 23–25, pp. 993–1009.
Valášek, M. , Sika, Z. , Bauma, V. , and Vampola, T. , 2004, “The Innovative Potential of Redundantly Actuated PKM,” Fourth Chemnitz Parallel Kinematics Seminar (PKS), Chemnitz, Germany, Apr. 20–21, pp. 20–21.
Valášek, M. , Bauma, V. , šika, Z., Belda, K. , and Píša, P. , 2005, “Design-by-Optimization and Control of Redundantly Actuated Parallel Kinematics Sliding Star,” Multibody Syst. Dyn., 14(3–4), pp. 251–267.
Wang, L. , Wu, J. , Wang, J. , and You, Z. , 2009, “An Experimental Study of a Redundantly Actuated Parallel Manipulator for a 5-DOF Hybrid Machine Tool,” IEEE/ASME Trans. Mechatronics, 14(1), pp. 72–81. [CrossRef]
Krut, S. , Company, O. , Rangsri, S. , and Pierrot, F. , 2003, “Eureka: A New 5-Degree-of-Freedom Redundant Parallel Mechanism With High Tilting Capabilities,” IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2003), Las Vegas, NV, Oct. 27–31, pp. 3575–3580.
Wu, J. , Wang, J. , Li, T. , and Wang, L. , 2007, “Performance Analysis and Application of a Redundantly Actuated Parallel Manipulator for Milling,” J. Intell. Rob. Syst., 50(2), pp. 163–180. [CrossRef]
Kim, J. , Park, F. C. , Ryu, S. J. , Kim, J. , Hwang, J. C. , Park, C. , and Iurascu, C. C. , 2001, “Design and Analysis of a Redundantly Actuated Parallel Mechanism for Rapid Machining,” IEEE Trans. Rob. Autom., 17(4), pp. 423–434. [CrossRef]
Constantinescu, D. , Chau, I. , DiMaio, S. P. , Filipozzi, L. , Salcudean, S. , and Ghassemi, F. , 2000, “Haptic Rendering of Planar Rigid-Body Motion Using a Redundant Parallel Mechanism,” IEEE International Conference on Robotics and Automation (ICRA), San Francisco, CA, Apr. 24–28, pp. 2440–2445.
Corbel, D. , Gouttefarde, M. , Company, O. , and Pierrot, F. , 2010, “Towards 100 g With PKM. Is Actuation Redundancy a Good Solution for Pick-and-Place?,” IEEE International Conference on Robotics and Automation (ICRA), Anchorage, AK, May 3–7, pp. 4675–4682.
Marquet, F. , Krut, S. , Company, O. , and Pierrot, F. , 2001, “ARCHI: A New Redundant Parallel Mechanism-Modeling, Control and First Results,” IEEE/RSJ International Conference on Intelligent Robots and Systems, Vol. 1, pp. 183–188.
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), Maui, HI, Oct. 29–Nov. 3, pp. 436–443.
Muller, A. , 2006, “Stiffness Control of Redundantly Actuated Parallel Manipulators,” IEEE International Conference on Robotics and Automation (ICRA), Orlando, FL, May 15–19, pp. 1153–1158.
Müller, A. , and Maisser, P. , 2007, “Generation and Application of Prestress in Redundantly Full-Actuated Parallel Manipulators,” Multibody Syst. Dyn., 18(2), pp. 259–275. [CrossRef]
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]
Wu, J. , Li, T. , Wang, J. , and Wang, L. , 2013, “Stiffness and Natural Frequency of a 3-DOF Parallel Manipulator With Consideration of Additional Leg Candidates,” Rob. Auton. Syst., 61(8), pp. 868–875. [CrossRef]
Wu, J. , Chen, X. , Li, T. , and Wang, L. , 2013, “Optimal Design of a 2-DOF Parallel Manipulator With Actuation Redundancy Considering Kinematics and Natural Frequency,” Rob. Comput. Integr. Manuf., 29(1), pp. 80–85. [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]
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]
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]
Kotlarski, J. , Heimann, B. , and Ortmaier, T. , 2012, “Influence of Kinematic Redundancy on the Singularity-Free Workspace of Parallel Kinematic Machines,” Front. Mech. Eng., 7(2), pp. 120–134. [CrossRef]
Zanganeh, K. E. , and Angeles, J. , 1994, “Instantaneous Kinematics and Design of a Novel Redundant Parallel Manipulator,” IEEE International Conference on Robotics and Automation (ICRA), San Diego, CA, May 8–13, pp. 3043–3048.
Bande, P. , Seibt, M. , Uhlmann, E. , Saha, S. , and Rao, P. , 2005, “Kinematics Analyses of Dodekapod,” Mech. Mach. Theory, 40(6), pp. 740–756. [CrossRef]
Zanganeh, K. E. , and Angeles, J. , 1994, “Mobility and Position Analyses of a Novel Redundant Parallel Manipulator,” IEEE International Conference on Robotics and Automation (ICRA), San Diego, CA, May 8–13, pp. 3049–3054.
Kotlarski, J. , Abdellatif, H. , and Heimann, B. , 2007, “On Singularity Avoidance and Workspace Enlargement of Planar Parallel Manipulators Using Kinematic Redundancy,” 13th IASTED International Conference on Robotics and Applications, Würzburg, Germany, Aug. 29–31, pp. 451–456. https://dl.acm.org/citation.cfm?id=1659997.1660091
Kotlarski, J. , Abdellatif, H. , Ortmaier, T. , and Heimann, B. , 2009, “Enlarging the Useable Workspace of Planar Parallel Robots Using Mechanisms of Variable Geometry,” ASME/IFToMM International Conference on Reconfigurable Mechanisms and Robots (ReMAR 2009), London, June 22–24, pp. 63–72. http://ieeexplore.ieee.org/document/5173811/
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]
Ebrahimi, I. , Carretero, J. A. , and Boudreau, R. , 2008, “Kinematic Analysis and Path Planning of a New Kinematically Redundant Planar Parallel Manipulator,” Robotica, 26(3), pp. 405–413. [CrossRef]
Cha, S.-H. , Lasky, T. , and Velinsky, S. , 2009, “Determination of the Kinematically Redundant Active Prismatic Joint Variable Ranges of a Planar Parallel Mechanism for Singularity-Free Trajectories,” Mech. Mach. Theory, 44(5), pp. 1032–1044. [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.
Kotlarski, J. , Thanh, T. D. , Heimann, B. , and Ortmaier, T. , 2010, “Optimization Strategies for Additional Actuators of Kinematically Redundant Parallel Kinematic Machines,” IEEE International Conference on Robotics and Automation (ICRA), Anchorage, AK, May 3–7, pp. 656–661.
Kotlarski, J. , Heimann, B. , and Ortmaier, T. , 2011, “Experimental Validation of the Influence of Kinematic Redundancy on the Pose Accuracy of Parallel Kinematic Machines,” IEEE International Conference on Robotics and Automation (ICRA), Shanghai, China, May 9–13, pp. 1923–1929.
Boudreau, R. , and Nokleby, S. , 2012, “Force Optimization of Kinematically-Redundant Planar Parallel Manipulators Following a Desired Trajectory,” Mech. Mach. Theory, 56, pp. 138–155. [CrossRef]
Gosselin, C. , 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]
Gosselin, C. , Isaksson, M. , Marlow, K. , and Laliberté, T. , 2016, “Workspace and Sensitivity Analysis of a Novel Nonredundant Parallel Scara Robot Featuring Infinite Tool Rotation,” IEEE Rob. Autom. Lett., 1(2), pp. 776–783. [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]
Corbel, D. , Company, O., and Pierrot, F. , 2007, “From a 3-DOF Parallel Redundant ARCHI Robot to an Auto-Calibrated ARCHI Robot,” ASME Paper No. DETC2007-34786.
Gosselin, C. , and Schreiber, L.-T. , 2016, “Kinematically Redundant Spatial Parallel Mechanisms for Singularity Avoidance and Large Orientational Workspace,” IEEE Trans. Rob., 32(2), pp. 286–300. [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]
Lambert, P. , Langen, H. , and Schmidt, R. M. , 2010, “A Novel 5 DOF Fully Parallel Robot Combining 3T1R Motion and Grasping,” ASME Paper No. DETC2010-28676.
Lambert, P. , and Herder, J. L. , 2014, “Self Dual Topology of Parallel Mechanisms With Configurable Platforms,” Computational Kinematics, Springer, New York, pp. 291–298. [CrossRef]
Yoon, J. , and Ryu, J. , 2005, “A Novel Reconfigurable Ankle/Foot Rehabilitation Robot,” IEEE International Conference on Robotics and Automation (ICRA), Barcelona, Spain, Apr. 18–22, pp. 2290–2295.
Nabat, V. , de la O Rodriguez, M. , Company, O. , Krut, S. , and Pierrot, F. , 2005, “Par4: Very High Speed Parallel Robot for Pick-and-Place,” IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Edmonton, AB, Canada, Aug. 2–6, pp. 553–558.
Rolland, L. , 1999, “The Manta and the Kanuk: Novel 4-DOF Parallel Mechanisms for Industrial Handling,” International Mechanical Engineering Congress & Exposition (IMECE'99), Nashville, TN, Nov. 15–20, pp. 1–14. https://hal.inria.fr/inria-00098914/en/
Shin, K. , Yi, B.-J. , and Kim, W. , 2014, “Parallel Singularity-Free Design With Actuation Redundancy: A Case Study of Three Different Types of 3-Degree-of-Freedom Parallel Mechanisms With Redundant Actuation,” Proc. Inst. Mech. Eng., Part C, 228(11), pp. 2018–2035. [CrossRef]
Nahon, M. A. , and Angeles, J. , 1992, “Real-Time Force Optimization in Parallel Kinematic Chains Under Inequality Constraints,” IEEE Trans. Rob. Autom., 8(4), pp. 439–450. [CrossRef]
Yi, B.-J. , and Freeman, R. A. , 1993, “Geometric Analysis of Antagonistic Stiffness in Redundantly Actuated Parallel Mechanisms,” J. Rob. Syst., 10(5), pp. 581–603. [CrossRef]
Kumar, V. , and Gardner, J. , 1990, “Kinematics of Redundantly Actuated Closed Chains,” IEEE Trans. Rob. Autom., 6(2), pp. 269–274. [CrossRef]
Cheng, H. , Liu, G. , Yiu, Y. K. , Xiong, Z. , and Li, Z. , 2001, “Advantages and Dynamics of Parallel Manipulators With Redundant Actuation,” IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Maui, HI, Oct. 29–Nov. 3, pp. 171–176.
Liu, G. , Wu, Y. , Wu, X. , Kuen, Y. , and Li, Z. , 2001, “Analysis and Control of Redundant Parallel Manipulators,” IEEE International Conference on Robotics and Automation (ICRA), Seoul, South Korea, May 21–26, pp. 3748–3754.
Garrido, R. , and Torres-Cruz, D. , 2004, “On PD Control of Parallel Robots With Redundant Actuation,” Fir st International Conference on Electrical and Electronics Engineering (ICEEE), Acapulco, Mexico, Sept. 8–10, pp. 356–360.
Wu, J. , Wang, J. , Wang, L. , and Li, T. , 2009, “Dynamics and Control of a Planar 3-DOF Parallel Manipulator With Actuation Redundancy,” Mech. Mach. Theory, 44(4), pp. 835–849. [CrossRef]
Tang, H. T. , Yao, J. T. , Cheng, L. , and Zhao, Y. S. , 2012, “Hybrid Force/Position Control Investigation of Parallel Machine Tool With Redundant Actuation,” Frontiers of Manufacturing and Design Science II (Applied Mechanics and Materials, Vol. 121), Trans Tech Publications, Zurich, Switzerland, pp. 2040–2044. [CrossRef]
Shang, W. , Cong, S. , Zhang, Y. , and Liang, Y. , 2009, “Active Joint Synchronization Control for a 2-DOF Redundantly Actuated Parallel Manipulator,” IEEE Trans. Control Syst. Technol., 17(2), pp. 416–423. [CrossRef]
Shang, W. , and Cong, S. , 2010, “Nonlinear Adaptive Task Space Control for a 2-DOF Redundantly Actuated Parallel Manipulator,” Nonlinear Dyn., 59(1–2), pp. 61–72. [CrossRef]
Kock, S. , and Schumacher, W. , 1998, “A Parallel x-y Manipulator With Actuation Redundancy for High-Speed and Active-Stiffness Applications,” IEEE International Conference on Robotics and Automation (ICRA), Leuven, Belgium, May 16–20, pp. 2295–2300.
Shang, W.-W. , Cong, S. , and Ge, Y. , 2012, “Adaptive Computed Torque Control for a Parallel Manipulator With Redundant Actuation,” Robotica, 30(3), pp. 457–466. [CrossRef]
Müller, A. , 2010, “Consequences of Geometric Imperfections for the Control of Redundantly Actuated Parallel Manipulators,” IEEE Trans. Rob., 26(1), pp. 21–31. [CrossRef]
Müller, A. , 2011, “Problems in the Control of Redundantly Actuated Parallel Manipulators Caused by Geometric Imperfections,” Meccanica, 46(1), pp. 41–49. [CrossRef]
Kock, S. , and Schumacher, W. , 2000, “A Mixed Elastic and Rigid-Body Dynamic Model of an Actuation Redundant Parallel Robot With High-Reduction Gears,” IEEE International Conference on Robotics and Automation (ICRA), San Francisco, CA, Apr. 24–28, pp. 1918–1923.
Belda, K. , Bohm, J. , and Valasek, M. , 2003, “State-Space Generalized Predictive Control for Redundant Parallel Robots,” Mech. Des. Struct. Mach., 31(3), pp. 413–432. [CrossRef]
Liu, G. F. , Yiu, Y. K. , and Li, Z. X. , 2002, “Inertia Equivalence Principle and Adaptive Control of Parallel Manipulators With Redundant Actuation,” American Control Conference (ACC), Anchorage, AK, May 8–10, pp. 3196–3201.
Shang, W. , and Cong, S. , 2014, “Robust Nonlinear Control of a Planar 2-DOF Parallel Manipulator With Redundant Actuation,” Rob. Comput. Integr. Manuf., 30(6), pp. 597–604. [CrossRef]
Merlet, J.-P. , 2006, “Jacobian, Manipulability, Condition Number, and Accuracy of Parallel Robots,” ASME J. Mech. Des., 128(1), pp. 199–206. [CrossRef]
Kong, X. , and Gosselin, C. M. , 2007, Type Synthesis of Parallel Mechanisms, Springer, New York.
Gogu, G. , 2008, Structural Synthesis of Parallel Robots, Springer, New York. [CrossRef] [PubMed] [PubMed]

Figures

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Fig. 1

Redundantly actuated parallel mechanisms: (a) general model of a redundantly actuated n-dof parallel mechanism with m actuators, where m > n and (b) example of a redundantly actuated 6dof parallel mechanism (8-HPS) with eight legs

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Fig. 2

Kinematically redundant parallel mechanisms. (a) Kinematically redundant u-dof parallel mechanism. The platform has m-dof, r of the legs are kinematically redundant, and (m − r) of the legs are not redundant. (b) Example of a kinematically redundant 6dof platform with a total of 9dofs. Three legs are redundant and contain one extra dof and one extra actuator (prismatic actuator at the base) each. The actuators in the redundant legs are placed in series. (c) Example of a kinematically redundant 6dof platform with a total of 9dofs. Three legs are redundant and contain one extra dof and one extra actuator (second prismatic cylinder) each. The actuators in the redundant legs are placed in parallel.

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Fig. 3

Kinematically redundant planar 4dof ((3 + 1)-dof) parallel mechanism with RPR legs. The redundant leg is in a singular configuration if points A3, S, and A4 are aligned.

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Fig. 4

Kinematically redundant leg with two actuators in parallel. The joints at A1 and A2 are Hooke joints, the joint at B is a spherical joint, and the joint at S is a revolute joint.

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Fig. 5

Kinematically redundant leg with three actuators in parallel and one in series. The joints at Ai, i = 1, 2, 3 are Hooke joints, and the joints at S and B are spherical joints.

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Fig. 6

Kinematically redundant leg with two actuators placed in series and one in parallel. The joints at A1 and A2 are Hooke joints, the joint at B is a spherical joint, and the joint at S is a revolute joint.

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Fig. 7

Examples of redundant parallel mechanisms obtained from a planar 3-RRR parallel mechanism. The actuated joints are represented with dark circles, while the unactuated joints are represented with white circles. (a) Original 3dof planar parallel mechanism (3-RRR). (b) Case 1: 3dof parallel mechanism with one leg replaced by a redundant leg of the type RRR (leading to a mechanism of the type RR R + 2R RR). (c) Case 2: 3dof parallel mechanism with one nonredundant leg added (leading to a mechanism of the type 4-RRR). (d) Case 3: 3dof parallel mechanism with one leg replaced by a redundant leg of the type RR RR (leading to a mechanism of the type RR RR + 2R RR). (e) Case 4: 3dof parallel mechanism with one leg replaced by a redundant leg of the type 2(RR)-RR (leading to a mechanism of the type 2(RR)-RR + 2R RR).

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Fig. 8

Simplified model and graph representation of kinematically redundant parallel mechanisms with intermediate bodies: (a) 12dof Dodekapod of Ref. [77], (b) 9dof redundant parallel mechanism proposed in Refs. [76] and [78], (c) graph representation of the 12dof Dodekapod of Ref. [77], and (d) graph representation of the 9dof redundant parallel mechanism of Refs. [76] and [78]

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