The kinematics of modular spatial hyper-redundant manipulators formed from RPS-type limbs

G.S. Chirikjian, Theory and Applications of Hyper-Redundant Robotic Manipulators, Doctoral Dissertation, California Institute of Technology, 1992. Chirikjian, 1994, A modal approach to hyper-redundant kinematics, IEEE Transactions on Robotics and Automation, 10, 343, 10.1109/70.294209 Chirikjian, 1995, Kinematically optimal hyper-redundant manipulator configurations, IEEE Transactions on Robotics and Automation, 11, 794, 10.1109/70.478427 Burdick, 1995, A ‘sidewinding’ locomotion gait for hyper-redundant robots, Advanced Robotics, 9, 195, 10.1163/156855395X00166 Bojinov, 2000, Emergent structures in modular self-reconfigurable Robots, vol. 2, 1734 Yanqiong, 2007, Modular structure of a self-reconfigurable robot, Frontiers of Mechanical Engineering in China, 2, 116, 10.1007/s11465-007-0020-z Kyriakopoulos, 1999, The NTUA snake: design, planar kinematics, and motion planning, Journal of Robotic Systems, 16, 37, 10.1002/(SICI)1097-4563(199901)16:1<37::AID-ROB4>3.0.CO;2-V Clement, 1990, Design of a snake-like manipulator, Robotics and Autonomous Systems, 6, 65, 10.1016/0921-8890(90)90017-U E. Paljug, T. Ohm, S. Hayati, The JPL serpentine robot: a 12-DOF system for inspection, in: Proceedings of the IEEE International Conference on Robotics and Automation, Nagoya, Japan, 1995, pp. 3143–3148. J.S. Pettinato, H.E. Stephanou, Manipulability and stability of a tentacle based robot manipulator, in: Proceedings of the IEEE International Conference on Robotics and Automation, vol. 1, Scottsdale, AZ, 1989, pp. 458–463. Hanan, 2003, Kinematics and the implementation of an elephant’s trunk manipulator and other continuum style robots, Journal of Robotic Systems, 20, 45, 10.1002/rob.10070 Yanming, 2003, Design and study of a novel hyper-redundant manipulator, Robotica, 21, 505, 10.1017/S0263574703005125 Wohlhart, 1994, Displacement analysis of the general spherical Stewart platform, Mechanism and Machine Theory, 29, 581, 10.1016/0094-114X(94)90096-5 Romdhane, 1999, Design and analysis of a hybrid serial–parallel manipulator, Mechanism and Machine Theory, 34, 1037, 10.1016/S0094-114X(98)00079-2 Gallardo-Alvarado, 2005, Kinematics of a hybrid manipulator by means of screw theory, Multibody System Dynamics, 14, 345, 10.1007/s11044-005-4196-x Lu, 2005, Solution and simulation of position-orientation for multi-spatial 3-RPS parallel mechanisms in series connection, Multibody System Dynamics, 14, 47, 10.1007/s11044-005-1355-z Lu, 2006, Solving driving forces of 2(3-SPR) serial–parallel manipulator by CAD variation geometry approach, ASME Journal of Mechanical Design, 128, 1349, 10.1115/1.2338577 M. Badescu, C. Mavroidis, Workspace analysis of reconfigurable robotic arms using parallel platforms, in: Proceedings of IMECE’03, Washingtom, DC, 2003. CD-ROM format Paper IMECE2003-42963. Raghavan, 1993, The Stewart platform of general geometry has 40 configurations, ASME Journal of Mechanical Design, 115, 277, 10.1115/1.2919188 C. Innocenti, Forward kinematics in polynomial form of the general Stewart platform, in: Proceedings ASME 25th Biennial Mechanisms Conference, Atlanta, 1998. CD-ROM format Paper DETC98/MECH-5894. Shai, 2006, Extension of graph theory to the duality between static systems and mechanisms, ASME Journal of Mechanical Design, 128, 179, 10.1115/1.2120827 Chirikjian, 1996, Evaluating efficiency of self-reconfiguration in a class of modular robots, Journal of Robotic Systems, 13, 317, 10.1002/(SICI)1097-4563(199605)13:5<317::AID-ROB5>3.0.CO;2-T G.J. Hamlin, A.C. Sanderson, TETROBOT modular robotics: prototype and experiments, in: Proceedings of the 1996 IEEE/RSJ International Conference on Intelligent Robots and Systems’96, IROS 96, Osaka, Japan, 1996, pp. 390–395. Hunt, 1983, Structural kinematics of in-parallel-actuated robot arms, ASME Journal of Mechanism Transmission and Automation in Design, 105, 705, 10.1115/1.3258540 Lee, 1987, Kinematic analysis of a three-degree-of-freedom in-parallel actuated manipulator, vol. 1, 345 Kim, 2003, Kinematic synthesis of a spatial 3-RPS parallel manipulator, ASME Journal of Mechanical Design, 125, 92, 10.1115/1.1539505 Liu, 2004, Direct singular positions of 3RPS parallel manipulators, ASME Journal of Mechanical Design, 126, 1006, 10.1115/1.1803851 Huang, 1996, Kinematic characteristics analysis of 3 DOF in-parallel actuated pyramid mechanism, Mechanism and Machine Theory, 31, 1009, 10.1016/0094-114X(96)84594-0 Fang, 1997, Kinematics of a three-degree-of-freedom in-parallel actuated manipulator mechanism, Mechanism and Machine Theory, 32, 789, 10.1016/S0094-114X(97)00008-6 Huang, 2001, Identification of principal screws of 3-DOF parallel manipulators by quadric degeneration, Mechanism and Machine Theory, 36, 893, 10.1016/S0094-114X(01)00036-2 S.K. Agrawal, Study of an in-parallel mechanism using reciprocal screws, in: Proceedings of 8th World Congress on TMM, 1991, pp. 405–408. Z. Huang, J. Wang, Instantaneous motion analysis of deficient-rank 3-DOF parallel manipulator by means of principal screws, in: Proceedings of A Symposium Commemorating the Legacy, Works, and Life of Sir Robert Stawell Ball Upon the 100th Anniversary of a Treatise on the Theory of Screws, 2000. Huang, 2002, Analysis of instantaneous motions of deficient-rank 3-RPS parallel manipulators, Mechanism and Machine Theory, 37, 229, 10.1016/S0094-114X(01)00075-1 Gallardo-Alvarado, 2008, Kinematics of 3-RPS parallel manipulators by means of screw theory, International Journal of Advanced Manufacturing Technology, 36, 598, 10.1007/s00170-006-0851-5 Rico, 1996, An application of screw algebra to the acceleration analysis of serial chains, Mechanism and Machine Theory, 31, 445, 10.1016/0094-114X(95)00089-H Rico-Martínez, 2000, Forward and inverse acceleration analyses of in-parallel manipulators, ASME Journal of Mechanical Design, 122, 299, 10.1115/1.1288360 Gallardo-Alvarado, 2006, Kinematics and singularity analysis of a 4-dof parallel manipulator using screw theory, Mechanism and Machine Theory, 41, 1048, 10.1016/j.mechmachtheory.2005.10.012 Innocenti, 1990, Direct position analysis of the Stewart platform mechanisms, Mechanism and Machine Theory, 25, 611, 10.1016/0094-114X(90)90004-4 Tsai, 1999 Gallardo-Alvarado, 2007, Kinematics of a class of parallel manipulators which generates structures with three limbs, Multibody System Dynamics, 17, 27, 10.1007/s11044-006-9033-3