Abstract
In this contribution, a systematic methodology for solving the kinematic and dynamic analyses of a modular spatial hyper-redundant manipulator built with an optional number of serially connected three-legged in-parallel manipulators are presented.
First, the kinematics and dynamics of the base module are carried out using the theory of screws and the principle of virtual work. Next, the expressions obtained for the base module are extended without significant effort to the spatial hyper-redundant manipulator under study. Finally, the proposed methodology of analysis is applied to a 18 degrees of freedom hyper-redundant manipulator.
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Yanqiong, F., Qinglei, D., Xifang, Z.: Modular structure of a self-reconfigurable robot. Front. Mech. Eng. China 2, 116–119 (2007)
Ropponen, T., Nakamura, Y.: Singularity-free parameterization and performance analysis of actuation redundancy. In: IEEE International Conference on Robotics and Automation, pp. 806–811 (1990)
Zergeroglu, E., Dawson, D.D., Walker, I.W., Setlur, P.: Nonlinear tracking control of kinematically redundant robot manipulators. IEEE/ASME Trans. Mechatron. 9(1), 129–132 (2004)
Kim, S.W., Park, K.B., Lee, J.J.: Redundancy resolution of robot manipulators using optimal kinematic control. In: IEEE International Conference on Robotics and Automation, pp. 683–688 (1994)
Hsia, T.C., Guo, Z.Y.: New inverse kinematic algorithms for redundant robots. J. Robot. Syst. 8, 117–132 (1991)
Suh, I.H., Shin, K.G.: Coordination of dual robot arms using kinematic redundancy. IEEE Trans. Robot. Autom. 5(2), 236–242 (1989)
Nguyen, L.A., Walker, I.D., Defigueiredo, R.J.P.: Dynamic control of flexible, kinematically redundant robot manipulators. IEEE Trans. Robot. Autom. 8(6), 759–767 (1992)
Chen, T.H., Cheng, F.T., Sun, Y.Y., Hung, M.H.: Torque optimization schemes for kinematically redundant manipulators. J. Robot. Syst. 11, 257–269 (1994)
Dasgupta, B., Mruthyunjaya, T.S.: Force redundancy in parallel manipulators: theoretical and practical issues. Mech. Mach. Theory 33, 727–742 (1998)
Gallardo-Alvarado, J., Alici, G., Aguilar-Nájera, C., Pérez-González, L.: A new family of non-overconstrained redundantly-actuated parallel manipulators. Multibody Syst. Dyn. (2007, submitted)
Mohamed, M.G., Gosselin, C.M.: Design and analysis of kinematically redundant parallel manipulators with configurable platforms. IEEE Trans. Robot. 21, 277–287 (2005)
Wang, J., Gosselin, C.M.: Kinematic analysis and design of kinematically redundant parallel manipulators. ASME J. Mech. Des. 126, 109–118 (2004)
Bi, Z.M., Gruver, W.A., Zhang, W.J., Lang, S.Y.T.: Automated modeling of modular robotic configurations. Robot. Autom. Syst. 54, 1015–1025 (2006)
Kryriakopoulos, K.J., Migadis, G., Sarriageorgidis, K.: The NTUA snake: Design, planar kinematics, and motion planning. J. Robot. Syst. 16, 37–72 (1999)
Shugen, M.: Naoki T.: Analysis of creeping locomotion of a snake-like robot on a slope. Auton. Robots 20, 15–23 (2006)
Paljug, E., Ohm, T., Hayati, S.: The JPL serpentine robot: a 12-DOF system for inspection. In: Proceedings of the IEEE International Conference on Robotics and Automation, Nagoya, Japan, pp. 3143–3148 (1995)
Pettinato, J.S.: Stephanou, h.E.: Manipulability and stability of a tentacle based robot manipulator. In: Proceedings of the IEEE International Conference on Robotics and Automation, Scottsdale, AZ, vol. 1, pp. 458–463 (1989)
Hanan, M.W., Walker, I.A.: Kinematics and the implementation of an elephant’s trunk manipulator and other continuum style robots. J. Robot. Syst. 20, 45–63 (2003)
Tanev, T.K.: Kinematics of a hybrid (parallel-serial) robot manipulator. Mech. Mach. Theory 35, 1183–1196 (2000)
Zheng, X.Z., Bin, H.Z., Luo, Y.G.: Kinematic analysis of a hybrid serial-parallel manipulator. Int. J. Adv. Manuf. Technol. 23, 925–930 (2004)
Carbone, G., Ceccarelli, M.: A serial-parallel robotic architecture for surgical tasks. Robotica 23, 345–354 (2005)
Carbone, G., Ceccarelli, M.: A stiffness analysis for a hybrid parallel-serial manipulator. Robotica 22, 567–576 (2005)
Gallardo-Alvarado, J.: Kinematics of a hybrid manipulator by means of screw theory. Multibody Syst. Dyn. 14, 345–366 (2005)
Lu, Y., Leinonen, T.: Solution and simulation of position-orientation for multi-spatial 3-RPS parallel mechanisms in series connection. Multibody Syst. Dyn. 14, 47–60 (2005)
Lu, Y., Hu, B.: Solving driving forces of 2(3-SPR) serial-parallel manipulator by CAD variation geometry approach. ASME J. Mech. Des. 128, 1349–1351 (2006)
Hunt, K.H.: Structural kinematics of in-parallel actuated robot arms. ASME J. Mech. Transpr. Autom. Des. 105, 705–712 (1983)
Lee, K.M., Sha, D.K.: Kinematic analysis of a three-degree-of-freedom in-parallel actuated manipulator. In: Proceedings IEEE International Conference on Robotics and Automation, vol. 1, pp. 345–350 (1987)
Kim, H.S., Tsai, L.-W.: Kinematic synthesis of a spatial 3-RPS parallel manipulator. ASME J. Mech. Des. 125, 92–97 (2003)
Liu, C.H., Cheng, S.: Direct singular positions of 3RPS parallel manipulators. ASME J. Mech. Des. 126, 1006–1016 (2004)
Huang, Z., Fang, Y.: Kinematic characteristics analysis of 3 DOF in-parallel actuated pyramid mechanism. Mech. Mach. Theory 31, 1009–1018 (1996)
Fang, Y., Huang, Z.: Kinematics of a three-degree-of-freedom in-parallel actuated manipulator mechanism. Mech. Mach. Theory 32, 789–796 (1997)
Huang, Z., Wang, J.: Identification of principal screws of 3-DOF parallel manipulators by quadric degeneration. Mech. Mach. Theory 36, 893–911 (2001)
Agrawal, S.K.: Study of an in-parallel mechanism using reciprocal screws. In: Proceedings of 8th World Congress on TMM 405-408 (1990)
Huang, Z., Wang, J.: Instantaneous motion analysis of deficient-rank 3-DOF parallel manipulators by means of principal screws. In: Proceedings of A Symposium Commemorating the Legacy, Works, and Life of Sir Robert Stawell Ball Upon the 100th Aniversary of A Treatise on the Theory of Screws (2000)
Huang, Z., Wang, J., Fang, Y.: Analysis of instantaneous motions of deficient-rank 3-RPS parallel manipulators. Mech. Mach. Theory 37, 229–240 (2002)
Gallardo, J., Orozco, H., Rodríguez, R., Rico, J.M.: Kinematics of a class of parallel manipulators which generates structures with three limbs. Multibody Syst. Dyn. 17, 27–46 (2007)
Gallardo, J., Orozco, H., Rico, J.M.: Kinematics of 3-RPS parallel manipulators by means of screw theory. Int. J. Adv. Manuf. Technol. Published on line (2007): http://dx.doi.org/10.1007/s00170-006-0851-5
Alizade, R., Bayram, C.: Structural synthesis of parallel manipulators. Mech. Mach. Theory 39, 857–870 (2004)
Zlatanov, D., Bonev, I.A., Gosselin, C.M.: Constraint singularities of parallel mechanisms. In: IEEE International Conference on Robotics and Automation, ICRA 2002, vol. 1, pp. 496–502 (2002)
Innocenti, C., Parenti-Castelli, V.: Direct position analysis of the Stewart platform mechanism. Mech. Mach. Theory 35, 611–621 (1990)
Tsai, L.-W.: Robot Analysis. Wiley, New York (1999)
Rico, J.M., Duffy, J.: An Application of screw algebra to the acceleration analysis of serial chains. Mech. Mach. Theory 31, 445–457 (1996)
Rico, J.M., Gallardo, J., Duffy, J.: Screw theory and higher order kinematic analysis of open serial and closed chains. Mech. Mach. Theory 34, 559–586 (1999)
Rico, J.M., Duffy, J.: Forward and inverse acceleration analyses of in-parallel manipulators. ASME J. Mech. Des. 122, 299–303 (2000)
Gallardo, J., Rico, J.M.: Screw theory and helicoidal fields. In: Proceedings of the ASME 1998 Design Engineering Technical Conference 1998. CD-ROM format, Paper DETC98/MECH-5893 (1998)
Lipkin, H.: Time derivatives of screws with applications to dynamic and stiffness. Mech. Mach. Theory 40, 259–273 (2005)
Gallardo, J., Rico, J.M., Frisoli, A., Checcacci, D., Bergamasco, M.: Dynamics of parallel manipulators by means of screw theory. Mech. Mach. Theory 38, 1113–1131 (2003)
Gallardo-Alvarado, J., Rico-Martínez, J.M.: Jerk influence coefficients, via screw theory, of closed chains. Meccanica 36, 213–228 (2001)
Ball, R.S.: A Treatise on the Theory of Screws. Cambridge University Press, Reprinted 1998
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Gallardo-Alvarado, J., Aguilar-Nájera, C.R., Casique-Rosas, L. et al. Solving the kinematics and dynamics of a modular spatial hyper-redundant manipulator by means of screw theory. Multibody Syst Dyn 20, 307–325 (2008). https://doi.org/10.1007/s11044-008-9121-7
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DOI: https://doi.org/10.1007/s11044-008-9121-7