Matrix modelling in dynamics of a 2-DOF orienting gear train

L.-C. Hsieh, K.-B. Sheu, Conceptual design of planetary bevel-gear trains for robotic wrist, in: Proceedings of 9th World Congress on the Theory of Machines and Mechanisms, Milan, 1995, pp. 1861–1865. Paul, 1983, Kinematics of robot wrists, International Journal of Robotic Researches, 2, 31, 10.1177/027836498300200103 Willis, 1982, On the kinematics of the closed epicyclic differential gears, ASME Journal of Mechanical Design, 104, 712, 10.1115/1.3256415 Ma, 1989, On the motion of oblique geared robot wrists, Journal of Robotic Systems, 5, 509, 10.1002/rob.4620060503 White, 1988, Epicyclical gears applied to early steam engines, Mechanism and Machine Theory, 23, 25, 10.1016/0094-114X(88)90006-7 Angeles, 2002 Gosselin, 1989, The optimum kinematics design of a spherical three-degree-of-freedom parallel manipulator, ASME Journal of Mechanical Design, 111, 202 C. Gosselin, M. Gagné, Dynamic models for spherical parallel manipulators, in: Proceedings of the IEEE International Conference on Robotics & Automation, Milan, 1995. Tsai, 1999 Tsai, 1987, An application of the linkage characteristic polynomial to the topological synthesis of planetary gear trains, ASME Journal of Mechanisms, Transmissions and Automation in Design, 109, 329, 10.1115/1.3258798 Tsai, 1988, The kinematics of spatial robotic bevel-gear trains, IEEE Journal on Robotics and Automation, 4, 150, 10.1109/56.2078 Staicu, 2008, A novel dynamic modelling approach for parallel mechanisms analysis, Robotics and Computer-Integrated Manufacturing, 24, 167, 10.1016/j.rcim.2006.09.001 Staicu, 2009, Dynamics analysis of the Star parallel manipulator, Robotics and Autonomous Systems, 57, 1057, 10.1016/j.robot.2009.07.005 Freudenstein, 1984, Kinematic analysis of robotic bevel-gear train, ASME Journal of Mechanisms, Transmissions and Automation in Design, 106, 371, 10.1115/1.3267421 Tsai, 1998, Dynamic analysis of geared robotic mechanisms using graph theory, ASME Journal of Mechanical Design, 120, 240, 10.1115/1.2826964 Chang, 1989, Topological synthesis of articulated gear mechanisms, IEEE Journal of Robotics and Automation, 6, 97, 10.1109/70.88121 Hedman, 1993, Transmission analysis: automatic derivation of relationships, ASME Journal of Mechanical Design, 115, 1031, 10.1115/1.2919252 H.-S. Yan, L.-C. Hsieh, Kinematic analysis of general planetary gear trains, in: Proceedings of 8th World Congress on the Theory of Machines and Mechanisms, Prague, 1991, pp. 153–157. Yan, 1994, Conceptual design of gear differentials for automatic vehicles, ASME Journal of Mechanical Design, 116, 565, 10.1115/1.2919415 Y.-W. Li, J. Wang, L.-P. Wang, X.-J. Liu, Inverse dynamics and simulation of a 3-DOF spatial parallel manipulator, in: Proceedings of the IEEE International Conference on Robotics & Automation ICRA’2003, Taipei, Taiwan, 2003, pp. 4092–4097. Dasgupta, 1998, A Newton–Euler formulation for the inverse dynamics of the Stewart platform manipulator, Mechanism and Machine Theory, 33, 1135, 10.1016/S0094-114X(97)00118-3 Lee, 1999, Kinematic and dynamic analysis of a double parallel manipulator for enlarging workspace and avoiding singularities, IEEE Transaction on Robotics and Automation, 15, 1024, 10.1109/70.817667 Geng, 1992, On the dynamic model and kinematic analysis of a class of Stewart platforms, Robotics and Autonomous Systems, 9, 237, 10.1016/0921-8890(92)90041-V Miller, 1992, The Lagrange-based model of delta-4 robot dynamics, Robotersysteme, 8, 49 Zhang, 1993, An efficient method for inverse dynamics of manipulators based on virtual work principle, Journal of Robotic Systems, 10, 605, 10.1002/rob.4620100505 Staicu, 2009, Explicit dynamics equations of the constrained robotic systems, Nonlinear Dynamics, 58, 217, 10.1007/s11071-009-9473-4 Staicu, 2010, Dynamics analysis of the Minuteman cover drive, European Journal of Mechanics–A/Solids, 29, 91, 10.1016/j.euromechsol.2009.07.001