Kinematics and dynamics of a 4- P RUR Schönflies parallel manipulator by means of screw theory and the principle of virtual work

Schönflies, 1886, Über gruppen von bewegungen, Math. Ann., 28, 319, 10.1007/BF02439997 Makino, 1982, SCARA robot and its family, 433 Pierrot, 2009, Optimal design of a 4-DOF parallel manipulator: From academia to industry, IEEE Trans. Robot., 25, 213, 10.1109/TRO.2008.2011412 Clavel, 1988, A fast robot with parallel geometry, 91 Angeles, 2006, Kinetostatic design of an innovative schönflies-motion generator, Proc. IMechE Part C, 200, 935, 10.1243/09544062JMES258 Rolland, 1999, The manta and the kanuk: Novel 4-dof parallel mechanisms for industrial handling, 831 Zhao, 2006, Mobility properties of a schoenflies type parallel manipulator, Robot. Comput. Integr. Manuf., 22, 124, 10.1016/j.rcim.2005.02.007 Cao, 2016, Type synthesis of fully-decoupled three-rotational and one-translational parallel mechanisms, Int. J. Adv. Robot. Syst., 13, 1, 10.5772/62684 Kang, 2016, Design of a new gravity balanced parallel mechanism with schönflies motion, Proc. IMechE Part C, 230, 3111, 10.1177/0954406215605862 Altuzarra, 2011, Optimal dimensioning for parallel manipulators: workspace, dexterity, and energy, ASME J. Mech. Des., 133, 10.1115/1.4003879 Amine, 2012, Singularity conditions of 3T1R parallel manipulators with identical limb structures, ASME J. Mech. Robot., 4, 10.1115/1.4005336 Masouleh, 2012, Solving the forward kinematic problem of 4-DOF parallel mechanisms (3T1R) with identical limb structures and revolute actuators using the linear implicitization algorithm, 969 Liu, 2012, Optimal design of a 4-DOF SCARA type parallel robot using dynamic performance indices and angular constraints, ASME J. Mech. Robot., 4, 10.1115/1.4006743 Yi, 2013, Multi-task oriented design of an asymmetric 3T1R type 4-DOF parallel mechanism, Proc. IMechE Part C, 227, 2236, 10.1177/0954406212473726 Corves, 2016, Design methodology for translational parallel manipulators exhibiting actuation redundancy, Proc. IMechE Part C, 230, 425, 10.1177/0954406215591048 Alessandro, 2014, Elastodynamic optimization of a 3T1R parallel manipulator, Mech. Mach. Theory, 73, 184, 10.1016/j.mechmachtheory.2013.10.010 Xie, 2015, Design and development of a high-speed and high-rotation robot with four identical arms and a single platform, ASME J. Mech. Robot., 7, 10.1115/1.4029440 Angeles, 2006, The design and prototyping of an innovative schöenflies motion generator, Proc. IMechE Part C, 220, 935, 10.1243/09544062JMES258 Kim, 2015, Development of a novel two-limbed parallel mechanism having schönflies motion, Proc. IMechE Part C, 229, 136, 10.1177/0954406214532633 Nurahmi, 2016, Reconfiguration analysis of a 4-RUU parallel manipulator, Mech. Mach. Theory, 96, 269, 10.1016/j.mechmachtheory.2015.09.004 Cervantes-Sánchez, 2016, An integrated study of the workspace and singularity for a schönflies parallel manipulator, J. Appl. Res. Tech., 14, 9, 10.1016/j.jart.2016.01.004 Cao, 2018, A method for stiffness analysis of overconstrained parallel robotic mechanisms with scara motion, Robot. Comput. Integr. Manuf., 49, 426, 10.1016/j.rcim.2017.08.014 Kong, 2004, Type synthesis of 3T1R 4-DOF parallel manipulators based on screw theory, IEEE Trans. Robot. Autom., 20, 181, 10.1109/TRA.2003.820853 Gogu, 2002, Structural synthesis of parallel robotic manipulators with decoupled motions Rizk, 2006, Precision study of a decoupled four degrees parallel robot including manufacturing and assembling errors, 1 Rat, 2010 Varshovi-Jaghargh, 2014, Forward kinematic problem of three 4-DOF parallel mechanisms (4-PRUR1, 4-PRUR2 and 4-PUU) with identical limb structures performing 3T1R motion pattern, Sci. Iran. B, 21, 1671 Gallardo-Alvarado, 2017, Análisis cinemático del manipulador paralelo 4-PRUR mediante la teoría de tornillos, Rev. Iberoam. Autom. Inf. Ind., 14, 299, 10.1016/j.riai.2017.03.001 Gallardo-Alvarado, 2016 Li, 2004, Mobility analysis of a novel 3-5r parallel mechanism family, ASME J. Mech. Des., 126, 79, 10.1115/1.1637651 Dai, 2004, Mobility of overconstrained parallel mechanisms, ASME J. Mech. Des., 128, 220, 10.1115/1.1901708 Masouleh, 2011, Kinematic analysis of 5-RPUR (3T2R) parallel mechanisms, Meccanica, 46, 131, 10.1007/s11012-010-9393-x Gallardo-Alvarado, 2014, A simple method to solve the forward displacement analysis of the general six-legged parallel manipulator, Robot. Comput. Integr. Manuf., 30, 55, 10.1016/j.rcim.2013.09.001 Verschelde, 1999, Algorithm 795: PHCpack: a general-purpose solver for polynomial systems by homotopy continuation, ACM Trans. Math. Soft., 25, 251, 10.1145/317275.317286 Bonev, 2003, Singularity analysis of 3-dof planar parallel mechanisms via screw theory, ASME J. Mech. Des., 125, 573, 10.1115/1.1582878 Choi, 2012, Singularity analysis of a four degree-of-freedom parallel manipulator based on an expanded 6 × 6 jacobian matrix, Mech. Mach. Theory, 57, 51, 10.1016/j.mechmachtheory.2012.06.008 Gosselin, 1990, Singularity analysis of closed-loop kinematic chains, IEEE Trans. Robot. Autom., 6, 281, 10.1109/70.56660 Amine, 2010, Singularity Analysis of Lower-Mobility Parallel Robots with an Articulated Nacelle Amine, 2011, Singularity analysis of the 4-RUU parallel manipulator using Grassmann-Cayley algebra, 1 Amine, 2011, Singularity analysis of the 4-RUU parallel manipulator based on grassmann-cayley algebra and grassmann geometry, 28 Amine, 2012, Singularity analysis of the h4 robot using grassmann-cayley algebra, Robotica, 30, 1, 10.1017/S0263574711001330 Borchert, 2015, Analysis of the mass distribution of a functionally extended delta robot, Robot. Comput. Integr. Manuf., 31, 111, 10.1016/j.rcim.2014.08.003 Jiang, 2015, Dynamic modeling and redundant force optimization of a 2-DOF parallel kinematic machine with kinematic redundancy, Robot. Comput. Integr. Manuf., 32, 1, 10.1016/j.rcim.2014.08.001 Xin, 2016, Closed-form dynamics of a 3-DOF spatial parallel manipulator by combining the lagrangian formulation with the virtual work principle, Nonlinear Dyn., 86, 1329, 10.1007/s11071-016-2967-y Liang, 2016, Optimum design of a novel redundantly actuated parallel manipulator with multiple actuation modes for high kinematic and dynamic performance, Nonlinear Dyn., 83, 631, 10.1007/s11071-015-2353-1 Wang, 2017, Kinematic/dynamic analysis and optimization of a 2-URR-RRU parallel manipulator, Nonlinear Dyn., 88, 503, 10.1007/s11071-016-3256-5 Chen, 2017, Dynamic modeling and performance analysis of the 3-PRRU 1t2r parallel manipulator without parasitic motion, Nonlinear Dyn., 10.1007/s11071-017-3665-0 Liang, 2017, Nonlinear dynamic modeling and performance analysis of a redundantly actuated parallel manipulator with multiple actuation modes based on FMD theory, Nonlinear Dyn., 89, 391, 10.1007/s11071-017-3461-x Zhang, 2018, Computationally efficient dynamic modeling of robot manipulators with multiple flexible-links using acceleration-based discrete time transfer matrix method, Robot. Comput. Integr. Manuf., 49, 181, 10.1016/j.rcim.2017.06.010 Tsai, 1999 X. Kong, C. Gosselin, Patent US6997669b2, 2006.