Dexterity of underactuated six degrees of freedom three dimensional redundant manipulators

We quantify the dexterity of underactuated robot manipulators equipped with active and passive joints. We discuss the harnessing of redundant degrees of freedom in a robotic manipulator in order to keep it in service. We assume that the passive joints are locked at an arbitrary known position. There are three important dexterity measures: workspace volume, reachability, and manipulability. We discuss the workspace volume of a six degrees of freedom, three dimensional, redundant manipulator with an arbitrarily located passive joint. References X. Xin, J.-H. She, T. Yamasaki and Y. Liu, Swing-up control based on virtual composite links for n-link underactuated robot with passive first joint, Automatica , 45(9):1986–1994, 2009. doi:10.1016/j.automatica.2009.04.023 M. Bergerman and Y. Xu, Dexterity of underactuated manipulators, ICAR , 719–724, 1997. doi:10.1109/ICAR.1997.620261 S, Yahya, M. Moghavvemi and H. A. F. Mohamed, Singularity Avoidance of a Six Degrees of Freedom Three Dimensional Redundant Planar Manipulator, Comput. Math. Appl. , 64(5):856–868, 2012. doi:10.1016/j.camwa.2011.12.073 S. Yahya, M. Moghavvemi and H. A. F. Almurib, Joint Torque Reduction of a Three Dimensional Redundant Planar Manipulator, Sensors , 12(6):6869–6892, 2012. doi:10.3390/s120606869 A. K. Pradeep, P. J. Yoder, R. Mukundan, R. J. Schilling, Crippled motion in robots, IEEE T. Aero. Elec. Sys. , 24(1):2–13, 1988. doi:10.1109/7.1030 R. G. Roberts, Quantifying the local fault tolerance of a kinematically redundant manipulator, Amer. Contr. Conf. , 3:1889–1893, 1995. doi:10.1109/ACC.1995.531215 R. G. Roberts and A. A. Maciejewski. A local measure of fault tolerance for kinematically redundant manipulators, IEEE Int. Conf. Robot. , 12(4):543–552, 1996. doi:10.1109/70.508437 S. Yahya, M. Moghavvemi and H. A. F. Mohamed. Geometrical approach of planar hyper-redundant manipulators: Inverse kinematics, path planning and workspace, Simul. Model. Pract. Th. , 19(1):406–422, 2011. doi:10.1016/j.simpat.2010.08.001 H. A. F. Mohamed, S. Yahya, M. Moghavvemi and S. S. Yang. A New Inverse Kinematics Method for Three Dimensional Redundant Manipulators, ICCAS-SICE , 1557–1562, 2009. http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=5335259&refinements%3D4274859776%26sortType%3Dasc_p_Sequence%26filter%3DAND%28p_IS_Number%3A5332438%29