Instantaneous kinematics and singularities of two types of under-actuated parallel wrists

Abstract

S-(nS)PU-SPU and S-(nS)PU-2SPU are two out of three types of under-actuated wrists that are generated from the “ordinary” wrists of type S-3SPU (fully-parallel wrists), by replacing a spherical pair (S) with a nonholonomic spherical pair (nS) according to the rules stated in [1]. Position analysis, controllability, and path planning of these two wrist types have been addressed and solved in two previous papers [2, 3] of this author. Their kinetostatics and singularity analysis have not been addressed, yet; and they are studied in this paper. [1] Grosch, P., Di Gregorio, R., and Thomas, F., 2010, “Generation of under-actuated manipulators with nonholonomic joints from ordinary manipulators,” ASME J. of Mechanisms and Robotics, 2(1): 011005-(8 pages). [2] Di Gregorio R., 2011, “Under-Actuated Nonholonomic Parallel Wrists,” In: Proc. of the 13th World Congress in Mechanism and Machine Science (IFToMM 2011), Guanajuato, México, 19-25 June, 2011, Paper No. A12-264 [3] Di Gregorio, R., 2011, “On the S-(nS)PU-SPU and S-(nS)PU-2SPU under-actuated wrists,” Procs. of the ASME 2011 International Design Engineering Technical Conference & Computers and Information in Engineering Conference, IDETC/CIE 2011, August 28-31, 2011, Washington (DC, USA), Paper No.: DETC2011-47541