With regard to planar parallel manipulators, a general classification of singularities into three groups is given. The classification scheme relies on the properties of instantaneous centers of rotation. This method is very fast and can easily be applied to the manipulators under study. The method is applied to a planar three-degrees-of-freedom parallel manipulator and all its singular configurations are found.
SugimotoK.DuffyJ. and HuntK. H., ‘Special configurations of spatial mechanisms and robot arms’, Mechanism and Machine Theory, 17(2) (1982), 119–132.
2.
LitvinF. L.YiZ.Parenti-CastelliV. and InnocentiC., ‘Singularities, configurations, and displacement functions for manipulators’, Int. J. Robotics Research, 5(2) (1986), 52–65.
3.
ShamirT., ‘The singularities of redundant robot arms’, Int. J. Robotics Research, 9(1) (1990), 113–121.
4.
MohamedM. G., Instantaneous Kinematics and Joint Displacement Analysis of Fully-Parallel Robotic Devices (Doctoral Dissertation, University of Florida, Gainesville, 1983).
5.
MerletJ. P., ‘Singular configurations of parallel manipulators and Grassmann geometry’, Int. J. Robotics Research, 8(5) (1989), 45–56.
6.
ZlatanovD.FentonR. G. and BenhabibB., ‘Singularity analysis of mechanisms and robots via a motion-space model of the instantaneous kinematics’, in Proceedings of the IEEE International Conference on Robotics and Automation (San Diego, 1994), pp. 980–985.
7.
ZlatanovD.FentonR. G. and BenhabibB., ‘Singularity analysis of mechanisms and robots via a velocity-equation model of the instantaneous kinematics’, in Proceedings of the IEEE International Conference on Robotics and Automation (San Diego, 1994), pp. 986–991.
8.
NotashL., ‘Uncertainty configurations of parallel manipulators’, Mechanism and Machine Theory, 33(12) (1998), 123–138.
9.
DanialiMohammadi H. R.Zsombor-MurrayP. J. and AngelesJ., ‘Singularity analysis of planar parallel manipulators’, Mechanism and Machine Theory, 30(5) (1995), 665–678.
10.
KozakK.Ebert-UphoffI.VoglewedeP. A. and SinghoseW., ‘Concept paper: On the significance on the lowest linearized natural frequency of a parallel manipulator as a performance measure for concurrent design’, in GosselinC. M. and Ebert-UphoffI. (eds), Proceedings of the Workshop on Fundumental Issues and Future Research Directions for Parallel Mechanisms and Manipulators (Quebec, 2002).
11.
AngelesJ., Rational Kinematics (Springer, New York, 1988).
