Graphical Analysis for Locating Direct Singular Positions of the Parallel Manipulator MIPS^#

Abstract

It is shown in this study the graphical analysis using velocity polygons may be used to locate direct singular positions of a limited degree-of-freedom (DOF) parallel manipulator. The three DOF parallel manipulator MIPS is treated for illustration. The conditions for the moving platform to become movable under zero driving speeds can be obtained using the graphical velocity analysis. Manipulator configurations satisfying these conditions are direct singular positions. Several direct singular positions are determined using this technique. In order to verify these singular positions, Jacobian matrix for this manipulator is also derived in this study, and singular positions determined from graphical analysis can make the Jacobian matrix singular.

Keywords:

• Direct kinematic singularity
• Graphical method
• Kinematics of machinery
• Parallel manipulator—MIPS
• Parallel robot

ACKNOWLEDGMENTS

The authors gratefully acknowledge that this study was partially supported by the National Science Council of ROC under grant no. NSC 93-2212-E032-015.

Notes

^#Communicated by P. Larochelle.