Direct Singular Positions of 3RPS Parallel Manipulators

In this study a procedure to obtain direct singular positions of a 3RPS parallel manipulator is presented. If the heights of three spherical joints, denoted by $d1n,$$d2n,$ and $d3n$ respectively, are used as coordinate axes, then the workspace of the moving platform may be represented as an inclined solid cylinder in this coordinate system. The location of a point on the solid circular cylinder determines a configuration of the manipulator’s moving platform. The procedure to locate direct singular positions consists of two steps, the orientation of the moving platform is assumed first, from which the horizontal position of the moving platform may be obtained. Then in the second step the heights that make determinant of the Jacobian matrix vanish may always be determined. Results show that unless the moving platform is normal to the base, in which case there exist only one or two singular configurations, otherwise there are always three singular configurations corresponding to a moving platform’s orientation.