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.

In this study a procedure to obtain direct singular positions of a 3RPS parallel manipulator is presented. If the heights of 3 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 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.

A grinding process model for an automatic grinding system with grinding force control is developed in this paper. This grinding system utilises an electric hand grinder, driven by a CNC machine centre and a force sensor for force measurement. This model includes compliance of the grinding system and is initially represented by a series of springs. The stiffness of each component is estimated in this study and it is found that the model may be simplified into a single spring-mass system. A corresponding PID controller is designed for the purpose of grinding force control, which calculates the appropriate CNC spindle displacement according to the force measured by the force sensor. Computer simulation results show that the system settling time is less than 0.25 s.

A boundary element technique has been developed to analyze interface cracks in a layered solid. The loading applied on the solid may be tension, compression, shear, or an arbitrary combination of these. Crack surfaces may be open, closed, or partially open and partially closed. In all these cases, energy release rates can always be determined by using this technique. Crack-tip conditions are determined by an iterative procedure so that they themselves are parts of the solutions of a problem. The numerical technique is utilized to analyze subsurface interface cracks in a layered solid. Results are shown for various materials and under various loading conditions.

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