Kinematic analysis for certain and uncertain eccentricity plane lapping processes with the ring polishing machine were studied and compared,pace vector and track equation about one point relative to examination piece on polishing pad were presented.

By explaining the method of conic "not set up " and total elimination and concluding the law of the straight-line where the mid-point trajectory and the mid-point sting are in,this paper demonstrates the method of solving the track equation where the strings of the mid-point trajectory and the mid-point strings are in.

Based on the basic principles of differential geometry the locus equation of the movement of the grinding wheel center during clearance face grinding of the major cutting edge of a ball nose end milling cutter with equal orthogonal clearance angle is deduced,which supply the NC grinding of the clearance face of a ball nose end milling cutter with a feasible mathematical mode

In this paper, by cross ratio, on affine plane, as to conic, we probe the locus equation of intersection point of two tangent lines with intersectional angle θ, and reveal several special examples about it.

The locus equation of the non - locatized interference fringe is given.

The ray trajectory equation and imaging of microlens arrays are presented.