Aiming at unidentity between theoretical research and practical processing, this paper, also at the first time, proposes the concept of cutting transition surface of the wormgear by hob, and correspondingly, establishes the conditions under which the solution of the turning point problem can be worked out.

Track synthesis of planar link mechanism that passing through two additional cusps;

But its a pity that all existed B_spline methods cannot reconstruct complicated surfaces with cusps and arrises.

The cusp catastrophe theory was described.

By virtue of sub- and supersolution method, it is shown that there are many nonnegative nontrivial spike-layer solutions and positive intermediate spike-layer solutions.

To meet the need of high accuracy in NC machining,several errors and its cause have been analyzed from actual geometric angle of tool because tool tip of NC programming differs from cutting point of tool.

The Tool Tip Offset in NC Turning;