Abstract:

：When workpiece is in combined location in non-coplanar planes, every location point is usually distributed at non-orthogonal and non-coplanar planes. The degree of freedom of workpice in fixtures is sometimes misjudged by using traditional positioning principle, which always leads to failure of fixture design. For this problem, the normal at location point where workpiece lies in fixtures is nominated as location normal. A set of geometry theorems that can judge the location state of workpiece are derived according to the amount of location normal and the geometry relationship between them. Some judging principles are given out for normal distribution corresponded with over-positioning of workpiece. The geometry theorem makes the judging method of degree of freedom more precise, simpler and more intuitive and over-positioning of workpiece can be avoided effectively at the same time. Several complicated examples are enumerated. The degree of freedom of workpiece can be judged and the solution can be given out for the unreasonable location by the means of using geometry theorem, which prove that the degree of freedom of workpiece in complicated location state can be judged quickly and accurately. The geometry theorem of workpiece location has developed and completed the location theory of workpiece and is good for correct judgment to the degree of freedom of workpiece in computer aided fixture design.

Key words: combined location in non-coplanar planes, degree of freedom analysis, geometry theorem, location normal, machine tool fixture design