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Mathematical modelling of geometric tolerance propagation, considering effects of datums

Abstract Every mechanical part is fabricated with variations in size and shape in the real world. Thus, tolerances are assigned to specify the tolerance zone corresponding to the allowable range of variation in the design shape within which the entire shape element must lie after the manufacturing process. Geometric tolerances constrain the size and the thickness of an individual shape element or its relative position and orientation with respect to the related datums. The effect of the tolerances given to the datums should be propagated to the orientation and the location tolerances in the proper order of precedence. This paper proposes a mathematical foundation for representing the propagation of geometric tolerances while considering the order of precedence of the datums. The effect caused by the tolerances of the datum can also be mathematically handled while considering the datum order of precedence.