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A new mathematical model based on DOF variation was purposed for linear orientation tolerance. According to ASME standard, the relationships between the constrained features and datum of linear parallelism, perpendicularity and angularity were analyzed respectively. The forms of tolerance zone were developed based on difference measurement requirements and conditions. The mathematical model of linear orientation tolerance was deduced systematically. By using this model, the semantics of tolerance was exactly represented and could be used by the following processing. An example was analyzed to show the effectiveness of this model in tolerance analysis.