According to Euclidean geometry, parallelism is defined as two straight lines being parallel if they lie in a plane and do not intersect. In three-dimensional space, this means that a straight line is parallel to a plane if it lies in the plane itself or does not intersect it. Likewise, two planes are parallel if they lie in each other or do not intersect each other. Two straight lines that do not lie in a plane are called skew. They are neither parallel nor do they intersect. In the form and position tolerances, parallelism is assigned to the direction tolerances in addition to perpendicularity and angularity. It thus represents a positional tolerance, and is defined for surfaces and axes. Toleranced surfaces must lie between two planes that are parallel to the reference. Toleranced axes must lie in a cylinder whose axis is parallel to the reference. Various optical and tactile measuring methods and devices are suitable for checking parallelism.

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