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Some examples of static equivalency in space using descriptive geometry and Grassmann algebra

This paper presents some examples of three- dimensional static equivalency using descriptive geometry and Grassmann algebra. In many static problems, it is convenient to replace existing force system with another, usually simpler, statically equivalent force system. Procedures for replacing two forces with two other forces which fulfil certain conditions (one of the forces on a given line or a force through a given point and a force in a given plane, including special cases with a point or a plane at infinity), thus providing unique replacement of a system of forces with two forces, and the procedure for replacing a single force with three components on three skew lines are described in the main part of the paper.

3D graphic statics, static equivalency, descriptive geometry, Grassmann algebra, Plücker coordinates, line geometry

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