Bi-directional Algebraic Graphic Statics : On Force Diagram Constraints

This paper presents a study exploring the capabilities of a new method, described by Akesson and Alic [1], which extends the capabilities of the algebraic graphic statics method, by Van Mele and Block [11]. The new method extends the algebraic graphic statics method by making it bi-directional i.e. allowing for determination of an updated form diagram by making direct interactive manipulations of the force diagram. In the new method, Newton’s method is used for solving a set of non-linear equations, to find an updated form diagram from given changes in the force diagram. Additional geometric constraints are introduced on the form diagram to obtain desired solutions. The implementation of the method as a back-end to an interactive application is discussed, and the usability of the method is shown in examples where the qualities of directly manipulating the force diagram are discussed. The main part of this paper will supplement Akesson and Alic [1] by presenting further studies of the application of constraints to the force diagram, and which shapes this leads to in the form diagram. Further, the paper will present how to adapt force and form diagrams for interactive graphical representations suitable for computers. (Less)