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Published December 1, 2023 | Published
Journal Article

Multi-configuration rigidity: Theory for statically determinate structures

  • 1. ROR icon California Institute of Technology


This paper introduces the concept of multi-configuration rigidity for kinematically indeterminate structures with elastic springs and unilateral constraints. A simple example is provided by a structure with a single mechanism and a spring that engages two different unilateral constraints. In each of these configurations, the structure can rigidly support loads up to a critical magnitude at which the unilateral constraints become inactive. The general design problem of embedding springs throughout a structure to achieve multi-configuration rigidity, with multiple unilateral constraints and springs, is studied. This problem is cast as a linear program that maximizes the critical loads required to break free from the unilateral constraints, in all target configurations. This problem can be efficiently solved with guarantees of optimality. The formulation is generally applicable to a variety of discrete structures (e.g., linkages, pin-jointed bars, or origami) with unilateral constraints (e.g., contacts or cables).

    Copyright and License

    © 2023 Elsevier.


    This research was funded by the Air Force Office of Scientific Research under award number FA9550-18-1-0566 directed by Dr. Ken Goretta.

    Data Availability

    No data was used for the research described in the article.

    Conflict of Interest

    The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

    Additional details

    February 1, 2024
    February 1, 2024