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An experimental method has been developed to locate unstable equilibria of nonlinear structures quasistatically. The technique involves loading a structure by the application of either a force or a displacement at a main actuation point while simultaneously controlling the overall shape using additional bidirectional probe points. The method is applied to a shallow arch, and unstable segments of its equilibrium path are identified experimentally for the first time. Shape control is a fundamental building block for the experimental - as opposed to numerical - continuation of nonlinear structures, which will significantly expand our ability to measure their mechanical response.