The toggle–brace–damper system (TBDS) is an effective displacement amplification damper occupying a large building space. The small deformation solution, which is widely used, cannot describe the feature that the displacement amplification capacity varies with the lateral displacement of the TBDS. This is not conducive to investigate the performance of the TBDS comprehensively. Therefore, the geometric design and optimization of the TBDS are lack of a theoretical basis. A generalized toggle–brace–damper system (GTBDS), a generalized form of TBDS, is proposed. It has a flexible layout and optimizes the space available. We also introduce an amplification factor of displacement increment (AFDI) that can accurately describe the performance of the GTBDS. The amplification capacity and the geometric sensitivity are two aspects of the performance. The influence of geometric parameters on the performance of the GTBDS is clarified based on the AFDI. Some regulations are also proposed to compare the performance of GTBDSs with different geometric constructions. Two geometric parameter optimization methods of the GTBDS are proposed to balance its amplification capacity, operation safety and geometric sensitivity. The relationship between the displacement amplification capacity and the energy dissipation capacity of the GTBDS is examined. The existing modal energy dissipation method (MEDM) is extended to calculate the additional damping ratio (ADR) provided by the GTBDS. Combining the calculation method of ADR and the geometric optimization methods of GTBDS, a multiperformance objectives design method of the GTBDS is proposed. The case analysis verifies the effectiveness and the feasibility of the design method.

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