A method of investigating quasi-static mechanisms is presented and applied to an overcenter mechanism and to a nose landing gear mechanism. The method uses static equilibrium equations along with equations describing the geometric constraints in the mechanism. In the spirit of bifurcation analysis, solutions to these steady-state equations are then continued numerically in parameters of interest. Results obtained from the bifurcation method agree with the equivalent results obtained from two overcenter mechanism dynamic models (one state-space and one multibody dynamic model), while a considerable computation time reduction is demonstrated with the overcenter mechanism. The analysis performed with the nose landing gear model demonstrates the flexibility of the continuation approach, allowing conventional model states to be used as continuation parameters without a need to reformulate the equations within the model. This flexibility, coupled with the computation time reductions, suggests that the bifurcation approach has potential for analyzing complex landing gear mechanisms.