Optimal Design of Rack-and-Pinion Steering Linkages

A mathematical model is developed for the design synthesis of rack-and-pinion steering linkages. The general objective is to minimize the difference between the steering centers over the full range of steering angle inputs while fitting into a reasonable space. Because there is a substantial amount of design art in these systems and the mathematical representation is not clear, the model, constraints, and objective actually “evolve” to the eventual desired form. The problem has multiple optima, and practical and heuristic considerations are used to choose suboptimal but more realistic solutions, once satisfactory optimal solutions are identified. These involve manipulation of the objective function, constraint set, and intitial guesses. Both leading and trailing link designs are considered, the former being slightly better. Limitations of the model are also presented.