A unified input–output analysis of four-bar linkages

Proposed in this paper is a unified, robust algorithm for the input–output analysis of planar, spherical and spatial four-bar linkages. Robustness is needed to account for architecture and algebraic singularities that are likely to occur, for example, when conducting an iterative optimization of the linkage at hand. The unified feature of the algorithm is based on the algebra of dual numbers and the Principle of Transference, which allows the extension of the algorithm developed for spherical linkages to their spatial counterparts by a simple dualization of the real geometric relations derived for the former. Numerical examples are included to demonstrate the application of the algorithm.