Mobility of mechanisms: a critical review

This paper presents a critical review on the calculation of the mobility, the main structural and kinematic parameter of a mechanism. We focus on a brief presentation and a critical analysis of various methods presented in the literature in the last 150 years, to clearly situate the different contributions to this very important subject of the theory of mechanisms. Thirty five approaches/formulas for mobility calculation are presented and their genesis, similarities and limitations are investigated. The various methods proposed in the literature for mobility calculation are grouped in two categories: approaches based on setting up the kinematic constraint equations and their rank calculation and formulas for a quick calculation of mobility without need to develop the constraint equations. We emphasize on the limits of formulas for quick calculation of mobility by applying them to a parallel robot with elementary legs and ascertaining that the results are erroneous. In fact, the formulas for quick calculation of mobility known in the literature do not fit for many classical or modern mechanisms. We explain why these formulas do not work for certain mechanisms and we propose a new formula for quick mobility calculation of parallel mechanisms with elementary legs.