Several important developing phases of the formulas for mobility calculation based on constraints are introduced. The shortcoming of the mobility formulas based on common constraints of loops of a mechanism is that virtual constraints must be calculated before determining the mobility of a mechanism with virtual constraints. In order to avoid the shortcoming, some new concepts including virtual loop, virtual-loop constraint and general-kinematic-pair constraint are used to analyze the relationship between mobility of links and constraint of kinematic pairs and a mobility formula based on common constraints of virtual loops is proposed. The formula is that the number of mobility of a mechanism is the sum of mobility of all links in the mecha-nism minus the sum of constraints of all kinematic pairs plus the sum of the common constraints of all virtual loops. The sum of over constraints of a mechanism is the sum of constraints of all virtual loops in the mechanism. This mobility formula expressed in terms of common constraints of virtual loops in a mechanism can avoid calculating virtual constraints. It is proved that the new formula is correct, simple and effective through the analysis of several different kinds of mechanisms.
