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. Several important developing phases of the formulas for mobility calculation based on constraints are introduced. The shortcoming of the mobility cycles 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 formulated. The formula is that number the 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 e xpressed 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.