New concept and new theory of mobility calculation for multi-loop mechanisms

In 2005, Gogu, a Frenchman, analyzed 35 different existing formulas for mobility calculation and pointed that the formulas for quick mobility calculation had some limitations and were not general. Therefore, looking for a general and simple mobility formula is still a hot topic in mechanisms. At the meantime, it is also an important topic to complete the mechanism theory. Gogu proposed a new method that can avoid determining virtual constraints in 2008, but the method is still not general. To solve the problem, this paper defines the new concepts of link-group rank, general-kinematic-pair rank, virtual pair, virtual loop, and virtual-loop rank, and gives a new simple and general formula. Our method converts multi-loop mechanisms into some independent virtual loops, simplifies the problem, avoids calculating virtual constraints, and reduces the calculation difficulty. It is proved that the new formula is simple, general and effective through the mobility analysis of several different kinds of mechanisms. The application of this formula will provide great convenience for general engineers in mobility calculation.