A new method of mobility calculation for planar mechanisms

The classical Grübler-Kutzbach formula for calculating mobility of planar mechanisms seems very simple, however, it is not easy to obtain a correct result for some special mechanisms. In particular, by making an investigation of some cases existing in dozens of current-use textbooks relating to "Theory of Machines and Mechanisms" and "Fundamental to Machine Design", it is found that some results derived from the well-known formula are not correct. For this reason, a new method of mobility calculation for planar mechanisms is proposed, which is establishing upon a derived Grübler-Kutzbach formula. In the proposed method and formula, the new concepts of real-constraint higher pair, redundant-constraint higher pair, full-constraint lower pair and half-constraint lower pair are introduced, thus the puzzle existing in the Grübler-Kutzbach formula can be solved effectively. The research is helpful for making the formula for calculating mobility of planar mechanisms more rigid and scientific.