Modified Formula of Mobility for Mechanisms

How to determine the degree of freedom (DOF) of parallel mechanisms (PMs) and multiloop spatial mechanisms has been a long standing problem, and it still is an active field of research with plenty open questions. Firstly, three categories formulas expressed with loop-unit are introduced from a new perspective of their treatment for the motion parameter of each independent closed loop(ICL). Secondly, based on some concepts and theory of link group, the analysis provides insight into why the previous formulas do not work for some multiloop mechanisms. Then a modified formula is presented by adding an addition index called loop-redundant-rank, meanwhile the steps of estimate of mobility property are presented. Finally a typical examples is selected to calculate the DOF with the formula mentioned above. And the results coincide with the prototype data, which shows the effectiveness of the proposed method to a certain extent. It can be seen that the formula presented in this paper can do quick mobility calculation and mobility property analyses of parallel mechanisms with elementary legs.