Self-locking analysis in multi degree of freedom mechanism and its application to parallel kinematic machines

In this paper, a new methodology to forecast self-locking condition in mechanism with more than 1 D.o.F. is suggested. First, the adopted friction model is introduced: it is derived from coulombian one after a linear approximation. Then, a mathematical elaboration shows the existence of an algebraic loop in the flow of forces: friction forces depend on normal forces that, themselves, depend on friction forces. The limit condition for self-locking occurs when the loop presents not-null solutions. An implementation of a "self-locking tool" based on this methodology is presented: it is able to forecast the most critical motion and friction coefficients that provoke mechanism self-locking. Finally, as example, an application of the tool on a two degree of freedom planar parallel mechanism shows the effectiveness of the suggested approach to self-locking analysis.