The effect of Coulomb friction on the existence and uniqueness of the forward dynamics problem

When Coulomb friction is added to rigid-body dynamics equations, the forward dynamic solution may not exist. and if it exists it is not necessarily unique. The author studies the existence and uniqueness properties of the forward solution of these equations. It is shown that existence and uniqueness problems arise even for a single degree-of-freedom system and conditions are derived under which such problems occur. A graphical method which clearly shows the number of solutions associated with each value of input torque is presented. A transmission element is used as an example of such a system