
115Friction-Induced Instabilities and Vibrations
Note that the force T = Rcosϕ is the compression force in the link. Equations
(6.29) and (6.30) form a system for the unknown
and R. In order to solve
the system, one should assume the value of
. However, if μtan(φ) > 2,
then two solutions exists for
:
=
±µ
mx
P(1 ta n( ))
(6.31)
and no solution exists for
.
The Painleve paradoxes indicate that the Coulomb friction is not always
compatible with the rest of the equations of mechanics. However, there is
an interesting relationship between the Painlevé paradoxes and the friction-
induced instabilities. If an elastical ...