  Sliding cable system with frictions is encountered in many engineering
applications. Such system is typically characterized by existences of complex
and varied motion states of different sliding nodes (pulleys), which leads to
significant difficulties for analysis. A very simple but effective linear
complementarity approach isdeveloped. Within this approach, the challenging and
significant issue of determinations of motion states of sliding nodes, as well
as calculations of their sliding lengths, can be handled in a standard linear
complementarity formulation, and can be solved using any available efficient
solver for linear complementarity problem (LCP). The proposed approach
eliminates the need for traditional cumbersome predictor-corrector-based
operations. It also opens a way to study the theory problem such as the
existence and uniqueness of the solution by using complementarity theories,
which is generally absent from existing literature given its complexity. The
uniqueness of the solution has been proved in this work, while the existence
issue remains open and deserves further investigation. Multi examples involving
both static and dynamic analyses are presented to demonstrate the effectiveness
of the proposed approach, as well as to reveal some novel phenomenon involved
in sliding cable system considering frictions. The results highlight the
ability of the method in accurately handling variegated motion states of
sliding nodes. The proposed approach, we think, has the potential to be a
popular method in dealing with multi-node sliding cable with frictions, given
its simplicity and effectiveness.
