Cable interference in cable-driven mechanisms (CDM) is a major challenge in their applications. The wrench closure workspace (WCW) in a fully constrained mechanism may not be realized unless cable interference is considered. This paper classifies all possible types of cable interferences for planar cable-driven mechanisms and presents an analytical solution to find the boundaries of the constant-orientation interference region. It is shown that interference between cables starts and ends when one end of a cable coincides with another cable which can be thought as lying a point on a line segment. This geometrical view is developed and applied to provide a framework for the analysis of cable interference. By subtracting the interference space form WCW, the interference-free workspace is obtained in which the robot is able to operate.