This article aims to address some of the current limitations of cable-driven parallel robots (CDPRs) by enabling regional changes in dynamic structure through collisions between cables and fixed objects placed in the work area (such as idler pulleys). This leads to the definition of a new class of robots referred to as variable structure cable-driven parallel robots (VSCRs). One of the major advancements from VSCRs is their ability to cover nonconvex reachable workspaces: a significant relaxation on the constraints of traditional CDPRs that is especially useful for circumventing obstacles and has implications for a wide range of applications. Specific examples of vertical farming and rehabilitation are demonstrated experimentally. It is shown that VSCRs can dramatically improve the reachability and accessible workspace of traditional CDPRs. In addition, an online method for solving the planar VSCR inverse kinematics problem is introduced, which is based on an extended cable model. The method is general and has been validated through experimental studies.