Workspace analysis is one of the most important issues in the robotic parallel manipulator design. However, the unidirectional constraint imposed by cables causes this analysis more challenging in the cable driven redundant parallel manipulators. Controllable workspace is one of the general workspace in the cable driven redundant parallel manipulators due to the dependency on geometry parameters in the cable driven redundant parallel manipulators. In this paper, a novel tool is presented based on interval analysis for determination of the boundaries and proper assessment of the enclosed region of Controllable workspace of cable-driven redundant parallel manipulators. This algorithm utilizes the fundamental wrench interpretation to analyze the Controllable workspace of cable driven redundant parallel manipulators. Fundamental wrench is the newly definitions that opens new horizons for physical interpretation of Controllable workspace of general cable driven redundant parallel manipulators. Finally, the proposed method is implemented on a spatial cable driven redundant manipulator of interest.

This investigation proposes Markov chain analysis of Controllable multi-server queue with balking. We incorporate an additional server which is added and removed at pre-specified threshold levels of queue size to control the balking behaviour of the customers. The steady state equations are constructed by assuming interdependent arrival and service processes which are characterized by bivariate Poisson distribution. Recursive approach is employed to establish the queue size distribution, which is further used to determine various performance indices.