Kinematics and singularity analysis of a planar cable-driven parallel manipulator

A cable-driven parallel manipulator (CDPM) possesses a number of promising advantages over the conventional rigid-link manipulators, such as the simple and lightweight mechanical structure, high-loading capacity, and large reachable workspace. However, due to the unilateral driving capability of the flexible cables, most of the well-developed modelling and analysis methods for conventional rigid-link mechanisms cannot be directly applied to CDPM. This paper focuses on the kinematics and singularity analysis of a specific type of CDPM, i.e., a completely restrained planar CDPM. Following an analytical approach, the forward displacement analysis leads to solve a fourth order polynomial equation. Hence, the solutions can be determined efficiently in symbolic forms. To verify the effectiveness of this method, a computation example is provided, in which four real solutions are found out. It is realized the Jacobian-based singularity analysis, where all cables are treated as rigid links, is incomplete for the CDPM. Based on the concept of the instantaneous center and taking into account the cable-tension condition, a new geometrical singularity analysis method is proposed, which is able to effectively identify all forward singularity configurations for a completely restrained planar CDPM.