The mobility or degrees of freedom is a fundamental issue in mechanisms and robotics. In this work, we investigate the mobility of parallel manipulators from a new point of view, and introduce a new concept, the pattern of transform matrix. It is shown that both general and modified Chebychev–Gruble–Kutzbach formulas are the special cases of the pattern analysis. We further propose a framework upon the pattern analysis of transform matrix to calculate the mobility, to evaluate the property of the motion, and to determine the exact-actuation arrangement. The proposed approach should be general enough to evaluate any existing parallel manipulator. Five parallel manipulators with special geometric conditions and lower mobilities are discussed.

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