Analysis of 2-DOF Parallel Mechanisms Based on Screw Theory

This paper introduces a two degree of freedom platform, which can realize pitching and the rolling motion. The limb constraint and the combined effect of all limb constraints can be described using screw theory. The linear dependence of all limb constraints can be judged geometrically and the properties of mobility can be obtained. Further, the geometrical conditions of existence of common constraint and redundant constraint are proposed with corresponding equations. A revised Grbler-Kutzbach criterion and a degree of freedom in terms of constraint analysis are proposed. The methodology introduced here is applicable to a 2-DOF parallel mechanisms.