The lower mobility hybrid mechanism has a special form of terminal constraints, and its terminal motion parameters are highly coupled. The parallel and serial modules of the hybrid mechanisms were often studied separately in the previous researches, resulting in the neglect of the research on the terminal constraint and motion coupling of the whole hybrid mechanism. There are defects in the constraint and motion analysis of this kind of mechanisms. The terminal constraint of the (2-RPU+UPU)+(RR) mechanism was analyzed by using the Grassmann-Cayley algebra. Based on the constraint equations, the terminal motion coupling model of this mechanism was established. Then the modified inverse kinematics of this mechanism was obtained subsequently. The result of terminal constraint analysis showed that the terminal constraint of the (2-RPU+UPU)+(RR) mechanism was a helical (1H) type constraint, and its degree of freedom was two rotational (2R), two translation (2T) and one 1H type motion. The result of motion coupling analysis showed that the 6-dimensional pose coupling relationship of the (2-RPU+UPU)+(RR) mechanism was expressed in the form of a multivariate coupling equation. The constraint analysis and motion coupling model of the (2-RPU+UPU)+(RR) mechanism established provided a reference for the terminal constraint and motion coupling analysis of lower mobility hybrid mechanisms.