The 3-rRPS metamorphic parallel mechanism can change its configurations thanks to the reconfigurable (rR) joint. The analysis in this paper will focus on one specific configuration where the moving-platform is able to perform 2-dof coupled rotational motions and 1-dof translational motion, which is well-known as 1T2R motion. In this configuration, the mechanism has two types of operation modes, i.e. x0 = 0 and x3 = 0, which have been extensively studied by many researchers. However, the dynamic behaviours of the mechanism in those two operation modes have not been studied. Accordingly, this paper presents the dynamic analysis of the 3-rRPS metamorphic parallel mechanism in both operation modes based on the Instantaneous Screw Axis (ISA). The types of operation mode are initially characterized by means of Euler-Quaternion parameters. The time derivative of transformation matrix is performed in each operation mode and the ISA can be determined. By using the ISA, velocities and accelerations of all points on the moving-platform can be evaluated, which become the foundation of the dynamic analysis in this paper. This approach can be applied to parallel mechanisms having multiple operation modes of different mobility.