Aiming at obtaining a larger workspace volume, a novel six degrees of freedom (6-DOF) reconfigurable parallel mechanism (RPM) is designed, and its structure parameters and driving modes are optimized. A kind of triple compound spherical joint and a kind of metamorphic prismatic joint are designed, and 81 driving modes are realized by switching actuated and passive modes. Based on the interval analysis theory, an interval discretization method (IDM) involving the prediction and correction of workspace is proposed to determine the workspaces of parallel mechanisms. Then an accurate and reliable method of the workspace volume calculation is put forward by introducing the critical interval multiplier. The structure parameters and driving modes of 3–2–1 configuration are optimized. The results show that: (i) the workspace volume is close to the maximum when γ is near 0 rad; (ii) the workspace volume after reconfiguration increases by about 1.27 times than that before reconfiguration; (iii) the reverse layout of actuated prismatic joints is more restrictive to the workspace volume than the identical layout. The research conclusions lay a theoretical foundation for practical applications.