This paper deals with the dynamic torsional stability problem of a family of partially-decoupled spherical parallel manipulators. The linearized equations of motion of the mechanical system are established to analyze the stability of the U-joint mechanism, resorting to the Floquet theory. Parametric stability charts of misalignment angles versus rotating speeds of the driving shaft are constructed to identify the unstable regions and critical shaft speeds, together with the effect of the parameters onto the manipulator stability. As a consequence, some criteria for the design and the operational speed of the manipulator, in terms of dynamic stability, are introduced.