<p>Cartesian stiffness decoupling is a key performance requirement for parallel manipulators used in advanced manufacturing and precision positioning systems. Owing to the strong nonlinearity of geometric constraints, existing studies on stiffness decoupling in Stewart platforms have largely relied on numerical optimization or symmetry-based case analysis, which restricts systematic design and global understanding. This paper presents an analytical characterization of the vanishing conditions of the off-diagonal stiffness terms in rotation-symmetric Stewart platforms. By introducing an angular-difference variable and applying the Cayley transformation, the original nonlinear trigonometric constraints are transformed into a tractable algebraic representation, enabling explicit identification and classification of admissible decoupled configurations. Within this formulation, previously reported discrete geometric configurations are shown to arise as particular parameter cases of the general solution, establishing a continuous solution structure across the parameter space. The solutions obtained constitute a necessary first step toward achieving Cartesian stiffness decoupling and spatial isotropy, providing practical guidance for stiffness-oriented parameter selection and mechanism design.</p>