The forward kinematics of a general six-degree-of-freedom parallel mechanism is a significant challenge in mechanism theory， following the displacement analysis of spatial 7R （R： revolute joint） mechanisms. Currently， there is no comprehensive analytical solution available. Using the zero-coupling “3-2-1” Stewart-type parallel robot as an example， this study investigates the number of solutions for the forward kinematics and analyzes the conditions under which the number of solutions varies. First， based on the rod length constraint equations and applying the tetrahedron principle， all eight sets of solutions for the robot’s forward kinematics are analytically derived. Then， by examining the positional characteristics of the moving spherical joints， the mathematical conditions required for the solution equations to yield 8， 4， 2， or 1 analytical solutions are identified. Furthermore， by considering the positional characteristics of the fixed spherical joints and integrating the forward kinematics algorithm， the factors influencing the number of real solutions are explored. Finally， the intrinsic relationship between the number of solutions to the forward kinematics of the parallel robot and Hunt’s singularities is analyzed. The findings of this research provide a theoretical foundation for the real-time control and trajectory planning of parallel robots.