The direct kinematics problem is the problem of finding the actual pose of the moveable manipulator platform from the active joints' coordinates, for example, the linear actuators' lengths. For parallel mechanisms, it cannot be solved unambiguously. By measuring the linear actuators' orientations and the orientation of the manipulator platform instead, this problem can be solved analytically, and the actual pose of the manipulator platform can be determined without requiring any linear actuators' lengths. As an example, inertial measurement units can be used to obtain the orientation and motion of any body. In this thesis, this approach is applied to the general Stewart-Gough platform and the general planar 3-RPR parallel mechanism, and several formulations for solving the direct kinematics problem are derived. By totally renouncing length measurements and using inertial measurement units for measuring the orientations instead, a comprehensive, compact, and low-cost sensor system can be achieved, which provides an explicit pose of the manipulator platform and is also applicable to other parallel mechanisms.