The direct kinematics problem of parallel mechanisms, that is, determining the pose of the manipulator platform from the linear actuators' lengths, is, in general, uniquely not solvable. For this reason, instead of measuring the lengths of the linear actuators, we propose measuring their orientations and, in most cases, also the orientation of the manipulator platform. This allows the design of a low-cost sensor system for parallel mechanisms that completely renounces length measurements and provides a unique solution of their direct kinematics.