In this article, the direct singular positions of the parallel manipulator Tricept are determined. An alternative 3 x 3 Jacobian matrix, simpler than the existing one, is obtained in this study. For a given moving platform's orientation, the determinant of this Jacobian matrix may be expressed as a cubic polynomial in moving platform's equation length. Direct singular positions may thus be obtained by solving cubic polynomial equations. For an arbitrarily chosen moving platform's orientation, there exists at least one moving platform's extension length that causes direct kinematic singularity. It is found that if moving platform's size is larger than a specific value, then within the moving platform's domain there exist two regions, in which direct kinematic singularities can only occur at positions impossible to reach.
Proceedings of the Institution of Mechanical Engineers, Part C, Journal of Mechanical Engineering Science 221(1), pp.109-117