New Direct Kinematic Formulation of 6 D.O.F Stewart-Cough Platforms Using the Tetrahedron Approach

The paper presents a single constraint equation of the direct kinematic solution of 6-dof (Stewart-Gough) platforms. Many research works have presented a single polynomial of the direct kinematics for several 6-dof platforms. However, the formulation of the polynomial has potential problems such as complicated formulation procedures and discrimination of the actual solution from all roots. This results in heavy computational burden and time-consuming task. Thus, to overcome these problems, we use a new formulation approach, called the Tetrahedron Approach, to easily derive a single constraint equation, not a polynomial one, of the direct kinematics and use two well-known numerical iterative methods to find the solution of the single constraint equation. Their performance and characteristics are investigated through a series of simulation.