Investigation of the forward kinematics of the Gough‐Stewart manipulator with natural coordinates

In this paper, we propose a forward kinematics model with natural coordinates for the Gough–Stewart manipulator and other spatial parallel mechanisms. The prevailing merits of this model are that the constraint equations are either quadratic or linear and the coordinates are fully Cartesian. As a result, the derivative matrix of the constraint equations only consists of linear or constant elements, which shows remarkable advantages in kinematic and dynamic analysis over those built through the rotation matrix, the elements of which often contain quadratic or transcendental functions. Application examples show that the virtues are obvious in the analysis of the kinematics of spatial parallel manipulators, especially for those with six full degrees of freedom (DoFs), including three translational DoFs and three rotational DoFs. In reality, this method is easily understood and will be widely used in engineering applications.