An efficient approach to the forward kinematics of a planar parallel manipulator with similar platforms

The forward kinematics of a parallel manipulator is so difficult that the analytical solutions of only a few parallel manipulators have been found. The forward kinematics of a three-degree-of-freedom planar parallel manipulator, where the base and the mobile platforms are two similar triangles, is studied in this paper and its analytical solution is provided. The final solution is two independent univariate quadratic equations. As well, the forward kinematics solution is simplified to the parallel manipulator where the two triangles are equilateral and a numerical example is presented.