Analytical Solution of the Forward Displacement Problem for Spherical Parallel Manipulators
It provides a closed-form solution for a known problem in robotics, but the approach is incremental as it applies existing algebraic techniques to specific manipulator types.
The paper presents an analytical method for solving the forward displacement problem of spherical parallel manipulators using quaternion algebra and Dixon's result, with a case study demonstrating its effectiveness.
In this paper, an analytical method that solves the forward displacement problem of several common spherical parallel manipulators (SPMs) is presented. The method uses the the quaternion algebra to restate the problem as a system of four quadrics in four variables and uses an algebraic geometry result by Dixon from 1908 to solve. In addition, a case study is presented for a specific SPM.