An Application of the Newton-Homotopy Continuation Method for Solving the Forward Kinematic Problem of the 3-RRS Parallel Manipulator

摘要

The forward kinematic problem (FKP) of the 3-RRS parallel manipulator is solved by means of the Newton-homotopy continuation method. The closure equations are formulated in the three-dimensional Euclidean spaces considering the coordinates of the centers of the spherical joints as unknown variables. The method is easy to follow and unlike the classical Newton-Raphson method it allows finding all the solutions of the FKP. A case study is included in the contribution in order to confirm the correctness of the method. In that concern, the numerical results obtained by means of the proposed method are verified with the aid of two different approaches such as the application of commercially available software like Maple16? and the application of the PHCpack, a general purpose solver for polynomial systems based on homotopy continuation.