Forward Kinematics of 3-RPS Parallel Mechanisms Using Conformal Geometric Algebra

In this paper, we propose a novel solution process for the forward kinematics of general 3-RPS parallel mechanisms based on conformal geometric algebra (CGA). First of all, the position of one of the three spherical joints is expressed in the rotational angle about the axis of one kinematic chain RPS. Secondly, the other two spherical joints can be determined by this angle via CGA operation. Thirdly, an explicit 16th-degree univariate polynomial equation is reduced from two geometric constraint equations. At last, one numerical example is employed to verify the solution procedure. The novelties of this paper lie in that (1) the modeling formulation and the elimination procedure have intrinsic geometric intuition due to the use of CGA and (2) the 16th-degree polynomial equation without extraneous roots is explicitly formulated and suitable for implementing the mathematics mechanization of this problem.

Study on Integrated Framework of Mathematical Mechanization for NC Trajectory Planning

In order to apply mathematical mechanization method during trajectory planning for NC machining, a platform framework is put forward which integrates the mathematics mechanization and trajectory planning. The essence and application of mathematical mechanization is analysis. The basic process and the correlation function of trajectory planning are discussed based on mathematical mechanization. The technology system of mathematical mechanization platform is established for the trajectory planning. And the operation flow of the mathematical mechanization platform is defined.

Inverse Kinematics Analysis of General 6R Manipulator Based on Groebner Basis-Sylvester Hybrid Method

In this paper we present a solution to the inverse kinematics problem for serial manipulator of general geometry. Using only seven equations which are consisted of Duffy’s four kinematical equations containing only three angles and three corresponding angles’ sincos identical equations instead of traditional fourteen equations, we reduce the inverse kinematics problem of the general 6R manipulator to a univariate polynomial with minimum degree based on Groebner-Sylvester method. From that, a conclusion can be drawn that the maximum number of the solutions is sixteen, generally. Also the mathematics mechanization method used in this paper can be extended to solve the other mechanism problem involving nonlinear equations symbolically.