CGA-based approach for direct kinematics of a novel reconfigurable parallel mechanism

In this article, we present a conformal geometric algebra (CGA) based unified modeling and solution procedure for direct kinematics of a kind of reconfigurable parallel mechanism(RPM). With the fact that the angle between specific joint axes of limbs remains constant, a set of geometric constraints for the direct kinematics of PM are determined. After translating unit direction vectors of these joint axes to the common starting point, the geometric constraints of the angle between the vectors are transformed into the distances between the endpoints of the vectors, the problems become easier to handle with CGA. The application of CGA in the direct kinematics of PMs has been extended, with keeping the advantages of geometric intuitiveness and elimination-free. Then, under the framework of CGA, a higher-order univariate polynomial equation for direct kinematic analysis of these parallel mechanisms(PMs) is derived. After solving this equation and back substitution, the position and pose of the moving platform can be obtained indirectly. A numerical example is utilized to confirm the effectiveness of the proposed method.