New kinematics Hessian matrixes of manipulators based on Skew-symmetric matrixes theory

摘要

A new approach is proposed for deriving the Hessian matrixes of parallel manipulators and their generative mechanisms using the skew-symmetric matrixes of translational/angular velocities and their combination formulae. First, several necessary skew-symmetric matrixes of the translational/angular velocities and their combination formulae are derived. Second, the differentiations of the sub-Jacobian matrixes are transformed into a multiplication of a general velocity transposition by sub-Hessian matrixes based on the derived formulae. Third, the sub-Hessian matrixes of a typical parallel manipulator and its generative mechanisms (the hybrid hand and the redundant kinematic hybrid manipulator) as well as their kinematic limbs are derived by differentiating the sub-Jacobian matrixes based on the derived the skew-symmetric matrixes of translational/angular velocities and their combination formulae. Finally, the formulae are derived for solving the Hessian matrixes and the accelerations of the typical parallel manipulator and the generative mechanisms. (C) 2018 Elsevier Inc. All rights reserved.