Formulation of unified kinematics for overconstrained Schönflies parallel mechanism using vectorial algebra. (September 2022)

• Record Type: Journal Article
• Authors: Zhang, Xing; Yang, Mingxing; Mu, Dejun; Wang, Hongrui
• Is Part Of: Proceedings of the Institution of Mechanical Engineers. Volume 236:Number 17(2022)
• Page Start: 9558
• Page End: 9567
• Publication Date: 2022-09
• Subjects: parallel manipulator -- Hessian matrix -- Jacobian matrix -- kinematics -- vectorial algebra; Mechanical engineering -- Periodicals; 621.05
• DOI: 10.1177/09544062221097878
• Languages: English
• ISSNs: 0954-4062

Abstract

This study establishes unified kinematics of Schönflies parallel manipulators (PMs) considering the constraint matrix. Based on vectorial algebra, the kinematics of 4-RRRRR PM is solved using the geometric relation between the links, which solves the PM problem that the vector method could not solve using several kinematic pairs and links. First, the overall Jacobian and Hessian matrices of the Schönflies PM are derived. Then, a complex 4-RRRRR PM was selected and the inverse displacement analysis is performed using a new strategy. The 6 × 6 Jacobian and 6 × 6 × 6 Hessian matrices of the mechanism are deduced. Finally, the kinematics is derived and the results are used to demonstrate the proposed method.