Forward Kinematics and Singularity Analyses of an Uncoupled Parallel Manipulator by Algebraic Screw Theory

Jaime Gallardo-Alvarado,Mario A Garcia-Murillo,Luis A Alcaraz-Caracheo,Felipe J Torres,X Yamile Sandoval-Castro

doi:10.1109/access.2021.3139644

Abstract

In this contribution, the Jacobian analysis of a four-legged six-degrees-of-freedom decoupled parallel manipulator is carried out through the screw theory. As an intermediate step, for the sake of completeness the inverse/forward displacement analysis as well as the computation of the workspace of the robot are achieved by taking advantage of the decoupled orientation and position of the moving platform. Afterward, the input/output equation of velocity of the parallel robot is obtained by harnessing of the properties of reciprocal screw systems. Once the Jacobian matrices are identified and investigated, the analysis of singularities for the robot manipulator emerges as a natural application of the Jacobian analysis. Numerical examples are included with the purpose to show the practicality and versatility of the method of kinematic analysis. Furthermore, the numerical results obtained by means of the theory of screws are successfully verified with the aid of commercially available software like ADAMS.

Highlights

T HE Jacobian matrices of parallel manipulators has been extensively investigated covering mainly subjects like performance and singularity analysis [1]–[10]
Simpler kinematics and improved maneuverability are some advantages of parallel manipulators with uncoupled kinematics over traditional parallel manipulators with coupled kinematics like the Gough-Stewart platform
The Jacobian analysis of the 3-RPRRC+RRPRU decoupled parallel manipulator is solved by using of the screw theory

Summary

INTRODUCTION

T HE Jacobian matrices of parallel manipulators has been extensively investigated covering mainly subjects like performance and singularity analysis [1]–[10]. By resorting to reciprocal-screw theory, Joshi and Tsai [12] derived full rank Jacobian matrices with the purpose to approach the singularity analysis of limited-dof parallel manipulators. In section "Jacobian matrices of the parallel manipulator" the Jacobians are systematically obtained through the formulation of the velocity analysis of the parallel manipulator by means of screw theory. In this regard, the Klein form plays a central role. Some conclusions are given at the end of the contribution

TOPOLOGY OF THE UNCOUPLED PARALLEL MANIPULATOR

DISPLACEMENT ANALYSIS

JACOBIAN MATRICES OF THE PARALLEL MANIPULATOR

SINGULARITY ANALYSIS

NUMERICAL APPLICATION

CONCLUSION