Article
Simplified Kinematics for a Parallel Manipulator Generator of the Schönflies Motion
Journal of Mechanisms and Robotics
(2016)
Abstract
This work is devoted to simplify the inverse–forward kinematics of a parallel manipulator generator of the 3T1R motion. The closure equations of the displacement analysis are formulated based on the coordinates of two points embedded in the moving platform. Afterward, five quadratic equations are solved by means of a novel method based on Gröbner bases endowed with first-order perturbation and local stability of parameters. Meanwhile, the input–output equations of velocity and acceleration are systematically obtained by resorting to reciprocal-screw theory. In that concern, the inclusion of pseudokinematic pairs connecting the limbs to the fixed platform and a passive kinematic chain to the robot manipulator allows to avoid the handling of rank-deficient Jacobian matrices. The workspace of the robot is determined by using a discretized method associated to its inverse–forward displacement analysis, whereas the singularity analysis is approached based on the input–output equation of velocity. Numerical examples are provided with the purpose to show the application of the method.
Disciplines
Publication Date
October, 2016
DOI
10.1115/1.4034884
Citation Information
Mohammad H. Abedin-Nasab, Jaime Gallardo-Alvarado and Daniel Lichtblau. "Simplified Kinematics for a Parallel Manipulator Generator of the Schönflies Motion" Journal of Mechanisms and Robotics Vol. 8 Iss. 6 (2016) p. 061020 Available at: http://works.bepress.com/mohammad-abedin-nasab/5/