Title :
Singularity condition of six-degree-of-freedom three-legged parallel robots based on grassmann-cayley algebra
Author :
Ben-Horin, Patricia ; Shoham, Moshe
Author_Institution :
Robotics Lab., Technion-Israel Inst. of Technol., Haifa
Abstract :
This paper addresses the singularity condition of a broad class of six-degree-of-freedom three-legged parallel robots that have one spherical joint somewhere along each leg. First, the actuator screws for each leg-chain are determined. Then Grassmann-Cayley algebra and the associated superbracket decomposition are used to find the condition for which the Jacobian (or rigidity matrix) containing these screws is rank-deficient. These tools are advantageous since they facilitate manipulation of coordinate-free expressions representing geometric entities, thus enabling the geometrical interpretation of the singularity condition to be obtained more easily. Using these tools, the singularity condition of (at least) 144 combinations of this class is delineated to be the intersection of four planes at one point. These four planes are defined by the locations of the spherical joints and the directions of the zero-pitch screws
Keywords :
Jacobian matrices; fasteners; legged locomotion; Grassmann-Cayley algebra; Jacobian matrix; rigidity matrix; singularity condition; six-degree-of-freedom three-legged parallel robots; zero-pitch screws; Actuators; Algebra; Associate members; Computational geometry; Fasteners; Jacobian matrices; Leg; Matrix decomposition; Parallel robots; Robot kinematics; Grassmann–Cayley algebra; singularity; three-legged robots;
Journal_Title :
Robotics, IEEE Transactions on
DOI :
10.1109/TRO.2006.878958