NDLI: Singularity condition of six-degree-of-freedom three-legged parallel robots based on grassmann-cayley algebra

Content Provider	IEEE Xplore Digital Library
Author	Ben-Horin, P. Shoham, M.
Copyright Year	2004
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
Sponsorship	IEEE Robotics and Automation Society
Starting Page	577
Ending Page	590
Page Count	14
File Size	1730776
File Format	PDF
ISSN	15523098
Volume Number	22
Issue Number	4
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2006-08-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Parallel robots Algebra Fasteners Jacobian matrices Computational geometry Robot kinematics Actuators Associate members Leg Matrix decomposition three-legged robots Grassmann–Cayley algebra singularity
Content Type	Text
Resource Type	Article
Subject	Control and Systems Engineering Electrical and Electronic Engineering Computer Science Applications

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