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Research Papers

Four-Pose Synthesis of Angle-Symmetric 6R Linkages

[+] Author and Article Information
Gábor Hegedüs

Applied Mathematical Institute,
Antal Bejczy Center for Intelligent Robotics,
Obuda University,
Budapest 1032, Hungary
e-mail: hegedus.gabor@nik.uni-obuda.hu

Josef Schicho

Johan Radon Institute for Computational
and Applied Mathematics,
Austrian Academy of Sciences,
Linz 4040, Austria
e-mail: josef.schicho@ricam.oeaw.ac.at

Hans-Peter Schröcker

Unit Geometry and CAD,
University Innsbruck,
Innsbruck 6020, Austria
e-mail: hans-peter.schroecker@uibk.ac.at

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANISMS AND ROBOTICS. Manuscript received September 20, 2013; final manuscript received November 14, 2014; published online March 23, 2015. Assoc. Editor: Andrew P. Murray.

J. Mechanisms Robotics 7(4), 041006 (Nov 01, 2015) (7 pages) Paper No: JMR-13-1185; doi: 10.1115/1.4029186 History: Received September 20, 2013; Revised November 14, 2014; Online March 23, 2015

We use the recently introduced factorization theory of motion polynomials over the dual quaternions and cubic interpolation on quadrics for the synthesis of closed kinematic loops with six revolute joints that visit four prescribed poses. The resulting 6R linkages are special in the sense that the relative motions of all links are rational. They exhibit certain elegant properties such as symmetry in the rotation angles and, at least in theory, full-cycle mobility. Our synthesis approach admits either no solution or two one-parametric families of solutions. We suggest strategies for picking good solutions from these families. They ensure a fair coupler motion and optimize other linkage characteristics such as total rotation angle or linkage size. A comprehensive synthesis example is provided.

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References

Figures

Grahic Jump Location
Fig. 1

Valid end-effector motions of different fairness

Grahic Jump Location
Fig. 2

The solution to our synthesis problem

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