0
Research Papers

Spatial Straight-Line Linkages by Factorization of Motion Polynomials

[+] Author and Article Information
Zijia Li

Johann Radon Institute for Computational
and Applied Mathematics,
Austrian Academy of Sciences,
Linz, 4040, Austria
e-mail: zijia.li@oeaw.ac.at

Josef Schicho

Johann Radon Institute for Computational
and Applied Mathematics,
Austrian Academy of Sciences,
Linz, 4040, Austria
e-mail: josef.schicho@risc.jku.at

Hans-Peter Schröcker

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

Manuscript received October 21, 2014; final manuscript received September 21, 2015; published online November 24, 2015. Assoc. Editor: J. M. Selig.

J. Mechanisms Robotics 8(2), 021002 (Nov 24, 2015) (6 pages) Paper No: JMR-14-1297; doi: 10.1115/1.4031806 History: Received October 21, 2014; Revised September 21, 2015; Accepted September 29, 2015

We use the recently introduced factorization of motion polynomials for constructing overconstrained spatial linkages with a straight-line trajectory. Unlike previous examples of such linkages by other authors, they are single-loop linkages and the end-effector motion is not translational. In particular, we obtain a number of linkages with four revolute and two prismatic joints and a remarkable linkage with seven revolute joints one of whose joints performs a Darboux motion.

FIGURES IN THIS ARTICLE
<>
Copyright © 2016 by ASME
Your Session has timed out. Please sign back in to continue.

References

Sarrus, M. , 1853, “ Note sur la transformation des mouvements rectilignes alternatifs, en mouvements circulaires; et réciproquement,” C. R. Akad. Sci., 36, p. 1038.
Pavlin, G. , and Wohlhart, K. , 1992, “ On Straight-Line Space Mechanisms,” Sixth International Conference on the Theory of Machines and MechanismsLiberec, Czechoslovakia, Sept. 8–10, pp. 241–246.
Kiper, G. , and Söylemez, E. , 2011, “ Modified Wren Platforms,” 13th IFToMM World Congress in Mechanism and Machine Science, Guanajuato, Mexico, June 1925, Paper No. A12_500.
Wohlhart, K. , 1996, “ Kinematotropic Linkages,” Recent Advances in Robot Kinematics, J. Lenarčič and V. Parenti-Casteli , eds., Kluwer Academic Publisher, Dordrecht, pp. 359–368.
Lee, C.-C. , and Hervé, J. M. , 2012, “ On the Vertical Darboux Motion,” Latest Advances in Robot Kinematics, J. Lenarcic and M. Husty , eds., Springer, Dordrecht,.
Hegedüs, G. , Schicho, J. , and Schröcker, H.-P. , 2013, “ Factorization of Rational Curves in the Study Quadric and Revolute Linkages,” Mech. Mach. Theory, 69(1), pp. 142–152. [CrossRef]
Husty, M. , and Schröcker, H.-P. , 2012, “ Kinematics and Algebraic Geometry,” 21st Century Kinematics, The 2012 NSF Workshop, J. M. McCarthy , ed., Springer, London, pp. 85–123.
Selig, J. , 2011, “ On the Geometry of Point-Plane Constraints on Rigid-Body Displacements,” Acta Appl. Math., 116(2), pp. 133–155. [CrossRef]
Hegedüs, G. , Schicho, J. , and Schröcker, H.-P. , 2015, “ Four-Pose Synthesis of Angle-Symmetric 6R Linkages,” ASME J. Mech. Rob., 7(4), p. 041006. [CrossRef]
Huang, L. , and So, W. , 2002, “ Quadratic Formulas for Quaternions,” Appl. Math. Lett., 15(15), pp. 533–540. [CrossRef]
Krames, J. , 1937, “ Zur aufrechten Ellipsenbewegung des Raumes (Über symmetrische Schrotungen III),” Monatsh. Math. Phys., 46(1), pp. 38–50. [CrossRef]
Bottema, O. , and Roth, B. , 1990, Theoretical Kinematics, Dover Publications, New York.

Figures

Grahic Jump Location
Fig. 1

An RPRRPR linkage with a straight-line trajectory

Grahic Jump Location
Fig. 2

A 7R linkage that generates a nonvertical Darboux motion

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In