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.
Issue Section:
Research Papers
References
1.
Sarrus
, M.
, 1853
, “Note sur la transformation des mouvements rectilignes alternatifs, en mouvements circulaires; et réciproquement
,” C. R. Akad. Sci.
, 36
, p. 1038
.2.
Pavlin
, G.
, and Wohlhart
, K.
, 1992
, “On Straight-Line Space Mechanisms
,” Sixth International Conference on the Theory of Machines and Mechanisms
Liberec, Czechoslovakia, Sept. 8–10, pp. 241
–246
.3.
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_500.4.
Wohlhart
, K.
, 1996
, “Kinematotropic Linkages
,” Recent Advances in Robot Kinematics
, J.
Lenarčič
and V.
Parenti-Casteli
, eds., Kluwer Academic Publisher
, Dordrecht, pp. 359
–368
.5.
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,.6.
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
.7.
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
.8.
Selig
, J.
, 2011
, “On the Geometry of Point-Plane Constraints on Rigid-Body Displacements
,” Acta Appl. Math.
, 116
(2
), pp. 133
–155
.9.
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
.10.
Huang
, L.
, and So
, W.
, 2002
, “Quadratic Formulas for Quaternions
,” Appl. Math. Lett.
, 15
(15
), pp. 533
–540
.11.
Krames
, J.
, 1937
, “Zur aufrechten Ellipsenbewegung des Raumes (Über symmetrische Schrotungen III)
,” Monatsh. Math. Phys.
, 46
(1
), pp. 38
–50
.12.
Bottema
, O.
, and Roth
, B.
, 1990
, Theoretical Kinematics
, Dover Publications
, New York.Copyright © 2016 by ASME
You do not currently have access to this content.
