The coupler surface of the RSRS mechanism

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Title: The coupler surface of the RSRS mechanism
Authors: Rojas, N
Dollar, AM
Item Type: Journal Article
Abstract: Two degree-of-freedom (2-DOF) closed spatial linkages can be useful in the design of robotic devices for spatial rigid-body guidance or manipulation. One of the simplest linkages of this type, without any passive DOF on its links, is the revolute-spherical-revolute-spherical (RSRS) four-bar spatial linkage. Although the RSRS topology has been used in some robotics applications, the kinematics study of this basic linkage has unexpectedly received little attention in the literature over the years. Counteracting this historical tendency, this work presents the derivation of the general implicit equation of the surface generated by a point on the coupler link of the general RSRS spatial mechanism. Since the derived surface equation expresses the Cartesian coordinates of the coupler point as a function only of known geometric parameters of the linkage, the equation can be useful, for instance, in the process of synthesizing new devices. The steps for generating the coupler surface, which is computed from a distance-based parametrization of the mechanism and is algebraic of order twelve, are detailed and a web link where the interested reader can download the full equation for further study is provided. It is also shown how the celebrated sextic curve of the planar four-bar linkage is obtained from this RSRS dodecic.
Issue Date: 18-Aug-2015
Date of Acceptance: 27-May-2015
ISSN: 1942-4302
Publisher: ASME
Start Page: 014505
End Page: 014505-5
Journal / Book Title: Journal of Mechanisms and Robotics
Volume: 8
Issue: 1
Copyright Statement: © 2015 by ASME
Notes: 10.1115/1.4030776
Publication Status: Published
Appears in Collections:Faculty of Engineering
Dyson School of Design Engineering

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