Novel spherical-planar and Bennett-spherical 6R metamorphic linkages with reconfigurable motion branches

Abstract A metamorphic linkage is capable of changing its motion branches and can be used as mechanisms for reconfigurable robots for various tasks. This paper presents two novel metamorphic linkages as the spherical-planar 6R metamorphic linkage and the Bennett-spherical 6R metamorphic linkage both of which have three various distinguished motion branches. Having established the close-loop equation of the spherical-planar 6R metamorphic linkage, the paper reveals the conditions of various motion branches and a set of transformations for switching motion branches. The paper further uses to reveal the inherent properties of this over-constrained metamorphic 6R linkage that is able to perform both spherical and planar motion with mobility one. Because of geometrical constraints at bifurcation points, the linkage is able to reconfigure to the deployed spherical motion branch, the planar motion branch and the folded spherical motion branch. The two spherical motion branches could be seen on both a large sphere that presents the deployed spherical motion and a small sphere that presents the folded spherical motion. This leads to the revelation of the novel Bennett-spherical 6R metamorphic linkage that has the transition from one deployed Bennett configuration branch to a spherical configuration branch and then to another folded Bennett configuration branch. Given the geometric parameters of both metamorphic linkages, it reveals that these linkages are special cases of Bricard line-symmetric 6R linkage.

[1]  Yan Chen,et al.  A 6R linkage reconfigurable between the line-symmetric Bricard linkage and the Bennett linkage , 2013 .

[2]  Jian S. Dai,et al.  Augmented Adjacency Matrix for Topological Configuration of the Metamorphic Mechanisms , 2011 .

[3]  R. Bricard.  Leçons de cinématique , .

[4]  Jian S. Dai,et al.  Finite Displacement Screw Operators With Embedded Chasles' Motion , 2012 .

[5]  Jian S. Dai,et al.  Axis Constraint Analysis and Its Resultant 6R Double-Centered Overconstrained Mechanisms , 2011 .

[6]  J.Eddie Baker,et al.  An analysis of the Bricard linkages , 1980 .

[7]  Wei Ye,et al.  A new family of reconfigurable parallel mechanisms with diamond kinematotropic chain , 2014 .

[8]  Jian S. Dai,et al.  A Kirigami-Inspired 8R Linkage and Its Evolved Overconstrained 6R Linkages With the Rotational Symmetry of Order Two , 2014 .

[9]  Jian S. Dai,et al.  Mobility Change in Two Types of Metamorphic Parallel Mechanisms , 2009 .

[10]  Paul Grodzinski,et al.  Link Mechanisms in Modern Kinematics , 1954 .

[11]  R. Bricard.  Mémoire sur la théorie de l'octaèdre articulé , 1897 .

[12]  Jian S. Dai,et al.  Geometric Constraint and Mobility Variation of Two 3SvPSv Metamorphic Parallel Mechanisms , 2013 .

[13]  H. Lipkin,et al.  Mobility of Overconstrained Parallel Mechanisms , 2006 .

[14]  C. Galletti,et al.  Single-loop kinematotropic mechanisms , 2001 .

[15]  Jian S. Dai,et al.  Trifurcation of the Evolved Sarrus-Motion Linkage Based on Parametric Constraints , 2014 .

[16]  Joseph Duffy,et al.  Special configurations of spatial mechanisms and robot arms , 1982 .

[17]  C. Barus.  A treatise on the theory of screws , 1998 .

[18]  Kenneth J. Waldron.  Hybrid overconstrained linkages , 1968 .

[19]  Jian S. Dai,et al.  Multi-furcation in a derivative queer-square mechanism , 2014 .

[20]  K Wohlhart.  Merging two general goldberg 5R linkages to obtain a new 6R space mechanism , 1991 .

[21]  Zhong You,et al.  Spatial 6R linkages based on the combination of two Goldberg 5R linkages , 2007 .

[22]  J. Dai,et al.  Mobility in Metamorphic Mechanisms of Foldable/Erectable Kinds , 1998 .

[23]  F. E. Myard.  Contribution à la géométrie des systèmes articulés , 1931 .

[24]  J. R. Jones,et al.  Matrix Representation of Topological Changes in Metamorphic Mechanisms , 2005 .

[25]  Xianwen Kong.  Type Synthesis of Single-Loop Overconstrained 6R Spatial Mechanisms for Circular Translation , 2014 .

[26]  Kenneth H. Hunt.  Special configurations of robot-arms via screw theory , 1986, Robotica.

[27]  A. Müller.  Higher derivatives of the kinematic mapping and some applications , 2014 .

[28]  C. Gosselin,et al.  CONSTRAINT SINGULARITIES AS CONFIGURATION SPACE SINGULARITIES , 2002 .

[29]  Jian S. Dai,et al.  Reconfiguration of Spatial Metamorphic Mechanisms , 2009 .