A Sarrus-like overconstrained eight-bar linkage and its associated Fulleroid-like platonic deployable mechanisms

This paper, for the first time, presents an overconstrained spatial eight-bar linkage and its application to the synthesis of a group of Fulleroid-like deployable platonic mechanisms. Structure of the proposed eight-bar linkage is introduced, and constrain and mobility of the linkage are revealed based on screw theory. Then by integrating the proposed eight-bar linkage into platonic polyhedron bases, synthesis of a group of Fulleroid-like deployable platonic mechanism is carried out; which is demonstrated by the synthesis and construction of a Fulleroid-like deployable tetrahedral mechanism. Further, mobility of the Fulleroid-like deployable platonic mechanisms is formulated via constraint matrices by following Kirchhoff’s circulation law for mechanical networks, and kinematics of the mechanisms is presented with numerical simulations illustrating the intrinsic kinematic properties of the group of Fulleroid-like deployable platonic mechanisms. In addition, a prototype of the Fulleroid-like deployable spherical-shape hexahedral mechanism is fabricated and tested; verifying the mobility and kinematic characteristics of the proposed deployable polyhedral mechanisms. Finally, application of the proposed deployable platonic mechanisms is demonstrated in the development of a transformable quadrotor. This paper hence presents a novel overconstrained spatial eight-bar linkage and a new geometrically intuitive method for synthesising Fulleroid-like regular deployable polyhedral mechanisms that have great potential applications in deployable, reconfigurable and multifunctional robots.

[1]  Zhong You,et al.  An Extended Myard Linkage and its Derived 6R Linkage , 2008 .

[2]  Jian S. Dai,et al.  Synthesis and Construction of a Family of One-DOF Highly Overconstrained Deployable Polyhedral Mechanisms (DPMs) , 2012 .

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

[4]  H. F. Verheyen.  THE COMPLETE SET OF JITTERBUG TRANSFORMERS AND THE ANALYSIS OF THEIR MOTION , 1989 .

[5]  Gökhan Kiper,et al.  Regular Polygonal and Regular Spherical Polyhedral Linkages Comprising Bennett Loops , 2009 .

[6]  G. Kiper,et al.  Polyhedral linkages synthesized using Cardan motion along radial axes Conference , 2007 .

[7]  Jian S. Dai,et al.  Mobility and Geometric Analysis of the Hoberman Switch-Pitch Ball and Its Variant , 2010 .

[8]  Guowu Wei,et al.  Overconstrained Mechanisms with Radially Reciprocating Motion , 2010 .

[9]  Thierry Lalibert,et al.  Polyhedra with Articulated Faces , 2007 .

[10]  Clément Gosselin,et al.  Expandable Polyhedral Mechanisms Based on Polygonal One-Degree-of-Freedom Faces , 2006 .

[11]  Gökhan Kiper.  Fulleroid-Like Linkages , 2009 .

[12]  Jian S. Dai,et al.  Synthesis of a Family of Regular Deployable Polyhedral Mechanisms (DPMs) , 2012, ARK.

[13]  J.Eddie Baker.  Overconstrained six-bars with parallel adjacent joint-axes , 2003 .

[14]  Karl Wohlhart,et al.  Polyhedral Zig-Zag Linkages , 2004 .

[15]  T. Davies.  Kirchhoff's circulation law applied to multi-loop kinematic chains , 1981 .

[16]  Karl Wohlhart,et al.  Double-Ring Polyhedral Linkages , 2012 .

[17]  Jian Feng,et al.  Kinematic of symmetric deployable scissor-hinge structures with integral mechanism mode , 2017 .

[18]  G. T. Bennett,et al.  The Skew Isogram Mechanism , 1914 .

[19]  Otto Röschel.  A Fulleroid-Like Mechanism Based on the Cube , 2013 .

[20]  Karl Wohlhart,et al.  Kinematics and Dynamics of the Fulleroid , 1997 .

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

[22]  Xianwen Kong,et al.  A Method for Constructing Reconfigurable Deployable Polyhedral Mechanism , 2016 .

[23]  Jian S. Dai,et al.  A Spatial Eight-Bar Linkage and Its Association With the Deployable Platonic Mechanisms , 2014 .

[24]  Rongqiang Liu,et al.  Design of Large Deployable Networks Constructed by Myard Linkages , 2011 .

[25]  Jian S. Dai,et al.  Dynamic Modelling and Simulation of a Deployable Quadrotor , 2018, 2018 International Conference on Reconfigurable Mechanisms and Robots (ReMAR).

[26]  Harvey Lipkin,et al.  A Note on Denavit-Hartenberg Notation in Robotics , 2005 .

[27]  Patrick W. Fowler,et al.  TWO-ORBIT SWITCH-PITCH STRUCTURES , 2012 .

[28]  Dario Floreano,et al.  Foldable and self-deployable pocket sized quadrotor , 2015, 2015 IEEE International Conference on Robotics and Automation (ICRA).

[29]  Karl Wohlhart,et al.  The Kinematics of Röschel Polyhedra , 1998 .

[30]  R. Bricard.  Leçons de cinématique , 1926 .

[31]  Xianwen Kong,et al.  A class of reconfigurable deployable platonic mechanisms , 2016 .

[32]  Bernard Roth,et al.  ANALYSIS AND SYNTHESIS OF OVERCONSTRAINED MECHANISMS , 1999 .

[33]  Zongquan Deng,et al.  Mobile Assemblies of Large Deployable Mechanisms , 2012 .

[34]  Constantinos Mavroidis,et al.  New and Revised Overconstrained Mechanisms , 1995 .

[35]  J. Michael McCarthy,et al.  Introduction to theoretical kinematics , 1990 .

[36]  J.Eddie Baker,et al.  A comparative survey of the bennett-based, 6-revolute kinematic loops , 1993 .

[37]  Xianwen Kong,et al.  Reconfigurable deployable polyhedral mechanism based on extended parallelogram mechanism , 2017 .

[38]  Jian S. Dai,et al.  Reconfigurable and Deployable Platonic Mechanisms with a Variable Revolute Joint , 2014 .

[39]  Jian S. Dai,et al.  Synthesis, Mobility, and Multifurcation of Deployable Polyhedral Mechanisms With Radially Reciprocating Motion , 2014 .

[40]  Otto Roeschel.  OVERCONSTRAINED MECHANISMS BASED ON TRAPEZOHEDRA , 2012 .

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

[42]  Sunil K. Agrawal,et al.  Polyhedral Single Degree-of-freedom Expanding Structures: Design and Prototypes , 2002 .

[43]  Xilun Ding,et al.  A family of reconfigurable deployable polyhedral mechanisms based on semiregular and Johnson polyhedra , 2018 .

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

[45]  Karl Wohlhart,et al.  Irregular Polyhedral Linkages , 2004 .

[46]  Jian Feng,et al.  A group-theoretic approach to the mobility and kinematic of symmetric over-constrained structures , 2016 .

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

[48]  Zhong You,et al.  On mobile assemblies of Bennett linkages , 2008, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.