Structure synthesis and statics analysis of a foldable stair

This paper proposes a foldable stair that can be deployed for use and folded for conservation and investigates the geometry and statics of the structure. It not only has the moving flexibility of a mechanism but also has the high stiffness and high strength of statically indeterminate structures. The primary linkage is a deployable scissor-like element which forms the staircase after expanding. This paper starts with the analysis of the geometry of planar four- and six-bar mechanisms and processes to synthesize the foldable stair and then investigates its statics. The paper further investigates redundant inner forces of every link based on the second Castigliano theorem, develops a foldable stair model, assembles and manufactures. Working experiments verify the theoretical results and the outstanding advantages over the general fixed stairs.

[1]  Gordon R. Pennock,et al.  Theory of Machines and Mechanisms , 1965 .

[2]  Juan Pérez Valcárcel,et al.  Two Way Deployable Spherical Grids , 1996 .

[3]  G. Tian,et al.  Inverse kinematic analysis for triple-octahedron variable-geometry truss manipulators , 2001 .

[4]  Zhong You,et al.  Threefold-symmetric Bricard linkages for deployable structures , 2005 .

[5]  Dong Shi-Lin,et al.  A Study on Space Masts Based on Octahedral Truss Family , 2001 .

[6]  Travis John Langbecker,et al.  Kinematic Analysis of Deployable Scissor Structure s , 1999 .

[7]  T. Tarnai,et al.  Zero stiffness elastic structures , 2003 .

[8]  Juan Pérez Valcárcel,et al.  Deployable cover on a swimming pool in Seville , 1996 .

[9]  F Escrig,et al.  Geometry of Expandable Space Structures , 1993 .

[10]  Charis J. Gantes,et al.  Geometric design of arbitrarily curved bi-stable deployable arches with discrete joint size , 2004 .

[11]  Shiyu Liu,et al.  Myard linkage and its mobile assemblies , 2009 .

[12]  Keith A. Seffen,et al.  Folding and deployment of curved tape springs , 2000 .

[13]  W W Gan,et al.  Numerical Approach to the Kinematic Analysis of Deployable Structures Forming a Closed Loop , 2006 .

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

[15]  Amde M. Amde,et al.  An algorithm for nonlinear stability analysis of an expandable self-erecting structure , 2001 .

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

[17]  Sergi Hernandez Juan,et al.  Tensegrity frameworks: Static analysis review. , 2008 .

[18]  Jian S. Dai,et al.  Mobility analysis of a complex structured ball based on mechanism decomposition and equivalent screw system analysis , 2004 .

[19]  Jian S. Dai,et al.  Linkages That Transfer Rotations to Radially Reciprocating Motion , 2010 .

[20]  Sergi Hernandez Juan,et al.  Tensegrity frameworks: Dynamic analysis review and open problems , 2009 .

[21]  Jin Mitsugi,et al.  Analyses of cable-membrane structure combined with deployable truss , 2000 .

[22]  Ashitava Ghosal,et al.  A constraint Jacobian based approach for static analysis of pantograph masts , 2010 .

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

[24]  Chen Wujun,et al.  A New Design Conception for Large Span Deployable Flat Grid Structures , 2002 .

[25]  A. Kaveh,et al.  Analysis of pantograph foldable structures , 1996 .

[26]  David Rubin,et al.  Introduction to Continuum Mechanics , 2009 .

[27]  Fulei Chu,et al.  The mechanism theory and application of deployable structures based on SLE , 2009 .

[28]  Robert D. Logcher,et al.  New Concepts for Deployable-Collapsable Structures , 1988 .

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

[30]  Ashitava Ghosal,et al.  Kinematics of pantograph masts , 2009 .

[31]  Ali Kaveh,et al.  Optimal Design of Pantograph Foldable Structures , 1999 .

[32]  Eyal Karni,et al.  Evaluation of Biological Deployable Systems , 2005 .

[33]  Robert Levy,et al.  Evaluation of Deployable Structures for Space Enclosures , 2001 .