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Zig-Zag Eight-Stage Tensegrity Torus Datasheet


Copyright © 2003-2004 by Bob Burkhardt
Last Revision: December 21, 2008

        Member Descriptions
        [name, end point names, weight (if in objective function),
        second power of length (if a constraint), member category,
        Obj/Con/Exc (put in objective function, use as a constraint or
        exclude from computations), flags]
        For assembly purposes, only the name and end point names are
        of interest.  The other information may be of interest after
        A Practical Guide to Tensegrity Design has been consulted.

<Member> st13a pt1A  pt3c   0.0  sqr(2.5)  1 Con CalcClear Inelastic *
<Member> st24a pt2A  pt4a   0.0  sqr(2.5)  1 Con CalcClear Inelastic *

<Member> guy1a pt1A  pt3b   1.00 0.0       3 Obj *
<Member> guy2a pt2A  pt4b   1.00 + 0.493154 0.0       3 Obj *

<Member> TS23a pt2A  pt3a   0.0  sqr(1.0)  2 Con *
<Member> tS23a pt2A  pt3b   0.0  sqr(1.0)  2 Con *

<Member> tT31a pt3a  pt1C+  2.00 + 0.493154 0.0       3 Obj *
<Member> tT42a pt4a- pt2C   2.00 0.0       3 Obj *

<Member> TS41a pt4a  pt1B+  0.0  sqr(1.0)  2 Con *
<Member> tS41a pt4a  pt1C+  0.0  sqr(1.0)  2 Con *

<Member> st13b pt1B  pt3a   0.0  sqr(2.5)  1 Con CalcClear Inelastic *
<Member> st24b pt2B  pt4b   0.0  sqr(2.5)  1 Con CalcClear Inelastic *

<Member> guy1b pt1B  pt3c   1.00 - 0.493154 0.0       3 Obj *
<Member> guy2b pt2B  pt4c   1.00 - 0.493154 0.0       3 Obj *

<Member> TS23b pt2B  pt3b   0.0  sqr(1.0)  2 Con *
<Member> tS23b pt2B  pt3c   0.0  sqr(1.0)  2 Con *

<Member> tT31b pt3b  pt1A+  2.00 0.0       3 Obj *
<Member> tT42b pt4b- pt2A   2.00 + 0.493154 0.0       3 Obj *

<Member> TS41b pt4b  pt1C+  0.0  sqr(1.0)  2 Con *
<Member> tS41b pt4b  pt1A+  0.0  sqr(1.0)  2 Con *

<Member> st13c pt1C  pt3b   0.0  sqr(2.5)  1 Con CalcClear Inelastic *
<Member> st24c pt2C  pt4c   0.0  sqr(2.5)  1 Con CalcClear Inelastic *

<Member> guy1c pt1C  pt3a   1.00 + 0.493154 0.0       3 Obj *
<Member> guy2c pt2C  pt4a   1.00 0.0       3 Obj *

<Member> TS23c pt2C  pt3c   0.0  sqr(1.0)  2 Con *
<Member> tS23c pt2C  pt3a   0.0  sqr(1.0)  2 Con *

<Member> tT31c pt3c  pt1B+  2.00 - 0.493154 0.0       3 Obj *
<Member> tT42c pt4c- pt2B   2.00 - 0.493154 0.0       3 Obj *

<Member> TS41c pt4c  pt1A+  0.0  sqr(1.0)  2 Con *
<Member> tS41c pt4c  pt1B+  0.0  sqr(1.0)  2 Con *


        Rotation Matrices
        Only part of the structure is specified using the members
        above.  The rest is generated using symmetry transformations.
        Here the first symmetry transformation is specified as a 3x3
        pre-multiplication matrix in row-major format.  Others are
        constructed by multiplying the first one by itself.  As with
        the members, the first item is always the label used for
        the transform.

<XMat> x1 cos(2*pi/4) (-sin(2*pi/4)) 0 sin(2*pi/4) cos(2*pi/4) 0 0 0 1
<CompositeXform> x2 x1 x1
<CompositeXform> x3 x1 x2


        In-Situ Member Lengths
        These are the lengths of the members when they are in place
        and prestress is applied.  The strut lengths are from
        screw-eye center to screw-eye center, as are the tendon lengths.
        These values are in model units.

    st13a:          2.5     st24a:          2.5     guy1a:      2.01029
    guy2a:      1.54864     TS23a:            1     tS23a:            1
    tT31a:     0.628066     tT42a:      1.06676     TS41a:            1
    tS41a:            1     st13b:          2.5     st24b:          2.5
    guy1b:      2.51316     guy2b:      2.51316     TS23b:            1
    tS23b:            1     tT31b:      1.06676     tT42b:     0.628066
    TS41b:            1     tS41b:            1     st13c:          2.5
    st24c:          2.5     guy1c:      1.54864     guy2c:      2.01029
    TS23c:            1     tS23c:            1     tT31c:      1.41420
    tT42c:      1.41420     TS41c:            1     tS41c:            1


        Relative Member Prestress Force Magnitudes
        These values are useful for developing an assembly
        strategy for the structure.  The tighter tendons are much
        easier to tie in place early on, while the looser tendons
        can be left to the last.  This information is also used
        to adjust tendon lengths since the measured length of a tendon
        will be shorter for a highly-stressed tendon with the same
        in-situ length as a tendon which is not so stressed.

    st13a:     -3.19754     st24a:     -5.55701     guy1a:      2.01029
    guy2a:      2.31236     TS23a:      3.50881     tS23a:      2.62149
    tT31a:      1.56587     tT42a:      2.13352     TS41a:      2.94064
    tS41a:      2.62149     st13b:     -4.80177     st24b:     -4.80177
    guy1b:      1.27378     guy2b:      1.27378     TS23b:      2.94064
    tS23b:      2.91878     tT31b:      2.13352     tT42b:      1.56587
    TS41b:      3.50881     tS41b:      2.59506     st13c:     -5.55701
    st24c:     -3.19754     guy1c:      2.31236     guy2c:      2.01029
    TS23c:      2.20944     tS23c:      2.59506     tT31c:      2.13099
    tT42c:      2.13099     TS41c:      2.20944     tS41c:      2.91878

        Average tendon force magnitude: 2.35175


        Worst-Case Clearances in Model Units
        These clearances are measured from member centerline to
        member centerline.  The labels of the two members are specified
        as well as a transformation for the second member.  If "id"
        is specified for the transformation, it means none was applied.

    0.236335    st24a     st24b        id
    0.236335    st13b     st13c        id


        Construction Lengths (in millimeters and halves)
        The construction length of a tendon is less than the in-situ
        length since when the tendon is measured off it isn't under
        any prestress force.  The construction length for the strut
        represents the length of a 5/16-inch-diameter wooden dowel.
        The tendons can be made of braided nylon fishing line.
        Prestress forces were assumed not to affect strut lengths.

        Elongation of Tendon of Unit Cross Section
        Under Force of Average Magnitude (fraction)> .02
        Length Scale Factor> 290/2.5
        Strut and Tendon Hub Adjustments - s;t> 5 3.5
        (The 5 mm adjustment for the strut is the amount
         the screw-eye center extends from the dowel.  The 3.5 mm
	 adjustment for the tendon is half the outer diameter of the
         screw eye.)

    st13a: 280 0     st24a: 280 0     guy1a: 222 1     guy2a: 169 1
    TS23a: 106 0     tS23a: 106 1     tT31a:  65 0     tT42a: 114 1
    TS41a: 106 1     tS41a: 106 1     st13b: 280 0     st24b: 280 0
    guy1b: 281 1     guy2b: 281 1     TS23b: 106 1     tS23b: 106 1
    tT31b: 114 1     tT42b:  65 0     TS41b: 106 0     tS41b: 106 1
    st13c: 280 0     st24c: 280 0     guy1c: 169 1     guy2c: 222 1
    TS23c: 107 0     tS23c: 106 1     tT31c: 154 1     tT42c: 154 1
    TS41c: 107 0     tS41c: 106 1

 

axial view of tensegrity torus
Axial View of the Eight-Stage Tensegrity Torus
with Point Labels

 

Schematic for the Tensegrity Torus
Schematic for the Tensegrity Torus

structure file:  torus/x3l08torus1.rc
 variable file:  torus/x3l08torus1.dat
    digit list:  src/mm.dls

CONTACT:

Bob Burkhardt
Tensegrity Solutions
Box 426164
Cambridge, MA 02142-0021
USA

e-mail: bobwb@juno.com

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