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Zig-Zag Six-Stage Tensegrity Torus Datasheet


Copyright © 2004 by Bob Burkhardt

        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 + 0.40 0.0       3 Obj *

<Member> TS23a pt2A  pt3a   0.0  sqr(0.92234)  2 Con *
<Member> tS23a pt2A  pt3b   0.0  sqr(0.92234)  2 Con *

<Member> tT31a pt3a  pt1C+  1.40 + 0.40 0.0       3 Obj *
<Member> tT42a pt4a- pt2C   1.40 0.0       3 Obj *

<Member> TS41a pt4a  pt1B+  0.0  sqr(0.92234)  2 Con *
<Member> tS41a pt4a  pt1C+  0.0  sqr(0.92234)  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 - 0.40 0.0       3 Obj *
<Member> guy2b pt2B  pt4c   1.00 - 0.40 0.0       3 Obj *

<Member> TS23b pt2B  pt3b   0.0  sqr(0.92234)  2 Con *
<Member> tS23b pt2B  pt3c   0.0  sqr(0.92234)  2 Con *

<Member> tT31b pt3b  pt1A+  1.40 0.0       3 Obj *
<Member> tT42b pt4b- pt2A   1.40 + 0.40 0.0       3 Obj *

<Member> TS41b pt4b  pt1C+  0.0  sqr(0.92234)  2 Con *
<Member> tS41b pt4b  pt1A+  0.0  sqr(0.92234)  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 + 0.40 0.0       3 Obj *
<Member> guy2c pt2C  pt4a   1.00 0.0       3 Obj *

<Member> TS23c pt2C  pt3c   0.0  sqr(0.92234)  2 Con *
<Member> tS23c pt2C  pt3a   0.0  sqr(0.92234)  2 Con *

<Member> tT31c pt3c  pt1B+  1.40 - 0.40 0.0       3 Obj *
<Member> tT42c pt4c- pt2B   1.40 - 0.40 0.0       3 Obj *

<Member> TS41c pt4c  pt1A+  0.0  sqr(0.92234)  2 Con *
<Member> tS41c pt4c  pt1B+  0.0  sqr(0.92234)  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/3) (-sin(2*pi/3)) 0 sin(2*pi/3) cos(2*pi/3) 0 0 0 1
<CompositeXform> x2 x1 x1


        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:      2.09336
    guy2a:      1.62933     TS23a:      0.92234     tS23a:      0.92234
    tT31a:     0.728105     tT42a:      1.25365     TS41a:      0.92234
    tS41a:      0.92234     st13b:          2.5     st24b:          2.5
    guy1b:      2.62470     guy2b:      2.62470     TS23b:      0.92234
    tS23b:      0.92234     tT31b:      1.25365     tT42b:     0.728105
    TS41b:      0.92234     tS41b:      0.92234     st13c:          2.5
    st24c:          2.5     guy1c:      1.62933     guy2c:      2.09336
    TS23c:      0.92234     tS23c:      0.92234     tT31c:      1.79050
    tT42c:      1.79050     TS41c:      0.92234     tS41c:      0.92234


        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:     -3.13132     st24a:     -4.79786     guy1a:      2.09336
    guy2a:      2.28106     TS23a:      3.06458     tS23a:      1.83734
    tT31a:      1.31059     tT42a:      1.75510     TS41a:      2.33437
    tS41a:      1.83734     st13b:     -4.52737     st24b:     -4.52737
    guy1b:      1.57482     guy2b:      1.57482     TS23b:      2.33437
    tS23b:      2.42868     tT31b:      1.75510     tT42b:      1.31059
    TS41b:      3.06458     tS41b:      2.26564     st13c:     -4.79786
    st24c:     -3.13132     guy1c:      2.28106     guy2c:      2.09336
    TS23c:      1.67473     tS23c:      2.26564     tT31c:      1.79050
    tT42c:      1.79050     TS41c:      1.67473     tS41c:      2.42868

        Average tendon force magnitude: 2.03423


        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.

    0.245277    st13a     tT42b        id
    0.208955    st13a     st13c        id
    0.200477    st24a     tT31a        id
    0.201645    st24a     st13b        id
    0.211264    st24a     st24b        id
    0.227265    st24a     TS41b        id
    0.238605    st24a     st13c        id
    0.238605    st24a     st13c        x1
    0.208955    st24a     st24c        id
    0.201645    st24a     guy1c        id
    0.243467    st24a     guy1c        x1
    0.201645    st24a     tS23c        id
    0.211264    st13b     st13c        id
    0.221504    st13b     tT31c        x2
    0.243467    st13c     guy2a        id
    0.201645    st13c     guy2a        x2
    0.227265    st13c     TS23a        id
    0.200477    st13c     tT42b        id
    0.201645    st13c     tS41b        x2
    0.245277    st24c     tT31a        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 the 5/16-inch-diameter wooden dowel.
        The tendons were 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: 231 0     guy2a: 178 0
    TS23a:  97 0     tS23a:  98 0     tT31a:  76 1     tT42a: 136 0
    TS41a:  97 1     tS41a:  98 0     st13b: 280 0     st24b: 280 0
    guy1b: 293 0     guy2b: 293 0     TS23b:  97 1     tS23b:  97 1
    tT31b: 136 0     tT42b:  76 1     TS41b:  97 0     tS41b:  98 0
    st13c: 280 0     st24c: 280 0     guy1c: 178 0     guy2c: 231 0
    TS23c:  98 1     tS23c:  98 0     tT31c: 197 0     tT42c: 197 0
    TS41c:  98 1     tS41c:  97 1

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

 

plane view of tensegrity torus
Plane View of the Six-Stage Tensegrity Torus
with Point Labels

 

Schematic for the Tensegrity Torus
Schematic for the Tensegrity Torus

structure file:  torus/x3l06torus1.rc
 variable file:  torus/x3l06torus1.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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