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Datasheet for X-Module Torus 2


Copyright © 2008 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> st13p    pt1A  pt3a   0.0  sqr(2.0)  1 Con CalcClear Inelastic *
<Member> st24p    pt2A  pt4a   0.0  sqr(2.0)  1 Con CalcClear Inelastic *

<Member> gird2ap  pt4a  pt1B+  0.0  sqr(1.0)  2 Con *
<Member> gird2bp  pt4a  pt1A+  0.0  sqr(1.0)  2 Con *

<Member> side2ap  pt2A  pt4b   1.9*1.0  0.0   3 Obj *
<Member> side2bp  pt4a  pt3a   1.0/1.9  0.0   3 Obj *
<Member> side2cp  pt2A  pt1B+  1.0      0.0   3 Obj *

<Member> gird1ap  pt2A  pt3a   0.0  sqr(1.0)  2 Con *
<Member> gird1bp  pt2A  pt3b   0.0  sqr(1.0)  2 Con *

<Member> side1ap  pt1A  pt3b   1.9*1.0  0.0   3 Obj *
<Member> side1bp  pt3a  pt4a-  1.0/1.9  0.0   3 Obj *
<Member> side1cp  pt1A  pt2B   1.0      0.0   3 Obj *

<Member> st13q    pt1B  pt3b   0.0  sqr(2.0)  1 Con CalcClear Inelastic *
<Member> st24q    pt2B  pt4b   0.0  sqr(2.0)  1 Con CalcClear Inelastic *

<Member> gird2aq  pt4b  pt1A+  0.0  sqr(1.0)  2 Con *
<Member> gird2bq  pt4b  pt1B+  0.0  sqr(1.0)  2 Con *

<Member> side2aq  pt2B  pt4a   1.0/1.9  0.0   3 Obj *
<Member> side2bq  pt4b  pt3b   1.9*1.0  0.0   3 Obj *
<Member> side2cq  pt2B  pt1A+  1.0      0.0   3 Obj *

<Member> gird1aq  pt2B  pt3b   0.0  sqr(1.0)  2 Con *
<Member> gird1bq  pt2B  pt3a   0.0  sqr(1.0)  2 Con *

<Member> side1aq  pt1B  pt3a   1.0/1.9  0.0   3 Obj *
<Member> side1bq  pt3b  pt4b-  1.9*1.0  0.0   3 Obj *
<Member> side1cq  pt1B  pt2A   1.0  0.0       3 Obj *

        Rotation Matrices and Transform Points
        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 3 by 3
        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.  In this case the base transform (specified
        in <XMat>) is just a rotation about the z-axis by 90°.

# rotation matrices
<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

# transform points
<XformPt> pt1A+ pt1A  x1
<XformPt> pt1B+ pt1B  x1
<XformPt> pt4a- pt4a  x3
<XformPt> pt4b- pt4b  x3

        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
        pin insertion point to pin insertion point, as are the tendon lengths.
        These values are in model units.

    st13p:            2     st24p:            2   gird2ap:            1
  gird2bp:            1   side2ap:      1.39911   side2bp:      1.66871
  side2cp:      1.37277   gird1ap:            1   gird1bp:            1
  side1ap:      1.39911   side1bp:      1.66871   side1cp:      1.37277
    st13q:            2     st24q:            2   gird2aq:            1
  gird2bq:            1   side2aq:      1.94984   side2bq:      1.04637
  side2cq:      1.23258   gird1aq:            1   gird1bq:            1
  side1aq:      1.94984   side1bq:      1.04637   side1cq:      1.23258

        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.

    st13p:     -4.32843     st24p:     -4.32843   gird2ap:      1.89009
  gird2bp:      1.67495   side2ap:      2.65831   side2bp:      0.87827
  side2cp:      1.37277   gird1ap:      1.67495   gird1bp:      1.36123
  side1ap:      2.65831   side1bp:      0.87827   side1cp:      1.37277
    st13q:     -5.70009     st24q:     -5.70009   gird2aq:      1.36123
  gird2bq:      2.46091   side2aq:      1.02623   side2bq:       1.9881
  side2cq:      1.23258   gird1aq:      2.46091   gird1bq:      1.89009
  side1aq:      1.02623   side1bq:       1.9881   side1cq:      1.23258

        Average tendon force magnitude: 1.65434

        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.
        The worst-case values are provided for strut-strut convergences
        and then for the strut-tendon convergences.

    0.203477    st13q     st24q        id
    0.203477    st13q     st24q        x3
    0.155202    st13q   gird2aq        x3
    0.155202    st24q   gird1bp        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 3/16-inch-diameter wooden dowel.
        The tendons were made of 12-lb.-test braided nylon fishing line.
        In this case, the attachment point at the hubs was a simple
        metal pin stuck into the end of the strut, so no member-length
        adjustments were necessary.  Prestress forces are assumed
        not to affect strut lengths.

        Elongation of Tendon of Unit Cross Section
        Under Force of Average Magnitude (fraction)> .02
        Length Scale Factor> 130/2
        Strut and Tendon Hub Adjustments - s;t> 0 0

    st13p: 130 0     st24p: 130 0   gird2ap:  63 1   gird2bp:  63 1
  side2ap:  88 0   side2bp: 107 1   side2cp:  88 0   gird1ap:  63 1
  gird1bp:  64 0   side1ap:  88 0   side1bp: 107 1   side1cp:  88 0
    st13q: 130 0     st24q: 130 0   gird2aq:  64 0   gird2bq:  63 0
  side2aq: 125 0   side2bq:  66 1   side2cq:  79 0   gird1aq:  63 0
  gird1bq:  63 1   side1aq: 125 0   side1bq:  66 1   side1cq:  79 0


axial view of tensegrity torus
Axial View of X-Module Torus 2
with Point Labels

structure file:  torus/x2l08torus2.rc
 variable file:  torus/x2l08torus2.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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