Make your own free website on Tripod.com

Datasheet for Skew Prism Arch


Copyright © 2007 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> end1a    pt1A pt1B  1.0 sqr(1.0) 2 Con *

<Member> strut13a pt1A pt2B -1.0 2.0      1 Con CalcClear *
<Member> guy1a    pt1A pt2A  1.0 2.0      3 Con *
<Member> eq1aa    pt2A pt3a  1.0 sqr(1.0) 2 Con *
<Member> eq1ba    pt2A pt3b  1.0 sqr(1.0) 2 Con *

<Member> strut24a pt3a pt3B -1.0 sqr(1.90158497148680) 1 Obj CalcClear *
<Member> guy2a    pt3A pt3a  1.0 sqr(1.28527187343639) 3 Con *
<Member> eq2aa    pt3A pt4a  1.0 sqr(1.0) 2 Con *
<Member> eq2ba    pt3A pt4b  1.0 sqr(1.0) 2 Con *

<Member> strut35a pt4a pt5b -1.0 sqr(2.11708545117312) 1 Obj CalcClear *
<Member> guy3a    pt4a pt5a  1.0 sqr(1.37257954094310) 3 Con *
<Member> eq3aa    pt4A pt5a  1.0 sqr(1.0) 2 Con *
<Member> eq3ba    pt4A pt5b  1.0 sqr(1.0) 2 Con *

<Member> strut46a pt4A pt5C -1.0 sqr(2.61688291892345) 1 Obj CalcClear *
<Member> guy4a    pt4A pt5B  1.0 sqr(1.37257954094310) 3 Con *
<Member> eq4aa    pt5A pt6a  1.0 sqr(1.0) 2 Con *
<Member> eq4ba    pt5A pt6b  1.0 sqr(1.0) 2 Con *

<Member> strut57a pt6a pt7b -1.0 sqr(1.90158497148680) 1 Obj CalcClear *
<Member> guy5a    pt6a pt7a  1.0 sqr(1.00893468194483) 3 Con *
<Member> eq5a     pt6A pt7a  1.0 sqr(1.0) 2 Con *

<Member> strut68a pt6A pt8a -1.0 sqr(2.23606797749979) 1 Con CalcClear *
<Member> guy6a    pt6A pt8c  1.0 2.0      3 Con *
<Member> eq6a     pt6A pt7b  1.0 sqr(1.0) 2 Con *

<Member> end2a    pt8a pt8b  1.0 sqr(1.0) 2 Con *

<Member> end1b    pt1B pt1C  1.0 sqr(1.0) 2 Con *

<Member> strut13b pt1B pt2C -1.0 4.0      1 Con CalcClear *
<Member> guy1b    pt1B pt2B  1.0 sqr(1.0) 3 Con *
<Member> eq1ab    pt2B pt3b  1.0 sqr(1.0) 2 Con *
<Member> eq1bb    pt2B pt3c  1.0 sqr(1.0) 2 Con *

<Member> strut24b pt3b pt3C -1.0 sqr(2.11708545117312) 1 Obj CalcClear *
<Member> guy2b    pt3B pt3b  1.0 sqr(1.00893468194483) 3 Con *
<Member> eq2ab    pt3B pt4b  1.0 sqr(1.0) 2 Con *
<Member> eq2bb    pt3B pt4c  1.0 sqr(1.0) 2 Con *

<Member> strut35b pt4b pt5c -1.0 sqr(1.90158497148680) 1 Obj CalcClear *
<Member> guy3b    pt4b pt5b  1.0 sqr(1.00893468194483) 3 Con *
<Member> eq3ab    pt4B pt5b  1.0 sqr(1.0) 2 Con *
<Member> eq3bb    pt4B pt5c  1.0 sqr(1.0) 2 Con *

<Member> strut46b pt4B pt5A -1.0 sqr(1.90158497148680) 1 Obj CalcClear *
<Member> guy4b    pt4B pt5C  1.0 sqr(1.28527187343639) 3 Con *
<Member> eq4ab    pt5B pt6b  1.0 sqr(1.0) 2 Con *
<Member> eq4bb    pt5B pt6c  1.0 sqr(1.0) 2 Con *

<Member> strut57b pt6b pt7c -1.0 sqr(2.61688291892345) 1 Obj CalcClear *
<Member> guy5b    pt6b pt7b  1.0 sqr(1.28527187343639) 3 Con *
<Member> eq5b     pt6B pt7b  1.0 sqr(1.0) 2 Con *

<Member> strut68b pt6B pt8b -1.0 4.0      1 Con CalcClear *
<Member> guy6b    pt6B pt8a  1.0 2.0      3 Con *
<Member> eq6b     pt6B pt7c  1.0 sqr(1.0) 2 Con *

<Member> end2b    pt8b pt8c  1.0 sqr(1.0) 2 Con *

<Member> end1c    pt1C pt1A  1.0 sqr(1.0) 2 Con *

<Member> strut13c pt1C pt2A -1.0 sqr(2.23606797749979) 1 Con CalcClear *
<Member> guy1c    pt1C pt2C  1.0 2.0      3 Con *
<Member> eq1ac    pt2C pt3c  1.0 sqr(1.0) 2 Con *
<Member> eq1bc    pt2C pt3a  1.0 sqr(1.0) 2 Con *

<Member> strut24c pt3c pt3A -1.0 sqr(2.61688291892345) 1 Obj CalcClear *
<Member> guy2c    pt3C pt3c  1.0 sqr(1.37257954094310) 3 Con *
<Member> eq2ac    pt3C pt4c  1.0 sqr(1.0) 2 Con *
<Member> eq2bc    pt3C pt4a  1.0 sqr(1.0) 2 Con *

<Member> strut35c pt4c pt5a -1.0 sqr(2.61688291892345) 1 Obj CalcClear *
<Member> guy3c    pt4c pt5c  1.0 sqr(1.28527187343639) 3 Con *
<Member> eq3ac    pt4C pt5c  1.0 sqr(1.0) 2 Con *
<Member> eq3bc    pt4C pt5a  1.0 sqr(1.0) 2 Con *

<Member> strut46c pt4C pt5B -1.0 sqr(2.11708545117312) 1 Obj CalcClear *
<Member> guy4c    pt4C pt5A  1.0 sqr(1.00893468194483) 3 Con *
<Member> eq4ac    pt5C pt6c  1.0 sqr(1.0) 2 Con *
<Member> eq4bc    pt5C pt6a  1.0 sqr(1.0) 2 Con *

<Member> strut57c pt6c pt7a -1.0 sqr(2.11708545117312) 1 Obj CalcClear *
<Member> guy5c    pt6c pt7c  1.0 sqr(1.37257954094310) 3 Con *
<Member> eq5c     pt6C pt7c  1.0 sqr(1.0) 2 Con *

<Member> strut68c pt6C pt8c -1.0 2.0      1 Con CalcClear *
<Member> guy6c    pt6C pt8b  1.0 sqr(1.0) 3 Con *
<Member> eq6c     pt6C pt7a  1.0 sqr(1.0) 2 Con *

<Member> end2c    pt8c pt8a  1.0 sqr(1.0) 2 Con *

        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.
        The values are in model units.

    end1a:            1  strut13a:      1.41421     guy1a:      1.41421
    eq1aa:            1     eq1ba:            1  strut24a:      1.90158
    guy2a:      1.28527     eq2aa:            1     eq2ba:            1
 strut35a:      2.11709     guy3a:      1.37258     eq3aa:            1
    eq3ba:            1  strut46a:      2.61688     guy4a:      1.37258
    eq4aa:            1     eq4ba:            1  strut57a:      1.90158
    guy5a:      1.00893      eq5a:            1  strut68a:      2.23607
    guy6a:      1.41421      eq6a:            1     end2a:            1
    end1b:            1  strut13b:            2     guy1b:            1
    eq1ab:            1     eq1bb:            1  strut24b:      2.11709
    guy2b:      1.00893     eq2ab:            1     eq2bb:            1
 strut35b:      1.90158     guy3b:      1.00893     eq3ab:            1
    eq3bb:            1  strut46b:      1.90158     guy4b:      1.28527
    eq4ab:            1     eq4bb:            1  strut57b:      2.61688
    guy5b:      1.28527      eq5b:            1  strut68b:            2
    guy6b:      1.41421      eq6b:            1     end2b:            1
    end1c:            1  strut13c:      2.23607     guy1c:      1.41421
    eq1ac:            1     eq1bc:            1  strut24c:      2.61688
    guy2c:      1.37258     eq2ac:            1     eq2bc:            1
 strut35c:      2.61688     guy3c:      1.28527     eq3ac:            1
    eq3bc:            1  strut46c:      2.11709     guy4c:      1.00893
    eq4ac:            1     eq4bc:            1  strut57c:      2.11709
    guy5c:      1.37258      eq5c:            1  strut68c:      1.41421
    guy6c:            1      eq6c:            1     end2c:            1

        Relative Member 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.

    end1a:      1.73205  strut13a:     -2.44949     guy1a:      2.44949
    eq1aa:      1.73205     eq1ba:      1.73205  strut24a:     -1.90158
    guy2a:      1.28527     eq2aa:      1.73205     eq2ba:      1.73205
 strut35a:     -2.11709     guy3a:      1.37258     eq3aa:      1.73205
    eq3ba:      1.73205  strut46a:     -2.61688     guy4a:      1.37258
    eq4aa:      1.73205     eq4ba:      1.73205  strut57a:     -1.90158
    guy5a:      1.00893      eq5a:      1.73205  strut68a:     -3.87298
    guy6a:      2.44949      eq6a:      1.73205     end2a:      1.73205
    end1b:      1.73205  strut13b:      -3.4641     guy1b:      1.73205
    eq1ab:      1.73205     eq1bb:      1.73205  strut24b:     -2.11709
    guy2b:      1.00893     eq2ab:      1.73205     eq2bb:      1.73205
 strut35b:     -1.90158     guy3b:      1.00893     eq3ab:      1.73205
    eq3bb:      1.73205  strut46b:     -1.90158     guy4b:      1.28527
    eq4ab:      1.73205     eq4bb:      1.73205  strut57b:     -2.61688
    guy5b:      1.28527      eq5b:      1.73205  strut68b:      -3.4641
    guy6b:      2.44949      eq6b:      1.73205     end2b:      1.73205
    end1c:      1.73205  strut13c:     -3.87298     guy1c:      2.44949
    eq1ac:      1.73205     eq1bc:      1.73205  strut24c:     -2.61688
    guy2c:      1.37258     eq2ac:      1.73205     eq2bc:      1.73205
 strut35c:     -2.61688     guy3c:      1.28527     eq3ac:      1.73205
    eq3bc:      1.73205  strut46c:     -2.11709     guy4c:      1.00893
    eq4ac:      1.73205     eq4bc:      1.73205  strut57c:     -2.11709
    guy5c:      1.37258      eq5c:      1.73205  strut68c:     -2.44949
    guy6c:      1.73205      eq6c:      1.73205     end2c:      1.73205

        Average tendon force magnitude: 1.67191

        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> 88/sqrt(2)
        Strut and Tendon Hub Adjustments - s;t> 0 0

    end1a:  61 0  strut13a:  88 0     guy1a:  85 1     eq1aa:  61 0
    eq1ba:  61 0  strut24a: 118 1     guy2a:  79 0     eq2aa:  61 0
    eq2ba:  61 0  strut35a: 131 1     guy3a:  84 0     eq3aa:  61 0
    eq3ba:  61 0  strut46a: 163 0     guy4a:  84 0     eq4aa:  61 0
    eq4ba:  61 0  strut57a: 118 1     guy5a:  62 0      eq5a:  61 0
 strut68a: 139 0     guy6a:  85 1      eq6a:  61 0     end2a:  61 0
    end1b:  61 0  strut13b: 124 1     guy1b:  61 0     eq1ab:  61 0
    eq1bb:  61 0  strut24b: 131 1     guy2b:  62 0     eq2ab:  61 0
    eq2bb:  61 0  strut35b: 118 1     guy3b:  62 0     eq3ab:  61 0
    eq3bb:  61 0  strut46b: 118 1     guy4b:  79 0     eq4ab:  61 0
    eq4bb:  61 0  strut57b: 163 0     guy5b:  79 0      eq5b:  61 0
 strut68b: 124 1     guy6b:  85 1      eq6b:  61 0     end2b:  61 0
    end1c:  61 0  strut13c: 139 0     guy1c:  85 1     eq1ac:  61 0
    eq1bc:  61 0  strut24c: 163 0     guy2c:  84 0     eq2ac:  61 0
    eq2bc:  61 0  strut35c: 163 0     guy3c:  79 0     eq3ac:  61 0
    eq3bc:  61 0  strut46c: 131 1     guy4c:  62 0     eq4ac:  61 0
    eq4bc:  61 0  strut57c: 131 1     guy5c:  84 0      eq5c:  61 0
 strut68c:  88 0     guy6c:  61 0      eq6c:  61 0     end2c:  61 0

        Material Quantities (in millimeters)
        Estimates of the total amount of material required to build
        the structure.  The adjustment in this case includes "waste":
        for the strut, the amount lost when sawing the strut from a
        length of dowel (1 mm from each end); for the tendons, the amount
        of extra needed to successfully tie the tendon (50 mm extra at
        each end).

        Elongation of Tendon of Unit Cross Section
        Under Force of Average Magnitude (fraction)> .02
        Length Scale Factor> 88/sqrt(2)
        Strut and Tendon Adjustments - s;t> -1, -50

                    Cross
         Type     Section    Quantity Count

            2           1     5721.57    36
            1           1     2390.78    18
            3           1     3130.48    18
        Strts                 2390.78    18
        Tndns                 8852.05    54


pedagogic view of skew prism arch
Skew Prism Arch with Point Labels

structure file:  mast/x3l6mast2b.rc
 variable file:  mast/x3l6mast2b.dat
    digit list:  src/mm.dls

CONTACT:

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

e-mail: bobwb@juno.com

Back to Structure Based on Laminated Skew Prisms

More Datasheets