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 1.6*1.2 0.0 3 Obj * <Member> side2bp pt4a pt3a 1.0/1.6 0.0 3 Obj * <Member> side2cp pt2A pt1B+ 1.6*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 1.2 0.0 3 Obj * <Member> side1bp pt3a pt4a- 1.0/1.6 0.0 3 Obj * <Member> side1cp pt1A pt2B 1.0/1.6 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 1.2/1.6 0.0 3 Obj * <Member> side2bq pt4b pt3b 1.6*1.0 0.0 3 Obj * <Member> side2cq pt2B pt1A+ 1.0/1.6 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 1.2 0.0 3 Obj * <Member> side1bq pt3b pt4b- 1.3*1.0 0.0 3 Obj * <Member> side1cq pt1B pt2A 1.3*1.0 0.0 3 Obj *
Special Note There are member pairs here which are symmetric, for which the symmetry has not been captured in the nominal symmetry transformations. This symmetry was preserved in the computations by treating the pairs symmetrically. The symmetric pairs are: side1aq -- side1ap, side1bq -- side1cq, side1bp -- side1cp, side2cp -- side2bq, side2bp -- side2cq, gird1ap -- gird2aq, gird1bp -- gird2bq, gird1aq -- gird2ap, gird1bq -- gird2bp, st24p -- st24q
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: 1.15998 side2bp: 1.36547 side2cp: 1.065 gird1ap: 1 gird1bp: 1 side1ap: 1.78993 side1bp: 1.95378 side1cp: 1.95378 st13q: 2 st24q: 2 gird2aq: 1 gird2bq: 1 side2aq: 1.64205 side2bq: 1.065 side2cq: 1.36547 gird1aq: 1 gird1bq: 1 side1aq: 1.78993 side1bq: 1.06234 side1cq: 1.06234
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: -4.37614 st24p: -5.14993 gird2ap: 2.18165 gird2bp: 1.31648 side2ap: 2.22716 side2bp: 0.85342 side2cp: 1.70400 gird1ap: 1.76087 gird1bp: 2.25247 side1ap: 2.14791 side1bp: 1.22111 side1cp: 1.22111 st13q: -5.81593 st24q: -5.14993 gird2aq: 1.76087 gird2bq: 2.25247 side2aq: 1.23154 side2bq: 1.70400 side2cq: 0.85342 gird1aq: 2.18165 gird1bq: 1.31648 side1aq: 2.14791 side1bq: 1.38105 side1cq: 1.38105 Average tendon force magnitude: 1.65483
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. 0.231115 st24p st13q x1 0.231115 st13q st24q id 0.215367 st24p gird2bq id 0.215367 st24q gird1bp id 0.237170 st24p side1bq 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 ¼-inch-diameter wooden dowel. The tendons were made of 15-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> 200/2 Strut and Tendon Hub Adjustments - s;t> 0 0 st13p: 200 0 st24p: 200 0 gird2ap: 97 1 gird2bp: 98 1 side2ap: 113 0 side2bp: 135 0 side2cp: 104 1 gird1ap: 98 0 gird1bp: 97 1 side1ap: 174 1 side1bp: 192 1 side1cp: 192 1 st13q: 200 0 st24q: 200 0 gird2aq: 98 0 gird2bq: 97 1 side2aq: 162 0 side2bq: 104 1 side2cq: 135 0 gird1aq: 97 1 gird1bq: 98 1 side1aq: 174 1 side1bq: 104 1 side1cq: 104 1
Axial View of X-Module Torus 1
with Point Labels
structure file: torus/x2l08torus1.rc variable file: torus/x2l08torus1.dat digit list: src/mm.dls |
CONTACT: Bob Burkhardt Tensegrity Solutions Box 426164 Cambridge, MA 02142-0021 USA e-mail: bobwb@juno.com |