Three-fold Tensegrity Prism With Orthogonal Struts

Copyright © 2004 by Bob Burkhardt

Hub ConnectivityThis shows how vectors (v1, v2, v3) are applied to the strut end points (p1, p1', p2, p2', p3, p3') to derive hub points (hp1a, hp1b, ...). Hub points are where tendons are connected to the strut. <VecPt> hp1a p1 + v1 <VecPt> hp1b p1 - v1 <VecPt> hp1a' p1' + v3 <VecPt> hp1b' p1' - v3 <VecPt> hp2a p2 + v2 <VecPt> hp2b p2 - v2 <VecPt> hp2a' p2' + v1 <VecPt> hp2b' p2' - v1 <VecPt> hp3a p3 + v3 <VecPt> hp3b p3 - v3 <VecPt> hp3a' p3' + v2 <VecPt> hp3b' p3' - v2Member 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. This figure was computed without benefit of symmetry transforms, but everything turned out very symmetric nevertheless. # struts <Member> strut1 p2' p1 -1.0 sqr(12.0) 1 Con CalcClear * <Member> strut2 p3' p2 -1.0 sqr(12.0) 1 Con CalcClear * <Member> strut3 p1' p3 -1.0 sqr(12.0) 1 Con CalcClear * # side tendons <Member> side1 hp1a' hp1b 1.0 0.0 3 Obj CalcClear * <Member> side2 hp2a' hp2b 1.0 0.0 3 Obj CalcClear * <Member> side3 hp3a' hp3b 1.0 0.0 3 Obj CalcClear * # end tendons <Member> end1 hp2a hp1a 1.0 sqr(8.38288) 2 Con CalcClear * <Member> end2 hp3a hp2a 1.0 sqr(8.38288) 2 Con CalcClear * <Member> end3 hp1a hp3a 1.0 sqr(8.38288) 2 Con CalcClear * <Member> end1' hp2b' hp1b' 1.0 sqr(8.38288) 4 Con CalcClear * <Member> end2' hp3b' hp2b' 1.0 sqr(8.38288) 4 Con CalcClear * <Member> end3' hp1b' hp3b' 1.0 sqr(8.38288) 4 Con CalcClear *Hub ConstructsThese items are just vectors corresponding to each of the struts. At some point the software will be modified so these items aren't necessary since it should be possible to treat any member as a vector without explicit constructs. <DiffVec> strut1v p2' p1 <DiffVec> strut2v p3' p2 <DiffVec> strut3v p1' p3Hub ConstraintsThese are constraints the hub vectors must meet. Each vector must be orthogonal to its strut and 0.5 inches long. <VecDotVec> hubdot1 strut1v v1 1.0 0.0 Con <VecLength> hublength1 v1 1.0 sqr(0.5) Con <VecDotVec> hubdot2 strut2v v2 1.0 0.0 Con <VecLength> hublength2 v2 1.0 sqr(0.5) Con <VecDotVec> hubdot3 strut3v v3 1.0 0.0 Con <VecLength> hublength3 v3 1.0 sqr(0.5) ConIn-Situ Member LengthsThese are the lengths of the members when they are in place and prestress is applied. These are raw unadjusted values and assume the hubs of the structure are single points. The values are in model units. strut1: 12 strut2: 12 strut3: 12 side1: 6.65617 side2: 6.65617 side3: 6.65617 end1: 8.38288 end2: 8.38288 end3: 8.38288 end1': 8.38288 end2': 8.38288 end3': 8.38288Relative Member Prestress Force MagnitudesThese 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. strut1: -10.4407 strut2: -10.4407 strut3: -10.4407 side1: 6.65617 side2: 6.65617 side3: 6.65617 end1: 4.33197 end2: 4.33197 end3: 4.33197 end1': 4.33197 end2': 4.33197 end3': 4.33197Construction Lengths (stakes and #18 twisted nylon twine (white) -- inches, 16ths and 32nds)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 a strut represents the distance between tendon attachment points on the strut assuming both attachment points are on the same side of the strut. Prestress forces are assumed to affect tendon lengths and not strut lengths. For this particular hub geometry, the ad hoc adjustment used in the first datasheet didn't work very well. Here no ad hoc adjustment is necessary since the hubs are included explicitly in the mathematical programming problem. The struts were cut from 1-inch by 1-inch hardwood garden stakes. The behavior of the #18 twisted nylon twine under stress is highly non-linear, so a look-up table was used to compute strains. stress-strain chart: v04oct_d/wellingtn.ssc Average Tendon Force Magnitude (chart units)> 20 Length Scale Factor> 1.0 (Things are scaled so model and construction units are the same.) Strut and Tendon Hub Adjustments - s;t> 0 0 (As seen above, hub connections were handled explicity in the mathematical programming problem, so no ad hoc adjustment is needed here to account for the hub connections.) strut1: 12 0 0 strut2: 12 0 0 strut3: 12 0 0 side1: 6 0 0 side2: 6 0 0 side3: 6 0 0 end1: 7 12 0 end2: 7 12 0 end3: 7 12 0 end1': 7 12 0 end2': 7 12 0 end3': 7 12 0Alternate Construction Lengths (stakes and #1 braided nylon twine (yellow) -- inches, 16ths and 32nds)For my version of the structure, I tied half the prisms (4) with this twine, and half with the twisted twine. This twine looks nicer and doesn't unravel like the twisted. This twine is also more elastic which is why the construction lengths are shorter. When used at the same tensions, as I do here, the mechanical properties of the braided twine seem equivalent to the white nylon twine.. The braided twine's behavior under stress is different from the behavior of twisted twine, so a different look-up table was used to compute strains. stress-strain chart: v02oct_s/evans.ssc Average Tendon Force Magnitude (chart units)> 20 Length Scale Factor> 1.0 Strut and Tendon Hub Adjustments - s;t> 0 0 strut1: 12 0 0 strut2: 12 0 0 strut3: 12 0 0 side1: 5 13 1 side2: 5 13 1 side3: 5 13 1 end1: 7 9 0 end2: 7 9 0 end3: 7 9 0 end1': 7 9 0 end2': 7 9 0 end3': 7 9 0

View of the Tensegrity Prism

with Point Labels

Cell of Cubic Lattice Constructed using

Tensegrity Prisms as Joints

structure file: tprism/x3prism_orthoj2.rc variable file: tprism/x3prism_orthoj2.dat digit list: src/standard.dls |

CONTACT:

Bob Burkhardt

Tensegrity Solutions

Box 426164

Cambridge, MA 02142-0021

USA

e-mail: bobwb@juno.com