Title: ????? ???? ?? ???? Tensegrity
1????? ???? ?? ???? Tensegrity
?????????? ?? ???? ??????? ?????? ?"? ???? ?????
??????? ?????? ???????, ?????? ???????
- ???? ??? ??
- ??????? ???? ??????? ?"? ???? ??
2???? ?????
- ????
- ??? ?????? Tensegrity ?
- ???, ???????? ????????
- ????? ???? (Form-Finding) ?? ???? Tensegrity
- ????? ??????
- ???? Guzman
- ???????????? Hennenberg
- ????? ????????
- ????? ??????
- ?????? ??????? ???? ???????
3??? ?????? Tensegrity ?
- Tension Integrity Tensegrity
- Fuller, 1975
????
4??????
- ?????? ??????
- Tensegrity ??? ?????? ??????? ???? ????? ??????
?????? ?????? ????? (integrity). ?????? ????
????? ??????? ?"? ????? ???? ????? - ????? ????? ????? ?????? (self-stress)
- ??????- ???? ????, ????? ??? ????
- ???? Tensegrity ?? ????? ??????? ?? ??? ????? ??
??????? ?????? ??????? ?????? (???????/struts)
???????? ?????? ??????? ?????? (?????)
5- ???? ???? ????-????
- ?????? ?????, ????? ???????.
????
6??? ????????.....
- ?? ?????? ?
- Loganson Karl1921 Study in balance?
- Richard Buckminster Fuller (1895-1983) ?
- K.D. Snenlson (1927- ) ?
????
7???????
- ?????????? ??????
- ???? ????
- ????????
- ????- ????? ?????? ??? ????
- ?????
????
8??????? ???????
????
9????
10????
11????
12(Form- Finding) ????? ????
13????? ???? - Tensegrity
- ???? ????? ????? "??????" ?????? ????, ?? ?? ??
???, ?????? ????? 7 ????? ?? ????? ?????? ????
Tensegrity ?????? ???? ?????? - ????? ????????
- ????? ??????
14????? ??????
- ????? ??????- ??????? ????? ???????? ?????? ?????
?????? ???? ?? ????? ?????? ?? ??????????, ???
????? ????? ?? ?????? ?????????. ????? ??????/
??-?????? ????? ?? ????? ?????? ?????? ??????
???. - ????? ?? ?????? ??? ??????? ???????? ????????.
- ????? ????? ??? ???? ????? ???? ?????? ?????,
????? ??? ????? ???????????? ?????? ??????.
15???? Guzman
- ???? ????? Miguel de Guzman ??????????? ?????
(2004). - ????? ??????
- ????? ?? ????????? ????? ????? ????? ????
Tensegrity ??????-????. - ????? ???? ??????? ?????? ?? ???? Tensegrity ??
???? ?????????? (??????, ????? ???? ??????? ???
???? ????????? ?????). - ????? ?????????? ????? ?? ???? Tensegrity
??????-????. - ???? ?? ????? ????? ??????-????.
Guzman
16??????? ???? Guzman
- ????????? ?? ???? Tensegrity ????? ?????? ?????
(????-???????) ?? ?????? ???? ??????? "??????"
(??? ??? ?? ????? ?????- K4). - ??? ??????? ?????, ??????? ??? ???? ??????,
?????? ??????. ???? ?????? ???? ???? ???? ??????
???? ???????? ????. - ??? ???? Tensegrity ??????? ????? ????
(self-stress) ?????? ?????? (?? ??????? ???????).
????? ?????? ?????? ???? ?? ??? ???? Tensegrity
????? ????. - ????? ????? ??? ??????? ?? ????? ??? ?? ???????
????? ??????-????. (??? ????? ?? ?????? ????? ??
?????? ?????? ?????, ????? ??? ?????? ?????).
Guzman
17??????
- ???? ? ?? ????? ???? ???? ?? ?????? ?ij
(????????) ??????. - ?ij ?ji ????? ??? ???????? ????? ????.
- ???? ?? ????? ???? ???? (self-stress) ?? ?????
?????? ????? ??? -
- ????? ??? ???? pi, ???? ????????
??? ???. - ?????? ????, ?????? ??? ????? ????? ?? ????
Tensegrity - ????? ?? ????????? ??? ???? ???? ????.
- ????? ?? ??? ????????? ??????? ???????
- ?? ?? ????? ???? ????.
Guzman
18??????
- ???? Tensegrity ,T(P), ??? ????? ????? ???? ???
?????? ij ???? ?ijgt0 ?????? ???? ?? ???? (??????
??????? ?? ??? ????? ?????? ?? ???), ??????? ????
?ijlt0 ?????? ???????? ??? ?????? ??????. ?????
??? ?ij0 ?????.
Guzman
19?????? Tensegrity ???????- ??????
- 4 ????? ?? ?????? ??-???????.
- ???????
- ?????? ??????
Guzman
20???? ????? ?? ???? Tensegrity
?????? 1 ?????
- ?? ???? Tensegrity ???? ?????? ????? ???? ??
??????. ?????? ?? ????? ??????? ???? ????. - ?????
- ????? Tensegrity ????, ????? ????? ?? ??????
??????? ??????, ?? ???? ??? ???? ???? ???? ?????
??? ?????? ???????? ???? ?????? ?????? ???. - ????? ?? ?????? ????? ????? ????? ????, ??? ?? ??
d2 ????? ????? ???????- ????? ????. - ???? ?? ?????? ??????, ??? ???? ?? ???? ??
???????? ??????? ??? ??????? ??????.
Guzman
21???? ????? ?? ???? Tensegrity
????
- ??? ??? ?? ?? ??? ????? ???????
- ????? ???? ????? ?????? ????? A
????? K ?????? ?? A,B,C,D ???? ???? ??????
(??? ??? ????? ?????). ???? ?? ???? ????
???? ??????? ???? AB ( ). ????
????? ???? ????? A ?? ????????? AC, AD ????
??????. ????? ???????? ????? ?????, ?? ?? ????
??????? ?? ???? A
- ????? ????? ????? ?? ???????? ????? ????
"??-???" ??????? ????? ???? ?? ???? ???? ?????
???? ????? A
Guzman
22???? ????? ?? ???? Tensegrity
????
- ???? ?????? ?? ?????? ??????, ?? ??? ???? ????,
???? ??? ???? ???? ???? ????? "???? ???" ?? ????
???? ????? ???? ???? ????? ????? ???? ???? ?????
????? ????. ???? ?????? ?? ????? ??????.
Guzman
23???? ????? ?? ???? Tensegrity
?????? 2 ?????
- ?? ???? ????? ?? ??????, ???? ???? ??? ?? ??
???, ??? ????? ?????, ??? ??? ???, ????
Tensegrity ??? ?????? ??? ?? ?????. ?? ????????
?????????? ??????? ??? ??? ???. - ?????
- N ?????? ?????? ?????? A1,A2,A3,..,AN.
- ?????? ????? A1,A2,A3,A4 ??????? ????.
- ????? ????, A5, ????? ????? ???? ?????? ??
A1,A2,A3,A5. - ????? ???? ????? ??????.
- ???? ?????? ????? ?? ??????? ??? ???? ?????.
Guzman
24????? ???? ????? ????? Guzman
????? ??- ??????
- ????? ????????? ??????? ???? ??????
- ?? ????? ?? ????????? ?? ????? ????? ????
Tensegrity ??????-????. - ?? ????, ?? ???? ?? ?????? ?????? ??????? ??
?????? ?????? ?? ???????.
Guzman
25????? ???? ????? ????? Guzman
Guzman
26????? ???? ????? ????? Guzman
????? ???? K4 !!! ????? ?????????? ?????? ??????
?????? ?????? ???? Tensegrity
???? ????? ?? ?????????? ??????? ???? ???????
????? ??? ??????? ??????? ??????
Guzman
27????? ???? ????? ????? Guzman
A
??? ???? ?????
C
B
B
????? ????????? ?? ????? ?? ????? BCEF ??? ??????
?????? ???????? ?????? (???? ???? ????? ????? ??
???? ????). ???????? ???????.
D
E
D
E
F
F
?????? ????? ????? ????? ???? ABCF. ????? ???? A
????? ????? ??? ?????? ???????? BF, CF ?????
?????? ???????
?????? ???? ?????? ?????? ????? ???? BDEF
????? ???? ?? ???? D . ??? ?????? ????? BE ??????
??????, ????
- A ?????
- ?? ????? ?? ?????? ???????? BF,CF
- ?? ??? ????? ??? F
- ?? ?? ??? ????? ??? ????? ??????
??? ??? ?? ????? ?? BF ?
Guzman
28????? ???? ????? ????? Guzman
A
A
C
C
B
B
D
E
F
F
??? ??? ?? ????? ?? BC ?
- A ?????
- ?? ????? ?? ?????? ???????? BF,CF
- ?? ??? ????? ??? F
- ?? ?? ??? ????? ??? ????? ??????
Guzman
29????? ?????? Guzman
- ??????? ???????
- ???? ????????? ??? ???? ???? ????.
- ???? ????????? ??????? ??????? ?? ?? ????? ????
????. - ????? ?????? ???? ????? ????? ???? ?????? ??
????????? ?????? ????? ???? Tensegrity, ??? ?????
?????????? ????? ????? Tensegrity ??? ????? ?????
???? ??????. - ????? ?????? ???? ????????? ????? ?? ????
Tensegrity ?????? ???? ???? ????, ????? ???? ??
?????? ?????? ?? ????? ?? ?? ????? ???? ?? ?????.
- ?? ???????? ?? Guzman ????? ???? ?????? ???? ??
????? ????? ??? ?????? ?? ?????? ????.
Guzman
30???????????? Hennenberg
- G(p) ??? ????? ????? ? ?d , i,j ??? ??? ?? G
?? ? Pi?Pj. - ???? ?? ???? ???? G, ?????? ???? ? d1 ?????
????? (3 ????? ????? ???-?????), ???? ???????
????? ??? pk ??? ????? ?? ??? ????? ?? pi ? pj
(?? ?? ????? ????). - 2 ????? ????? ?? pk ? pi ?? pj
- d-1 ????? ????? ?????? ????? ?? G.
- ???? pk ???? ?????? ?????? ?????-????.
Hennenberg
31???????????? Hennenberg
- ????
- ?? ??? G ???? ??? n-2 ????? (n- ??' ??????),
?????? ?????? ????? ??? 3, ???? ?????? ?????? ??
???????????? Hennenberg ?????? ?????, ????
??????? ???? K4. - ???? ??????
- ???? ????? ?? ??? G ??? n-2 ????? ?????
????? ????? ??? K4. ?? ?????? ?????? ?????? ????
??????? ???? G.
Hennenberg
32????? ????? ??????
- ???? ????? ?????Hennenberg ???? ???? ????
eH2n-2. ???? ??????? ?????? ????? Guzman ????
eG3n/2. ???? ???? ngt4. ????? ????????????
Hennenberg ?????? ????? ???? ??? ????? ??????
?????? ?????? ???? 4 (?? ????). - ?????? Hennenberg ?? ?????? ???? ??????. ????? ??
???? ???? ????? ???????. ????? Guzman ??? ??????
???? ?????? (???? ?????? ?????? ????????). - ???????????? Hennenberg ????? ?? ???? e2n-2
????? ?? ???? ??????. ???? Guzman, ?????? ????
?????? ????? ??? ?? ??????? e2n-2 - ???????????? Hennenberg ???? ???????????? ????
????? Guzman. ?????? ??? ??????? ???????? ?? ???
???? ?? ????? ?????? ????? Tensegrity , ??? ????
?? ????? ?? ???? ?????? ?????? ?????.
33????? ????????
- ???? ?????? ???? ???? ????? ???? ???????? ???
????????. - ?? ????????
- ???? ???????? ???? ??????? ?? ?????? ????????.
- ???? ?? ????? ?? ????? ??? ?????? ?? ????? ?????
????? ????
34????? ????????
- ???? ????? ????????
- ???? ???????.
- ???? ??????????? ?? ????????.
- ???? ????????? ????? ??????.
????? ????
351. ???? ???????
- ???? ???? ???? ??? ?????? ??????? ????? ????? ??
??????. - ???? ??????? ?????? ?? V ?????? ????? ??????
?????? ???????? ????? ??????. - ????? ????? ?????? ???????? , ???? ???? ? ???
?????? ?????? ??????? ??? ????? ???? Tensegrity
????. -
- ???? ????? ????? ??????? ?? ????? ?????? ?????.
???? ???? Tensegrity ????????? ??? ????? ???????
????? ????? ?????? ???? ?"? ????? ???? ?? ??????
?????? ???? ??????. - ?????? ????? ???????? ?????? ???? ????? ?? ????
???? ????? ???????.
???? ??????? ???? 12 ???? ??????? ??? ?????
?????? ??? .2?j/v j ??? ??? ??? ? V. ??
?????????? ?????
???? ????? ????, lc , ????? ?? ??????, ls , ????
???? ??????? ????
362. ???? ??????????? ?? ????????
- ???? ?? ????? ?? ????? ????? ????? ?? ?? ????
Tensegrity ?????? ??????? ??????. - ??????? ?????? ??? ????? ?????????? ???????
??????. - ??????? ????? ??? ?? ????, ??? ????? ?? ???
?????? ???? ?? ??????? ???????????? ??? ???????
?????????. - ????? ???????? ??????? ??? ?????? ????
-
- Minimize f(x,y,z)
- Subject to gi(x,y,z)0 for i1,.,n
- ??????? ????? ????? ?????,??????, ????? ?????? ??
??? ????????
????? ????
372. ???? ??????????? ?? ????????
- ???? ?? ?????? ???? (Pellegrino)
- ?????? ??????
- ?? ???? ????? ????? ????? lc1 ?????? ???????.
- ??? ??????? ????? ???? ????? ????? ?????? ????
?????.
- ????? ???????? ??????? ???? ??????
- ???? c1, c2,.,c6 ?? ???? ?????? ??????? ?????
?????? s1,s2,s3 ?? ????????
????? ????
382. ???? ??????????? ?? ????????
- ???????
- ????? ????? ??????? ?????? (????? Matlab).
- ?????? ????? ?????????? ????? ???? ?????????
?????, ?? ??? ????? ????? ????? ??? ??????? ??
????????. - ???????
- ???? ???????? ???? ???? ?? ?? ????? ????? ??????
(?????? ??????? ??????). - ??? ??? ????? ????? ?????? ???????? ????????
??????.
393. ???? ?????????- ????? ??????
- ????? ???????????? ??????? ?????, ???? ??????
????? ???????? ??????, ?????? ?????-????? ?????
?????? ?"? ????????? ?? ??????? ???????? - ????
- K ?????? ???????
- M ?????? ????
- D ?????? ?????? (damping)
- f ????? ?????? ?????????
- ?? ?????? ??????,
??????? ??????? ?????? - ???? ????????????
????????.
????? ????
403. ???? ?????????- ????? ??????
- ???????
- ????? ????? ??????? ???? ?????? ??? ???? ?????
????. - ???????
- ????? ??????????? ??? ???? ???? ?????? ???.
- ???? ????? ???? ?????? ???? ????? ????? ???
?????? ????????, ??? ??? ????? ?? ????? ??????
???????? ??? ??????? ???.
????? ????
41????? ??????
- ?????? ??? ?????? ?? ???? ???? ???????????
?????????? ????? ??????? ??????? ?? ???????? ???. - ??? ?? ????? ??????? ??? ??????? ?????
- ???? ???????
- ???? ?????? ???? (force density)
- ???? ??????? ??????
- ???? ???????????? ????????
????? ????
421. ???? ???????
???? ??? ?????? ???? ??? ????? ????? ???????
???????? ?????? ???? ????? ????? ??? qij
?????? ??? ??? ????? ?????. ????? ??????
????? ????? ????? 1 ?????? z ? y ????
?????? ????? ?? ??? ??????? ??? ????? ?? ??????
?????? ??? ????? ?? ????? ??? ?? ??????
?????? ????? ????????
432. ???? ?????? ????
- ????? ????? ?"????" ?????? ????? ????? ?????
????? ??????? ?? ????????? ??????, ?????? ??
??????? ????????. - ??????, ?????? ?????-????? ?????? x ????? ?????,
i, ??? - ????
- t ???? ??????
- l ???? ??????
- f ????? ?????? ?????????
- lij ??? ??????? ?? ???????????? ???? ???????
????? ????????. - ????? ????? ????? ??? qijtij/lij
- q ???? ?????? ???? ????? ???? ????? ???? ??????
????? ????? ?????.
????? ??? b ??????? ? n ?????, ???????
?????-????? ?????? x ?????? ?????? ????? ???
???? Cs ?????? ??????? bxn Q ??????
???????? ?????? ?? ???????? ????. xs ?????
????? ?? ??????????? x. fx ????? ??????
????????? ??????? ?? ?????? ?????? x.
????? ????
442. ???? ?????? ????
????? ?????? ????? ????? ???? (self-stress) ??
???? ??? ????? ??????? ????? ???? ?????
????????. ???? ????? ?????
????? ??? b ??????? ? n ?????, ???????
?????-????? ?????? x ?????? ?????? ????? ???
???? Cs ?????? ??????? bxn Q ??????
???????? ?????? ?? ???????? ????. xs ?????
????? ?? ??????????? x. fx ????? ??????
????????? ??????? ?? ?????? ?????? x.
??????? ????? ?????? ???????? y ? z. D ????
?????? ?????? ???? ????? ????? ?????? ??? ????
??? Q ? Cs ????? ????
453. ???? ??????? ??????
- ????? ???? ??? ?????? ????
- ????
- ?ijgt0 ??????
- ?ijlt0 ????????
?? ????? ????? ?? ?????? ??????? ?? ??? ????
?????? ???? ???? ??? ???????? ??????? ?ij
???? ????????? ???? qij ???? ??????? ???? ????
???? ????? ?? ???? ????? ?????? ?? ????
Tensegrity, ?? ???? ???? ??? ?????? ??....
????? ????
463. ???? ??????? ??????
????? ????? ??????? ?????? ???? ??????? ?
???? ?????? ?? ?????? ????, ??????? ?????
???????? ??????? ?? ????????. ?????? ?? ???? ???
??????? ????? ????? ????????? ?? ??????.
??? ????? ????? dn ????? ?? ??????????? ?- x,y,z
?? p. ????? ????? ????
474. ???? ???????????? ????????
???? Tensegrity
???? ???????? b
m ?????
o ??????? (???????? ??? ???????
??-?????? ??????)
bmo
????? ?? ??????????? ??????? ???? ?????? ????????
?? ?????? ???????????? ?? ????????
gg1,g2,.,gNT . ???-???? N3xO
(x,y,?) ???? ???? N5xO (x,y,z,?,f)
????? ????
484. ???? ???????????? ????????
???? ?????? ?????? (self stress) ?????? ??????
tt1,t2,,tMT ??????-???? ?? ???????? ????????
???? ????? ????????. ????? ?? ??????? ?????-????
??? ????? ??????? ?? ????? ????? ???? ?????? ??
?????? ??????? ??????. ???? ????? ????? ?? ?????
????? dg, ?? ??? ??????? ?? ????????. ??????
????? ?? ??? j ??? ????? ?? ?????? ???? A
NXM
????? ????
494. ???? ???????????? ????????
- ?????? ??????? ??? ?? ?? ?????? (???????? ??
????? ?? ?????) ???? tTdl(At)Tdg - ?????? ???? ????? ?? ???? ???? ??? ????? ?????
dg. ????? At0 - ???? ???? ?? ?? ????? ???? ??? ??????? ?????
- ?????? ?? ???????? ????
rank AltM - ?? ??????? ??????? ???? ???? ?????
tjgt0 for j1,2,.,M
????? ????
50????? ??????? ????? ????? ?????
- ????? ???? ?? ?????? ????? 7 ????? ???????? ????
??????
1. ????? ????????
2. ????? ??????
??????? ??????????? ?? ???? ??????? ?? ????????
?? ???? ??????? ?? ??????, ???? ???? ???? ????
???? ????? ?????.
- ???? ??????? ????? ?????? ?? ????????
- ?????? ?? ?????? ?????? ???????????? ????? ??????
???? - ??? ?????? ????? ?????? ?????? ????? ??
??????????? ?????.
- ???? ??????????? ?? ????????
- ???? ????????? ????? ??????
?????? ???????????? ??????-???? ???????? ??? ??
?????? ??????? ?????.
- ???? ??????? ????? ?????? ?? ????????
- ???? ?????? ???????????? ?????.
- ???? ?????? ?? ????? ???????? ?? ?????? ?????????.
- ???? ?????? ???? (force density)
- ???? ??????? ??????
- ???? ???????????? ????????
????? ????????????
- ????? ???? ?? ????? ?? ????? .
- ????? ?????????? ?????????
51?????? ??????? ???? ???????
- ???? ????? ????? ??????? ????
- ??? ???? ????? ???? ??????? ????? ??? ????? ????
- ???? Guzman
- ?????? ???? ????? ????? ???? ?????? ?? ?????????
?????? ????? ???? Tensegrity, ?????? ??????????
????? ????? Tensegrity ??? ????? ????? ????
?????? - ????? ???? ?????-????- ????? ????? ?????? ??????
- ???????????? Hennenberg ?????? ????? Tensegrity
????? ??? ??? ????? ???? ????? ??????