????? ???? ?? ???? Tensegrity - PowerPoint PPT Presentation

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Title:

????? ???? ?? ???? Tensegrity

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Title: Form Finding of tensegrity structures Author: asaf katz Last modified by: offer shai Created Date: 5/16/2005 6:33:04 PM Document presentation format – PowerPoint PPT presentation

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Tags: dc | motors | tensegrity

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Transcript and Presenter's Notes

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
  1. ???? ???? ????-????
  2. ?????? ?????, ????? ???????.

????
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
????? ????????
  • ???? ????? ????????
  • ???? ???????.
  • ???? ??????????? ?? ????????.
  • ???? ????????? ????? ??????.

????? ????
35
1. ???? ???????
  • ???? ???? ???? ??? ?????? ??????? ????? ????? ??
    ??????.
  • ???? ??????? ?????? ?? V ?????? ????? ??????
    ?????? ???????? ????? ??????.
  • ????? ????? ?????? ???????? , ???? ???? ? ???
    ?????? ?????? ??????? ??? ????? ???? Tensegrity
    ????.
  • ???? ????? ????? ??????? ?? ????? ?????? ?????.
    ???? ???? Tensegrity ????????? ??? ????? ???????
    ????? ????? ?????? ???? ?"? ????? ???? ?? ??????
    ?????? ???? ??????.
  • ?????? ????? ???????? ?????? ???? ????? ?? ????
    ???? ????? ???????.

???? ??????? ???? 12 ???? ??????? ??? ?????
?????? ??? .2?j/v j ??? ??? ??? ? V. ??
?????????? ?????
???? ????? ????, lc , ????? ?? ??????, ls , ????
???? ??????? ????
36
2. ???? ??????????? ?? ????????
  • ???? ?? ????? ?? ????? ????? ????? ?? ?? ????
    Tensegrity ?????? ??????? ??????.
  • ??????? ?????? ??? ????? ?????????? ???????
    ??????.
  • ??????? ????? ??? ?? ????, ??? ????? ?? ???
    ?????? ???? ?? ??????? ???????????? ??? ???????
    ?????????.
  • ????? ???????? ??????? ??? ?????? ????
  • Minimize f(x,y,z)
  • Subject to gi(x,y,z)0 for i1,.,n
  • ??????? ????? ????? ?????,??????, ????? ?????? ??
    ??? ????????

????? ????
37
2. ???? ??????????? ?? ????????
  • ???? ?? ?????? ???? (Pellegrino)
  • ?????? ??????
  • ?? ???? ????? ????? ????? lc1 ?????? ???????.
  • ??? ??????? ????? ???? ????? ????? ?????? ????
    ?????.
  • ????? ???????? ??????? ???? ??????
  • ???? c1, c2,.,c6 ?? ???? ?????? ??????? ?????
    ?????? s1,s2,s3 ?? ????????

????? ????
38
2. ???? ??????????? ?? ????????
  • ???????
  • ????? ????? ??????? ?????? (????? Matlab).
  • ?????? ????? ?????????? ????? ???? ?????????
    ?????, ?? ??? ????? ????? ????? ??? ??????? ??
    ????????.
  • ???????
  • ???? ???????? ???? ???? ?? ?? ????? ????? ??????
    (?????? ??????? ??????).
  • ??? ??? ????? ????? ?????? ???????? ????????
    ??????.

39
3. ???? ?????????- ????? ??????
  • ????? ???????????? ??????? ?????, ???? ??????
    ????? ???????? ??????, ?????? ?????-????? ?????
    ?????? ?"? ????????? ?? ??????? ????????
  • ????
  • K ?????? ???????
  • M ?????? ????
  • D ?????? ?????? (damping)
  • f ????? ?????? ?????????
  • ?? ?????? ??????,
    ??????? ??????? ??????
  • ???? ????????????
    ????????.

????? ????
40
3. ???? ?????????- ????? ??????
  • ???????
  • ????? ????? ??????? ???? ?????? ??? ???? ?????
    ????.
  • ???????
  • ????? ??????????? ??? ???? ???? ?????? ???.
  • ???? ????? ???? ?????? ???? ????? ????? ???
    ?????? ????????, ??? ??? ????? ?? ????? ??????
    ???????? ??? ??????? ???.

????? ????
41
????? ??????
  • ?????? ??? ?????? ?? ???? ???? ???????????
    ?????????? ????? ??????? ??????? ?? ???????? ???.
  • ??? ?? ????? ??????? ??? ??????? ?????
  • ???? ???????
  • ???? ?????? ???? (force density)
  • ???? ??????? ??????
  • ???? ???????????? ????????

????? ????
42
1. ???? ???????
???? ??? ?????? ???? ??? ????? ????? ???????
???????? ?????? ???? ????? ????? ??? qij
?????? ??? ??? ????? ?????. ????? ??????
????? ????? ????? 1 ?????? z ? y ????
?????? ????? ?? ??? ??????? ??? ????? ?? ??????
?????? ??? ????? ?? ????? ??? ?? ??????
?????? ????? ????????
43
2. ???? ?????? ????
  • ????? ????? ?"????" ?????? ????? ????? ?????
    ????? ??????? ?? ????????? ??????, ?????? ??
    ??????? ????????.
  • ??????, ?????? ?????-????? ?????? x ????? ?????,
    i, ???
  • ????
  • t ???? ??????
  • l ???? ??????
  • f ????? ?????? ?????????
  • lij ??? ??????? ?? ???????????? ???? ???????
    ????? ????????.
  • ????? ????? ????? ??? qijtij/lij
  • q ???? ?????? ???? ????? ???? ????? ???? ??????
    ????? ????? ?????.

????? ??? b ??????? ? n ?????, ???????
?????-????? ?????? x ?????? ?????? ????? ???
???? Cs ?????? ??????? bxn Q ??????
???????? ?????? ?? ???????? ????. xs ?????
????? ?? ??????????? x. fx ????? ??????
????????? ??????? ?? ?????? ?????? x.
????? ????
44
2. ???? ?????? ????
????? ?????? ????? ????? ???? (self-stress) ??
???? ??? ????? ??????? ????? ???? ?????
????????. ???? ????? ?????
????? ??? b ??????? ? n ?????, ???????
?????-????? ?????? x ?????? ?????? ????? ???
???? Cs ?????? ??????? bxn Q ??????
???????? ?????? ?? ???????? ????. xs ?????
????? ?? ??????????? x. fx ????? ??????
????????? ??????? ?? ?????? ?????? x.
??????? ????? ?????? ???????? y ? z. D ????
?????? ?????? ???? ????? ????? ?????? ??? ????
??? Q ? Cs ????? ????
45
3. ???? ??????? ??????
  • ????? ???? ??? ?????? ????
  • ????
  • ?ijgt0 ??????
  • ?ijlt0 ????????

?? ????? ????? ?? ?????? ??????? ?? ??? ????
?????? ???? ???? ??? ???????? ??????? ?ij
???? ????????? ???? qij ???? ??????? ???? ????
???? ????? ?? ???? ????? ?????? ?? ????
Tensegrity, ?? ???? ???? ??? ?????? ??....
????? ????
46
3. ???? ??????? ??????
????? ????? ??????? ?????? ???? ??????? ?
???? ?????? ?? ?????? ????, ??????? ?????
???????? ??????? ?? ????????. ?????? ?? ???? ???
??????? ????? ????? ????????? ?? ??????.
??? ????? ????? dn ????? ?? ??????????? ?- x,y,z
?? p. ????? ????? ????
47
4. ???? ???????????? ????????
???? Tensegrity
???? ???????? b
m ?????
o ??????? (???????? ??? ???????
??-?????? ??????)
bmo
????? ?? ??????????? ??????? ???? ?????? ????????
?? ?????? ???????????? ?? ????????
gg1,g2,.,gNT . ???-???? N3xO
(x,y,?) ???? ???? N5xO (x,y,z,?,f)
????? ????
48
4. ???? ???????????? ????????
???? ?????? ?????? (self stress) ?????? ??????
tt1,t2,,tMT ??????-???? ?? ???????? ????????
???? ????? ????????. ????? ?? ??????? ?????-????
??? ????? ??????? ?? ????? ????? ???? ?????? ??
?????? ??????? ??????. ???? ????? ????? ?? ?????
????? dg, ?? ??? ??????? ?? ????????. ??????
????? ?? ??? j ??? ????? ?? ?????? ???? A
NXM
????? ????
49
4. ???? ???????????? ????????
  • ?????? ??????? ??? ?? ?? ?????? (???????? ??
    ????? ?? ?????) ???? tTdl(At)Tdg
  • ?????? ???? ????? ?? ???? ???? ??? ????? ?????
    dg. ????? At0
  • ???? ???? ?? ?? ????? ???? ??? ??????? ?????
  • ?????? ?? ???????? ????
    rank AltM
  • ?? ??????? ??????? ???? ???? ?????
    tjgt0 for j1,2,.,M

????? ????
50
????? ??????? ????? ????? ?????
  • ????? ???? ?? ?????? ????? 7 ????? ???????? ????
    ??????


1. ????? ????????
2. ????? ??????
??????? ??????????? ?? ???? ??????? ?? ????????
?? ???? ??????? ?? ??????, ???? ???? ???? ????
???? ????? ?????.
  • ???? ??????? ????? ?????? ?? ????????
  • ?????? ?? ?????? ?????? ???????????? ????? ??????
    ????
  • ??? ?????? ????? ?????? ?????? ????? ??
    ??????????? ?????.
  • ???? ??????????? ?? ????????
  • ???? ????????? ????? ??????

?????? ???????????? ??????-???? ???????? ??? ??
?????? ??????? ?????.
  • ???? ??????? ????? ?????? ?? ????????
  • ???? ?????? ???????????? ?????.
  • ???? ?????? ?? ????? ???????? ?? ?????? ?????????.
  • ???? ?????? ???? (force density)
  • ???? ??????? ??????
  • ???? ???????????? ????????

????? ????????????
  • ????? ???? ?? ????? ?? ????? .
  • ????? ?????????? ?????????

51
?????? ??????? ???? ???????
  • ???? ????? ????? ??????? ????
  • ??? ???? ????? ???? ??????? ????? ??? ????? ????
  • ???? Guzman
  • ?????? ???? ????? ????? ???? ?????? ?? ?????????
    ?????? ????? ???? Tensegrity, ?????? ??????????
    ????? ????? Tensegrity ??? ????? ????? ????
    ??????
  • ????? ???? ?????-????- ????? ????? ?????? ??????
  • ???????????? Hennenberg ?????? ????? Tensegrity
    ????? ??? ??? ????? ???? ????? ??????
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