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B H 0DԔ P ,$@ 0B I 6ZDԔ:,$D 0B J NDԔ?"0@NNN?N  ,$D   0Xz *> K ,$D  0`B L 0DԔ*fB M 6ZDԔ>B N NDԔ?"0@NNN?Nt,$D   0\ O 0[NM |  Joint velocity Vertex potential Link relative velocity Edge potential difference2XH Y ZaN"`c   91c  Z Z]N"`k Br  92c  [ ZXhN"` :j{  93c  \ Z0lN"` Zs  94c  ] ZpN"`K Gw  95c  ^ ZxtN"`V <  96c  _ ZHwN"`V   97c  ` Z {N"`  98c  b Z~N"`=   99c  e ZhN"`?%U 91c  g Z8N"`g 92c  h ZN"`p 99c  j ZN"`,p 93c  l ZXN"` 94c  m Z(N"`L| 95c  o ZN"`U,$  0 97c  p Z؜N"`,$ 0 96c  q Z+B#style.visibility<*D%(D' =%(DM' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<*H%(D' =-6B-randombar(horizontal)*<3<*HD' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*I%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*K%(D' =%(tD7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*J%(D' =-s6Bwipe(down)*<3<*JD' =%(hD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*o%(D' =%(\D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*N%(D' =-s6Bwipe(down)*<3<*ND' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*p%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*q%(++0+oN ++0+pN ++0+qN +A  77LL7(  "  s 0e0e    BC DEXF( @   8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E|| W(t3n@7 M z.G` @       "B` Rcw=F qR  "m~bB  c $Ԕ?"\2  C Y?#" `qR^R @ 6 3 ^R  6  ! ^R  6oQZB  c $3fԔ?" ZB  c $3fԔ?"8 : ZB  c $3fԔ?"+  ZB  c $3fԔ?"  ZB  c $3fԔ?"  ZB  c $3fԔ?"  ZB  c $Ԕ?"WZ2  S Ԕ?#" `SZ2  S Ԕ?#" `KF 9 I  }$  3 BLCDE4FԔ j5#LD<yV $` @    c"$` 9 I\2  C Y?#" `VF jJf  fbB B c $Ԕ?"J=\2  C Y?#" `jfF  7  bB  c $Ԕ?"D7\2  C Y?#" ` }>F gqp  2Ty1  s 0e0e    BC DELF$ @  Ԕ 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||_#@:ry@hD1Y @      "B` *\2  C Y?#" `?pb2  S Y?#" `gqZB  c $3fԔ?" T2  S ?" t T2 ! S ?" * ZB " c $3fԔ?"MT2 # S ?"`T2 $ S ?" U NB % C ?"< u B2 & # ?" s B2 ' # ?" 7r TB ( S 1?"  T2 ) S ?"  T2 * S ?"  T2 + S ?"! T2 , S ?"# Y T2 - S ?"e-a^R . 6?J` / s *"`%` 0 s *"`y ( E f 1 0Z"`Klf` 2 s *"` ) x 3 c $N  N F   4  bB 5 c $3fԔ?" \2 6 S ?"] \2 7 S ?"  B 8 NDԔ?"0@NNN?Nt 9 TN"`c   91c  : TN"`k Br  92c  ; TxN"` :j{  93c  < TN"` Zs  94c  = T0N"`K Gw  95c  > TN"`V <  96c  ? 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ZB  c $Ԕ?"l  ZB  c $Ԕ?" &  ZB  c $Ԕ?"l   ZB  c $Ԕ?"r  ZB  c $Ԕ?"l l ZB  c $Ԕ?"r  f  0A?"+ q F    B NC NEF1?(MMM(@`c"$` V &  6Pl A $G4  #   c BCDEFԔ 'r9jB@  c"$` M bZB  c $Ԕ?"%"F eH   eHbB  c $Ԕ?"e#b2   S Ԕ?#" `HZB ! c $Ԕ?"eZB " c $Ԕ?"F l #  l2 $ BUENG7I(QԔ? ȬUU`TȬUU`T(`TU`T(`T#" `lb2 % S Ԕ?#" `l"F ' &  'bB ' c $Ԕ?"'b2 (  S Ԕ?#" `j^"F   )   bB * c $Ԕ?" cb2 +  S Ԕ?#" `8F   ,   bB - c $Ԕ?" n2 .  s *Ԕ?#" ` U(b2 /  S Ԕ?#" `TB 0 S ?"Y $  T2 1 S 8c?"U r T2 2 S 8c?"Y v TB 3 S Ԕ?"j Q  F  p 4   pn 5  0A?"Up 6   B NC NEF1?(MMM(@`c"$`< &\2 7  C g ?#" `+R\2 8  C g ?#" `E+jR\2 9  S 8c?"u  T2 : S 8c?"  $ T2 ; S 8c?"   < < P< HStatic Structurecz # y c >   3  ,$D 0B ? TLD3fԔ?"0@NNN?Ny  B @ NDԔ?"0@NNN?N# >c A 0DPC I  TRod internal force Flow through the edge2+B B 6D3fԔf 3 O ,$@ 0F  W| C  ?0  D  TP"`V,$- 0 91c  E  TP"`R,$' 0 92c  F  TP"`! ,$! 0 99c  G  TXP"` I},$ 0 93c  H  TP"`,$ 0 94c  I  T|P"`  ,$= 0 95c  J  T$P"` ,$3 0 97c  K  TP"`{,$ 0 96c  L  TP"`!RQ,$7 0 98c  M  TS"` F  91c  N  TDS"`   92c  O  TS"`S O  99c  P  T S"`g   =3  c  Q  T S"`   94c  R  TS"` FH  95c  S  T0S"`   97c  T  T S"` y  96c  U  TS"`' W| 98c  [ Bx S  `}  S   tԨ\y޽h& ?Ԩ!@\"`/ % $  ̙33`X___PPT108+iMD' = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(DG' =4@BBBB%()@@D' =1:Bvisible*o3>+B#style.visibility<*> %(D' =-s6Bcircle(in)*<3<*> D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*B %(D+' =4@BBBB%()?)?D' =.G7 BBBBBYM 2.77778E-7 2.71676E-6 L 0.07292 -0.43838 *3>*B ppt_xB ppt_y=@0BBAApBBUU=Bs`<*B +:P  5@-@mmK?(   F  p   !xn  0A?"Up   B NC NEF1?(MMM(@`c"$`< &\2  C g ?#" `+R\2  C g ?#" `E+jR\2  S 8c?"u  TB  S Ԕ?"s Z 4F  b     b   bB  c $̙Ԕ?"  bB  c $̙Ԕ?"b  bB  c $̙Ԕ?"&  bB  c $̙Ԕ?" b  bB  c $̙Ԕ?"h  bB  c $̙Ԕ?"b b bB  c $̙Ԕ?"h  ZB  c $Ԕ?"  ZB  c $Ԕ?"l  ZB  c $Ԕ?" &  ZB  c $Ԕ?"l   ZB  c $Ԕ?"r  ZB  c $Ԕ?"l l ZB  c $Ԕ?"r  f  0A?"+ q F    B NC NEF1?(MMM(@`c"$` V &  6<0Sl A $G4  #   c BCDEFԔ 'r9jB@  c"$` M bZB  c $Ԕ?"%"F eH  eHbB  c $Ԕ?"e#b2   S Ԕ?#" `HZB ! c $Ԕ?"eZB " c $Ԕ?"F l # l2 $ BUENG7I(QԔ? ȬUU`TȬUU`T(`TU`T(`T#" `lb2 % S Ԕ?#" `l"F ' & 'bB ' c $Ԕ?"'b2 ( S Ԕ?#" `j^"F   )  bB * c $Ԕ?" cb2 + S Ԕ?#" `8F   ,  bB - c $Ԕ?" n2 . s *Ԕ?#" ` U(b2 / S Ԕ?#" `TB 0 S ?"Y $  T2 1 S 8c?"U r T2 2 S 8c?"Y v TB 3 S Ԕ?"j Q  F  p 4  pn 5 0A?"Up 6  B NC NEF1?(MMM(@`c"$`< &\2 7 C g ?#" `+R\2 8 C g ?#" `E+jR\2 9 S 8c?"u  T2 : S 8c?"  $ T2 ; S 8c?"   < <>S< HStatic StructurecF # y c =  3  B > TLD3fԔ?"0@NNN?Ny  B ? NDԔ?"0@NNN?N# >c^B @ 6D3fԔf 3 O F  W| A ?0  B TDS"`V 91c  C TGS"`R 92c  D T0KS"`!  99c  E TS"` I} 93c  F TPS"` 94c  G T@TS"`   95c  H TWS"`  97c  I TZS"`{ 96c  J T@S"`!RQ 98c  K T`S"` F  91c  L TeS"`   92c  M TcS"`S O  99c  N TkS"`g   =3  c  O TLdS"`   94c  P TdsS"` FH  95c  Q TvS"`   97c  R TqS"` y  96c  S T|S"`' W| 98c  T c `S0e0e #" 0e `}  S 2 U S 8c?"  ,$@ 0tz    V  # ,$@ 0\2 W S 8c?"  B X # BCDEdF. F#e)V&.KK4KBi6 (Qe}1@        `"`  `B Y 0DԔ  B Z NDԔ?"0@NNN?ND  B [B NDԔ?"0@NNN?N R B \ NDԔ?"0@NNN?N  B ] NDԔ?"0@NNN?N  B ^B NDԔ?"0@NNN?N Q B _ NDԔ?"0@NNN?NA  `B ` 0DԔ  2 a S 8c?",$@ 0tz    b ,$D 0\2 c S 8c?"  B d # BCDEdF. 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T y.=/ Ka#  p  La d@ABCEFg K@`C".o/bB Ma 3 g y.=/<2 Na # g .;/T y.=/ Oa# K Pa d@ABCEFg K@`C".o/bB Qa 3 g y.=/<2 Ra # g .;/T y.=/ Sa#  S  Ta d@ABCEFg K@`C".o/bB Ua 3 g y.=/<2 Va # g .;/<2 Wa # g D k T y.=/ Xa# k '  Ya d@ABCEFg K@`C".o/bB Za 3 g y.=/<2 [a # g .;/<B \aB # g nJ<B ]a # g  R <B ^a # g ) <B _a # g @ A <B `a # g j<2 aa # g , S <2 ba # g  " J<2 ca # g 0<2 da # g s" <2 ea # g D k <2 fa # g `0 ga @ABCDE(Fg  9d@mKn@ i J ^ ha 6__B ia c $D  ,$D   0 ja 0\ v ,$  0 e3Due to links 1 and 9 being located on the same line4 24x ka c $t\@l  \ H ` 0޽h ?/  `` 33___PPT10.Q@+-3Dj' = @B D%' = @BA?%,( < +O%,( < +D' =%(D' =%(DG' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<* `%(D' =-6B'blinds(horizontal)*<3<* `D' =%(D' =%(D1' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*`%(D' =-m6Bbox(in)*<3<*`D1' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*Aa%(D' =-m6Bbox(in)*<3<*AaD ' =%(D' =%(D)' =4@BBBB%()?)?D}' =.E7 BBBBBWM -3.33333E-6 1.84971E-6 L 0.01268 0.4037 *3>*B ppt_xB ppt_y=@0BBAApBB;BN><*`D)' =4@BBBB%()?)?D}' =.E7 BBBBBWM 2.77778E-6 1.21387E-6 L 0.00937 0.42058 *3>*B ppt_xB ppt_y=@0BBAApBB;B7W><*AaD ' =%(DP ' =%(D)' =4@BB BB%(D' =-g6B fade*<3<*AaD' =1:Bhidden*o3>+B#style.visibility<*Aa%(D)' =4@BB BB%(D' =-g6B fade*<3<*`D' =1:Bhidden*o3>+B#style.visibility<*`%(DG' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<*`%(D' =-6B'blinds(horizontal)*<3<*`DG' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<*c`%(D' =-6B'blinds(horizontal)*<3<*c`D' =%(D' =%(DG' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<*`%(D' =-6B'blinds(horizontal)*<3<*`Dz' =%(D"' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*ja%(D1' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*ia%(D' =-m6Bbox(in)*<3<*ia+8+0+ja\ +<@  h(    Hl\ 5 `  \   T\3fԔ?"6@`NNN?N>y : B @ TD3fԔ?"0@NNN?N  lB  TD3fԔ?"0@NNN?N5~B  TD3fԔ?"0@NNN?NL5~LB  TD3fԔ?"0@NNN?N 5~ B  TD3fԔ?"0@NNN?N 5~ B  TD3fԔ?"0@NNN?Nq5~q  H\ 3fԔ?"6@ NNN?N  BLinkages (2 $  H\ 3fԔ?"6@ NNN?N  G Plane Trusses(2$~  HL\ 3fԔ?"6@ NNN?N_ @,$D 0 2Potential difference = = Linear relative velocityF3(fN  H\ 3fԔ?"6@ NNN?Nv #0,$ 0 dFlow = = Force:(f  H\ 3fԔ?"6@ NNN?NL_ ,$ 0 :Sum of potential differences at any circuit equals to zeroH;(f3f  H\ 3fԔ?"6@ NNN?N4b  ,$ 0 )Sum of flows at any cutset equals to zeroH*(f3fL  H8\ 3fԔ?"6@ NNN?N( _ " ,$  0 b Flow = Force: (33c  H\ 3fԔ?"6@ NNN?N . ,$ 0 y#Potential Difference = Displacement:$(3 3  H\ 3fԔ?"6@ NNN?N _ -,$  0 )Sum of flows at any cutset equals to zeroH*(3  H\ 3fԔ?"6@ NNN?N j -,$ 0 :Sum of potential differences at any circuit equals to zeroH;(3B  TD3fԔ?"0@NNN?N{5~{  H\ 3fԔ?"6@ NNN?N_ r LKinematical Analysis(  H\\ 3fԔ?"6@ NNN?N r cStatical Analysis( 6  H\ 3fԔ?"6@ NNN?N  ,$ 0 LDeformation Analysis(B  TD3fԔ?"0@NNN?N 5~ =  H4\ 3fԔ?"6@ NNN?N > ,$  0 SSingular position detection(H  0޽h ? 33f3 %%___PPT10$.g@}+lAD"' = @B D{"' = @BA?%,( < +O%,( < +D' =%(D' =%(DM' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<* 3%(D' =-6B-randombar(horizontal)*<3<* 3D ' =%(D' =%(DZ' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-6B-randombar(horizontal)*<3<* D ' =%(D' =%(DZ' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B-randombar(horizontal)*<3<*D ' =%(D' =%(DZ' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B-randombar(horizontal)*<3<*D ' =%(D' =%(DZ' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B-randombar(horizontal)*<3<*D ' =%(D' =%(DZ' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B-randombar(horizontal)*<3<*D ' =%(D' =%(DZ' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B-randombar(horizontal)*<3<*D ' =%(D' =%(DZ' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B-randombar(horizontal)*<3<*D ' =%(D' =%(DZ' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B-randombar(horizontal)*<3<*D' =%(D' =%(Dm' =A@BB#BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-g6B fade*<3<*D' =+4 8?HCB4DBCBB*k3>'Bstyle.rotation<*D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*++0+ \ ++0+\ ++0+\ ++0+\ ++0+\ ++0+\ ++0+\ ++0+\ ++0+\ +  ~~`"~(  z "   jz,$D  0ZB  s *Do ` H ZB  s *Doh M y ZB  s *DoM w l   # BCDEFo@"`d j   # B;CeDEFo;e@"`& m   # B+CnDEFo+n@"` t M f   N ^8c@"@ ( R  K1. 2G33  N ^8c@"@N R  K2. 2G33  N^8c@"@, R x $  K3. 2G33  N^8c@"@ 2 B  K4. 2G33  N^8c@"@N  K5. 2G33  N^8c@"@h ` 2  K6. 2G33ZB B s *Do) g 2  Z3vd @31@" `C `B  0D1@ "   3 B;CeDEF1;e@"` + `B  0D1 #M Z  j  3  * s 8  Z3vd @31@" `U  2  Z3vd @31@" `z ] n  03d1@" ` j Z  j   3 h     Z3vd @31@" `U  2   Z3vd @31@" `z ] n   03d1@" ` j Z  j   3 `    Z3vd @31@" `U  2  Z3vd @31@" `z ] n  03d1@" ` j   N&^8c@"@8 " K7. 2G332  Z3vd @31@" ` T k 2  Z3vd @31@" ` C 2  Z3vd @31@" `@    h0e0e    BCODE(F @ 3 5% 8c8c     ?A)BCD|E|| cTPO0.8 @   # "0e@  `    @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab o z ` b Ș  6 &,$@ 0ZB ɘ s *Do,  ZB ʘ s *Dog  ZB ˘ s *Do -  ̘ s BVCuDEFo@Vu@3"`  ͘ s BVCuDEFo@Vu@3"`  Θ s BVCuDEFo@Vu@3"`n v ϘB s BVCuDEFo@Vu@3"`   И s BVCuDEFo@Vu@3"`  G  јB s BVCuDEFo@Vu@3"`  Ҙ H(/^Ҙ8c@Dd  VA'8 2CC Ә H04^Ә8c@g <  VB'8 2CC Ԙ H89^Ԙ8c@ _  VC'8 2CCZ  j  ՘3 `, : ֘ Hvd @1@" `U  2 ט Hvd @1@" `z ] n ؘ 0d1@" ` j Z  j  ٘3 T#b ژ Hvd @1@" `U  2 ۘ Hvd @1@" `z ] n ܘ 0d1@" ` j Z  j  ݘ3 ( d r  ޘ Hvd @1@" `U  2 ߘ Hvd @1@" `z ] n  0d1@" ` j zN @   0p T  c $X99?T @ T    # CT    6A^ &  MA0(2G33  64F^   j6(2g3g3  6G^Q  Kr.(2G33xN N    N v T  c $X99?N  T    #  Z   6O^ &  KB.(233  6T^   j6(2g3g3  6R^   Kr.(2G33xN      T  c $X99?  T    #    6]^ &  KC.(233  6W^   j6(2g3g3  6(`^! 8  Kr.(2G33F 0 M   2X   H4j^MrMr38c@"`E[ K4. 2G 33  <m^MrMr38c"`S0 K2. 2G 33  <\q^MrMr38c"`s b  K6. 2G 33  C B5CDEF3o@5@3"`  C BVCuDEF3o@Vu@3"`  ]  3 BCGDEF3o@G@3"`xG  C BC)DEF3o@)@3"`G  C BCDEF3o@@3"`CJ  C BCDEF3o@@3"`y~ 2  Nvd @31@" `g2  Nvd @31@" `j 2  Nvd @31@" `1g(  Hw^MrMr38c@"`5  K1. 2G 33  C BVCuDEF3o@Vu@3"` WQ 2  Nvd @31@" ` A vT  j  #  t -  Tvd @31@" `U  2  Z3vd @31@" `z ] t  63d31@" ` j T  j  # M  Z3vd @31@" `U  2  Z3vd @31@" `z ] t  63d31@" ` j T  j  #   Z3vd @31@" `U  2 ˜ Z3vd @31@" `z ] t Ø 63d31@" ` j | Ę  X0e0e    BQCDEF @ 3 o 8c8c     ?A)BCD|E||QT5H q#q@  # "0e@  `    @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab }  Ř H^MrMrŘ38c@"`d] K3. 2G 33 Ƙ H^MrMrƘ38c@"`aS K5. 2G 33 ǘ <ԇ^MrMrǘ38c"`.   K7. 2G 33F `~   ' = 'N ,. 3   0~ I   H^8c@ EA( 2C,  H^8c@ EB( 2C  H(^8c@W ,v  EC( 2C  H@^8c@5 C1& 2C,  <4^8c4 C3& 2C  <^8c5/  C2& 2C  <8^8cx C4& 2C  <^8c  R 54 2C C  6 ^8c   C6& 2C  6^8c   C7& 2C  C B5CDEFo@5@3"`   C BVCuDEFo@Vu@3"`  I  3 BCGDEFo@G@3"`F  C BC)DEFo@)@3"`F   C BCDEFo@@3"`AJ3 lB  <D1@ .   C BCDEFo@@3"` 2  Bvd @1@" `v32  Bvd @1@" `*n2  Hvd @1@" `  Z  j  3 `J X  Hvd @1@" `U  2  Hvd @1@" `z ] n  0d1@" ` j Z  j  3 r#  Hvd @1@" `U  2  Hvd @1@" `z ] n  0d1@" ` j Z  j  3 (   Hvd @1@" `U  2  Hvd @1@" `z ] n  0d1@" ` j   6^l A $G4  # 2 H T<^q1?"6@`NNN?NW   @ Deformations  2 I T^q1?"6@`NNN?N0  h  :Forces   0e0e    BNCDEF N 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||Nwm5@  "0e@`     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abqK*,$D 0>  N^Ԕ?"0@NNN?N ,$  0 TMechanism in singular position  B(^ ')i  ^ l  o   o,$D 0   Z^Ԕ?"0@NNN?N  ?2"g   Z<^Ԕ?"0@NNN?N =   ?1"g   Z^Ԕ?"0@NNN?N   ?5"g   Z ^Ԕ?"0@NNN?N@ o  ?6"g   ZT^Ԕ?"0@NNN?N I  ?4"g   Z^Ԕ?"0@NNN?NU p)  ?3"g  tԨ\y޽h& ?Ԩ!@\"` ̙33xp___PPT10P+ D' = @B DG' = @BA?%,( < +O%,( < +D' =%(D' =%(D<' =A@BBBB0B%()?)?D' =.K7 BBBBB]M -3.33333E-6 -1.05653E-6 L 0.00278 -0.35982 *3>*B ppt_xB ppt_y=@0BBAApBBa :B5Y8<*HD' =%(D@' =%(D)' =4@BB BB%(D' =-g6B fade*<3<*D' =1:Bhidden*o3>+B#style.visibility<*%(D+' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*Ș%(D' =-g6B fade*<3<*ȘD' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =%(D' =%(DD' =A@BBBB0B%()?)?D' =.S7 BBBBBeM -3.88889E-6 -4.63392E-7 L -3.88889E-6 -0.34221 *3>*B ppt_xB ppt_y=@0BBAApBBB-U/<*ID' =%(D' =%(D9' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-u6Bwipe(right)*<3<*D' =%(D' =%(D)' =4@BB BB%(D' =-g6B fade*<3<*D' =1:Bhidden*o3>+B#style.visibility<*%(D+' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-g6B fade*<3<*D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(++0+H^ ++0+I^ ++0+^ +,<  BBh (  hf h 0A?"+ q F  h  B NC NEF1?(MMM(@`c"$` V &ZB h c $Ԕ?"  ZB h c $Ԕ?"b  ZB h c $Ԕ?" &  ZB h c $Ԕ?"b   ZB h c $Ԕ?"h  ZB  h c $Ԕ?"b b ZB  h c $Ԕ?"h    h 6D^l A $G4  h # TB  h S ?"Y $  T2 h S 8c?"U r T2 h S 8c?"Y v f h 0A?"UpTB h S Ԕ?"j Q   h  B NC NEF1?(MMM(@`c"$` <&T2 h C g ?#" `+RT2 h C g ?#" `+EjRT2 h S 8c?" u T2 h S 8c?"  $ T2 h S 8c?"  ^R h@ 6 + ^R h 6  ^R h 6lIZB h c $Ԕ?" ZB h c $Ԕ?"5 7 ZB h c $Ԕ?"(  ZB h c $Ԕ?"  ZB h c $Ԕ?"  ZB  h c $Ԕ?"  ZB !h c $Ԕ?" T2 "h S ?" l T2 #h S ?" ' ZB $h c $Ԕ?"ET2 %h S ?" R NB &h C ?"9 r B2 'h # ?" k B2 (h # ?" /j TB )h S 1?"  F   *h   bB +h c $Ԕ?" \2 ,h S ?"] \2 -h S ?"  T2 .h S ?"  T2 /h S ?" T2 0h S ?" V T2 1h S ?"b%Y^R 2h 6<B` 3h s *"`"` 4h s *"`v  B f 5h 0Z"`Hdc` 6h s *"` !  7h < `!  KKinematical Linkagec 8h <$`< HStatic Structurec 9h B`  `}  ` z   :h  ,$D 0bB ;h c $Ԕ?" \2 h 0D3fԔ F ,$@ 0B ?h 6ZD3fԔ~w0,$@ 0B @h 6ZD3fԔ~v0,$D 0) Ah N`3fԔ?"0@NNN?Nd t ,$  0 ??"g 3fB Bh 0D3fԔ F ,$@ 0 h tԨ\y޽h& ?Ԩ!@\"`/ 'h(h ̙33___PPT10+ȓĿD' = @B Dv' = @BA?%,( < +O%,( < +D' =%(%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*:h%(D' =%(D+' =4@BBBB%()?)?D' =.G7 BBBBBYM -1.38889E-6 2.89151E-7 L 0.00452 0.03308 *3>*B ppt_xB ppt_y=@0BBAApBB?;B*<<*:hD9' =4@BBBB%(D' =/u8AC*Q3> Br<*:hDR' =%(DM' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<*>h%(D' =-6B-randombar(horizontal)*<3<*>hDM' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<*?h%(D' =-6B-randombar(horizontal)*<3<*?hD' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*Bh%(D' =4@BBBB%())))?D' =1:Bvisible*o3>+B#style.visibility<*@h%(Dn' =%(D' =4@BBBB%()?)?Dj' =.27 BBBBBgM -2.77778E-7 2.22222E-6 C 0.00938 -0.00949 0.01875 -0.01898 0.04896 -0.00833 C 0.07917 0.00231 0.11598 0.05092 0.18125 0.06389 C 0.24653 0.07685 0.34358 0.07315 0.44063 0.06944 *3>*B ppt_xB ppt_y=0BB aaaA<*>hD' =%( D)' =4@BB BB%(D' =-g6B fade*<3<*>hD' =1:Bhidden*o3>+B#style.visibility<*>h%(D8' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*Ah%(D' =-g6B fade*<3<*AhDF' =%(D=' =A@BBBB0B%(D' =0l9 CCBB*<3<*AhD' =A@BBBB0B%(D' =,54*3>!Bstyle.color='`B@BPB<*AhD' =%(DF' =A@BBBB0B%(D' =/u8CC*Q3> Br<*Ah++0+Ah` ++0+Ah` ++0+Ah` ++0+Ah` + 0C(CYYlB(  lJ l C "A copy: B l 0DԔz*,$D 0B l 0DԔ ,$D  0B l 0DԔ Z b,$D 0B l 0DԔ 6 ,$D 0B l 0DԔ",$D 0B l 0DԔ&,$D 0B  l 0DԔ 4,$D 0  l  HBC DEFB8c((}<6J } }}#UpB{8 fU  ~ #f  c w PL -t  8 y bzK} @             `3"` r ,$D  0B  l 0DԔ*<  ,$D 0B  l 0DԔk,$D  0B  l 0DԔz ,$D 0B l 0DԔ R ,$D 0B l 0D3fԔl ,$D 0B l 0DԔ :,$D 0B l 0DԔP ,$D 0B l 0DԔx,$D  0\  l  0e0e    B*CDEpF0 @  8c 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||_:$z3,0g8@m  K  " )068:8*OUh2@         s " 0e@        @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abd"8,$D  0B l BD1?"0@NNN?Nzz,$D2  0B l BD1?"0@NNN?N,$@1  0B l 0DԔR$ $,$D 0B l 0DԔ $,$D 0B l 0DԔ| N $,$D  0B l 0DԔd ,$D 0B l 0DԔ^,$D4  0B l 0DԔ/,$@3  0B l 0DԔ  ,$D/ 0B l 0DԔL Pp ,$D. 0B l 0DԔ F ,$D- 0B l 0DԔ l ,$D, 0B  l 0DԔ> b ,$D+ 0B !l 0DԔZ @~ ,$D* 0B "l 0DԔ,$D( 0B #l 0DԔp J,$D) 0B $l 0DԔ&J,$D' 0B %l 0DԔl.,$D& 0B &l 0DԔ6t>,$D% 0B 'l 0DԔP V ,$D  0B (l 0DԔ& < ,$D 0B )l 0DԔZ $ ~  ,$D 0B *l 0DԔ  T ,$D 0B +l 0DԔt ,$D 0B ,l 0DԔ>"|,$D 0B -l 0DԔJ,$D 0B .l 0DԔ$6,$D 0B /l 0DԔx z ,$D 0B 0l 0DԔ : ,$D! 0B 1l 0DԔ vp ,$D" 0B 2l 0DԔ 6 ,$D# 0B 3l 0DԔL  ,$D$ 0z   4l  ,$D0 0B 5lB HD8c?"0@NNN?N*tB 6lB HD8c?"0@NNN?N` B 7lB HD8c?"0@NNN?N 4 B 8lB HD8c?"0@NNN?N  B 9lB HD8c?"0@NNN?N B :l HD8c?"0@NNN?NN Z B ;l HD8c?"0@NNN?N B l HD8c?"0@NNN?N*B ?l HD8c?"0@NNN?N N B @l HD8c?"0@NNN?Nv & B Al HD8c?"0@NNN?Nn4 ^ B Bl HD8c?"0@NNN?NR  B Cl HD8c?"0@NNN?N  B Dl HD8c?"0@NNN?N$ 4 p B El HD8c?"0@NNN?NJ B Fl HD8c?"0@NNN?N  B Gl HD8c?"0@NNN?NX  B B Hl HD8c?"0@NNN?N XB B Il HD8c?"0@NNN?N  B Jl HD8c?"0@NNN?N>  \B Kl HD8c?"0@NNN?N `4B Ll HD8c?"0@NNN?N2 Ml 68c?"6@`NNN?N.R,$D5 0B Nl BD3338c?"0@NNN?N,$@6  0B Ol BD3338c?"0@NNN?N ,$D7  0B Pl 0DԔ,$D 0fz    Ql   ,$D8 06 Rl  A ~ 2 Sl 68c?"6@`NNN?N  b r$2( Tl #" 8 8`B Ul 0DԔ$(`B Vl 0DԔ$2(B WlB HD8c?"0@NNN?N-r$fr$" Xl 6S` G Face force  a variable associated with each face of the structuresDD f Yl NdW` fԔ?"6@`NNN?N |,$D9 0 The internal force in the element of the structure is equal to the vector difference between the face forces of the faces adjacent to it.wH l 0޽h ? 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HD8c?"0@NNN?N N B @ HD8c?"0@NNN?Nv & B A HD8c?"0@NNN?Nn4 ^ B B HD8c?"0@NNN?NR  B C HD8c?"0@NNN?N  B D HD8c?"0@NNN?N$ 4 p B E HD8c?"0@NNN?NJ B F HD8c?"0@NNN?N  B G HD8c?"0@NNN?NX  B B H HD8c?"0@NNN?N XB B I HD8c?"0@NNN?N  B J HD8c?"0@NNN?N>  \B K HD8c?"0@NNN?N `4B L HD8c?"0@NNN?NXB P 0DԔ" X 6H` G Face force  a variable associated with each face of the structuresDD f Z 6`  G RFace forces can be considered a multidimensional generalization of mesh currents. 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( 2F0  0i ?4$ For more information contact Dr. Offer Shai Department of Mechanics, Materials and Systems Faculty of Engineering Tel-Aviv University This and additional material can be found at: http://www.eng.tau.ac.il/~shai \P3l3. ff3B 0H  0޽h ? 33___PPT10i.= l+D=' = @B ++xKhAlMjj K@ŶA6*]۔FnFk(ԋ7ED"?gA&"63knb /f}'o^G<\p4)1DFEbiWp,d. ܦ0/+a!wޒZ9 a;):#Htd+2I` ΃'O==Hꂧ]"DB)H=s^ς"_njuJ_m?C:[RG;켢)`?#kmCުS\K48u58j}v-5`-͈u 0lv-P'Q;S/r/s@Vr Z(Pdک@: c@Z2 T . 3.8 'i <  R "Yme 0Oh+'0 U `h  0 < HT\aTransforming knowledge from various engineering fields to statics through graph representations s Daniel Rubinkno Daniel Rubinkno24iMicrosoft PowerPointe f@_@ @/GSg  )'    """)))UUUMMMBBB999|PP3f333f3333f3ffffff3f̙3ff333f333333333f33333333f33f3ff3f3f3f3333f33̙33333f333333f3333f3ffffff3f33ff3f3f3f3fff3ffffffffff3ffff̙fff3fffff3fff333f3f3ff3ff33f̙̙3̙ff̙̙̙3f̙3f333f3333f3ffffff3f̙3f3f3f333f3333f3ffffff3f̙3f3ffffffffff!___www4'A x(xKʦ """)))UUUMMMBBB999|PP3f3333f333ff3fffff3f3f̙f3333f3333333333f3333333f3f33ff3f3f3f3333f3333333f3̙33333f333ff3ffffff3f33f3ff3f3f3ffff3fffffffff3fffffff3f̙ffff3ff333f3ff33fff33f3ff̙3f3f3333f333ff3fffff̙̙3̙f̙̙̙3f̙3f3f3333f333ff3fffff3f3f̙3ffffffffff!___wwwի۫իի֫֫իիիիЫիի֫ի֫իիիիի֫֫֫֫֫֫իիܫիի֫֫֫֫֫֫֫իЫիիիի櫫֫֫֫ի֫֫ի֫ի֫ի֫իЫի֫֫۫իիիݫ֫իܫ׫ܫ֫ܫݫ֫ܫݫܫ֫֫֫իի۫֫ի֫櫫֫ի֫ի櫫Ϋԫݫݫ׫ݫݫ֫ܫܫ֫ܫ֫֫֫֫ܫ֫֫֫֫֫իիի櫫իիի櫫櫫ݫܫ׫֫׫ܫ֫֫֫֫իիի櫫իܫ֫֫ݫ֫֫֫۫֫ի֫֫իիի֫֫իիիի֫ݫ֫ݫ֫֫֫֫ܫܫ֫֫֫֫֫իի֫իի֫ݫܫ֫֫֫֫֫իիիիիέέέϭέέέέϳέέέέέέέέέέέέέέϭέέέέϳέέέέέέԭγέԭέέ歭ϭԭέέϭέγέέέϭέέέέԭέέέԭγέԭέέ歭ϭԭέέϭέγέέέέέέϭέδյִմմϭεյ溴ճմִխռմֵ歭дյԴ歭ϭԴճֵմյճέέ歭έέγέέέέέέέέέδֳִִܻխֵմյִܵյִέϻռ⼭ֵδܵջֳϳδմִִճϺִܴܵέέέέέռֵۼܵջֵܻϵܴջջկݻ歭έջϭδֵֻϴֺմԯܵۻδεγܵάέέܵ歴ִԴֳܻխֳۻֳֵ۵ܵմϴյյ泴۵ֵϭյܵϻִִֵֺֻܴܻմέȭϴϭ洴ϭϴϭϴϴέϴϳ歭ܼ׻歭洴ϭϴϭԴϳϴϴϭݼܭϻܼݼܼϧNjNjǧܼݺݻNjNjǧǭNjǬ޼ܭǭNjǬǭNjNjdžNjܼNjǭNjNjdžNjdžǧNjdžǬǧNjǧֵNjdžǧNjdžǬǧNjNjdžǧNJdžNjǦNjNjNjdžǦNjNjϼ֬džNjdžǧNJdžNjǦdžNjNjdžǦdžǦdžNjǦǧdždždžǧµdždždžǦdžNjǦǧdždždžNjdždžNJǧNJNjǧdždžNjNj׼ϋǧNjdždžNJǧNJNjǧdždžNjǦdžǬNJdžǦǦǦNJdžNjNJdždždžǦdžǬNJdžǦǦǦNJǦdždždždždžφdždždždždždždždždždždžNJdždžǧǦǦdžǧǦdždždžǦǦǦǦdždždžNJdždžǧǦǦdžǧǦdždždžǦdždžǧdždždždždžǦǦdždždžNjdždždždžǧdždždždždžǦǦdžǦNjǦdždždžNjNJdždždžǦdždždždždždžNJǦNjǦdždždžNjNJdždždžǦdždždždždžǦdždžǦǦdžǦǬdžNjdždžǦdždžǦǦdž՜.+,D՜.+,      6 On-screen ShowTel-Aviv University { 'ArialTimes New Roman Wingdings MT ExtraBatangArial Unicode MSעיצוב ברירת מחדלMicrosoft Equation 3.0Slide 1Outline of the Talk AConstructing the graph corresponding to the kinematical linkage AConstructing the graph corresponding to the kinematical linkage AConstructing the graph corresponding to the kinematical linkage AConstructing the graph corresponding to the kinematical linkage [The variables associated with the graph correspond to the physical variables of the systemQThe potential differences in the graph representations satisfy the potential law9Now, consider a plane truss and its graph representation9Now, consider a plane truss and its graph representation,The flows in the graph satisfy the flow lawConstructing the dual graphConstructing the dual graphDConsequently there is a duality between linkages and plane trussesThe relative velocity of each link of the linkage is equal to the internal force in the corresponding rod of its dual plane truss.iThe equilibrium of forces in the truss = = compatibility of the relative velocities in the dual linkage-Checking system rigidity through the duality4Using duality relation to detect singular positions4Using duality relation to detect singular positionsaDeriving a new entity – face force == dual to the absolute linear velocity in the dual linkage Slide 21 Slide 22PIt was proved that face forces manifest some properties of electric potentials. Slide 24SMaxwell Diagram lines in the diagram are associated with the rods of the structure{The coordinates of the points in the Maxwell diagram correspond to the face forces in the corresponding faces of the truss<Verifying truss-linkage duality through the work of Maxwell<Verifying truss-linkage duality through the work of Maxwell<Verifying truss-linkage duality through the work of Maxwell@Further research – form finding problem in tensegrity systems Slide 31  Fonts UsedDesign TemplateEmbedded OLE Servers Slide Titles 8@ _PID_HLINKSAxhttp://www.eng.tau.ac.il/~shai$_ Daniel RubinDaniel Rubin  !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&5Root EntrydO)PicturesSGCurrent UserSummaryInformation(