Proiect Mecs Predat
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Transcript of Proiect Mecs Predat
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Corp Cupla Punct Restricţii
1-2 T D 22-3 RR BC 1
1-3 R A 2
2-4 RR EF 1
1-4 R G 2
Calculul mobilităţii:M=3(n-1)-Σr=3(4-1)-8=1
Unde:
M-mobilitatea M=1
S-spaţialitatea S =
n!-n"m#$"l de !o$p"$i n!=%
Din &apt"l !# '$ =( $e)"lt# !# *om a*ea ( e!"aţii !" ( ne!"nos!"te
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Cinematica corpurilor
• Co$p 1-Ba)a
• Co$p 2:
2+2+2, ϕ Y
( e!"aţii de $est$i!ţii eomet$i!e
• Co$p :
++, ϕ Y 1 e!"aţie de $est$i!ţie !inemati!
• Co$p %:
%+%+%, ϕ Y
s1-*.t/=+
• Cop$ 1 - ba)a = !o$p & 10
• M1 1 p"n!t ale ida3"l"i de int$a$e
Defnim punctele
4"n!t .n/ /1.1n
Χ/1.
1n Υ
A1D1G1 + +
M1 +
1 +
Co$p 2
De&inim p"n!tele
4"n!t .n/ /2.2n
Χ /2.2n
Υ
C2 +
D2 + +
E2 +
M2 +
2 +
Co$p
De&inim p"n!tele
4"n!t .n//.
n Χ/.
n Υ
A + +
B
Co$p %
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De&inim p"n!tele
4"n!t .n/ /.n
Χ/.
n Υ
F% + +G%
Des!$ie$ea $est$i!ţiile eomet$i!e:
Rest$i!ţia T dint$e !o$p"$ile 1-2 din p"n!t"l M1 1≡ M1 15
+
1
1
1
22
22
11
=
Υ Χ
Υ Χ
Υ Χ
N N
M M
M M
6
+
1
1
1
22
22
11
=
Υ Χ
Υ Χ
Υ Χ
N N
M M
N N
[ ]
Υ
ΧΜ+
Υ
Χ=
Υ
ΧΟ /1.
/1.
1
1
1
1
1
1
1
M
M
O
O
M
M
[ ]
Υ
ΧΜ+
Υ
Χ=
Υ
Χ/2.
/2.
2+
2
2
2
2
2
2
M
M
O
O
M
M
F1:
( )( ) ( )( ) +22222121= Υ− Υ Χ− Χ− Υ− Υ Χ− Χ
N M N M M M M M
F2:
( )( ) ( )( ) +21212121= Υ− Υ Χ− Χ− Υ− Υ Χ− Χ
M M M M M N M N
F:
+
1
M
M
MM
MM
22
22
21
21 =
Χ− Υ
Χ− Χ
Χ− Υ
Χ− Χ T
Rest$i!ţia RR dint$e !o$p"$ile 2- din p"n!t"l C2B=d5
( ) ( ) 22222
d BC BC
= Υ− Υ− Χ− Χ
2
/2.
2
/2.sin!os
2222ϕ ϕ
C C OC Υ− Χ+ Χ= Χ
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/1.
22 C C Χ= Χ
2
/2.
2
/2.sin!os
2222ϕ ϕ
C C OC Υ− Χ+ Υ= Υ
/2.
22 C C
Χ= Υ
F:
( ) ( ) 22/.
/./2.2
/.
/./2. !os!os!os!os22222222
d B BOC B BOC
= Υ− Χ− Υ− Υ+ Υ+ Χ− Χ− Χ ϕ ϕ ϕ ϕ
=7
( ) ( ) 22/./2.2
/./2. !os!os222222
d BOC BOC
= Χ− Υ− Υ+ Χ− Χ− Χ ϕ ϕ
Rest$i!ţia R dint$e !o$p"$ile -1 din p"n!t"l A1≡A5
[ ]
Υ
ΧΜ+
Υ
Χ=
Υ
ΧΟ /1.
/1.
1
1
1
1
1
1
1
A
A
O
O
A
A
[ ]
Υ
ΧΜ+
Υ
Χ=
Υ
ΧΟ /1.
/1.
2
2
2
2
2
2
2
A
A
O
O
A
A
F%:
+!ossinsin!os 1/1.
1
/1.
/.
/.
111= Υ+ Χ− Χ− Υ− Χ+ Χ ϕ ϕ ϕ ϕ
A AO A AO
F8:
+sin!os!ossin 1/1.
1
/1.
/.
/.
111= Υ+ Χ− Υ− Υ+ Χ+ Υ ϕ ϕ ϕ ϕ
A AO A AO
Rest$i!ţia R$ dint$e !o$p"$ile %-2 din p"n!t"l E2F=d55
( ) ( ) 22222
d F E F E
= Υ− Υ− Χ− Χ
2
/2.
2
/2.sin!os
2222ϕ ϕ
E E O E Υ− Χ+ Χ= Χ
/1.
22 E E Χ= Χ
2
/2.
2
/2.sin!os
2222ϕ ϕ
E E O E Υ− Χ+ Υ= Υ
/2.
22 E E Χ= Υ
F:
( ) ( ) 22/.
/./2.2
/.
/./2. !os!os!os!os22222222
d F F O E F F O E
= Υ− Χ− Υ− Υ+ Υ+ Χ− Χ− Χ ϕ ϕ ϕ ϕ
=7
( ) ( ) 22/./2.2
/./2. !os!os222222
d F O E F O E
= Χ− Υ− Υ+ Χ− Χ− Χ ϕ ϕ
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Rest$i!ţia R dint$e !o$p"$ile %-1 din p"n!t"l G1≡G%5
[ ]
Υ
ΧΜ+
Υ
Χ=
Υ
ΧΟ /1.
/1.
1
1
1
1
1
1
1
G
G
O
O
G
G
[ ]
Υ
ΧΜ+
Υ
Χ=
Υ
ΧΟ /1.
/1.
2
%
%
%
%
%
%
G
G
O
O
G
G
F%:
+!ossinsin!os 1/1.
1
/1.
%
/%./%.
111%%%= Υ+ Χ− Χ− Υ− Χ+ Χ ϕ ϕ ϕ ϕ
GGOGGGO
F8:
+sin!os!ossin 1/1.
1
/1.
%
/%.
%
/%.
111%%%= Υ+ Χ− Υ− Υ+ Χ+ Υ ϕ ϕ ϕ ϕ
GGOGGO
Corpul 3:
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Corpul 4:
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Corpul 2:
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4)Reprezentarea grafca a unctiilor cinematice:
Corpul 1 :
