76
B. M˘ anescu et al.
Fig. 1 Mechanism
ϕ 3
4
ϕ
2
ϕ
1
ϕ
O
C
A
C
E
Y
X
B
1
2
C
3
C
4
C
5
C
D
e
d
Y
E
α 2
θ
θ
1
2
modify the extreme positions of the piston D, which implies the variation of the
compression ratio.
The position of the mechanism is obtained from the relations:
OA cos ϕ 1 + AC cos ϕ 2 + CE cos ϕ 4 = d, OA sin ϕ 1 + AC sin ϕ 2 + CE sin ϕ 4 = y E
(1)
x A = OA cos ϕ 1 , y A = OA sin ϕ 1 ,
(2)
x C = OA cos ϕ 1 + AC cos ϕ 2 , y C = OA sin ϕ 1 + AC sin ϕ 2 ,
(3)
(x − x A )
2
+ (y − y A )
2
= AB
2
, (x − x C )
2
+ (y − y C )
2
= BC
2
,
(4)
(x − x B )
2
+ (y − y B )
2
= BD
2
, x = e,
(5)
ϕ 3 = arctg
y D − y B
x D − x B
, λ = arccos
AC
2
+ BC
2
− AB
2
2AC · BC
,
(6)
x B = OA cos ϕ 1 + AC cos ϕ 2 + CB cos(λ − ϕ 2 ),
y B = OA sin ϕ 1 + AC sin ϕ 2 + CB sin(λ − ϕ 2 ).
(7)
The velocities are deduced from:
˙
x A = −OAω sin ϕ 1 , ˙
y A = O Aω cos ϕ 1 , v A = OAω,
(8)