Influence of Eccentricity of Drive Mechanisms …
511
v B = ω 1 · AB
(5)
v C B = ω 2 · C B
(6)
The relations between the velocities are:
v Bx
v By
=
cos θ − sin θ
sin θ cos θ
·
0
v B
⇒
v Bx = −v B · sin ϕ
v By = v B · cos ϕ
(7)
v Cx
v Cy
=
v Bx
v By
+
cos ϕ − sin ϕ
sin ϕ cos ϕ
·
0
v C B
⇒
v C = v Bx − v C B · sin ϕ
0 = v By + v C B · cos ϕ
(8)
v Mx
v My
=
v Bx
v By
+
cos ϕ − sin ϕ
sin ϕ cos ϕ
·
−ω 2 · N M
ω 2 · B N
⇒
v Mx = v Bx − ω 2 · y
0 = v By + ω 2 · x
(9)
3.3 Study of Accelerations
In order to determine the accelerations of the points of the slider-crank (Fig. 7), the
following formulas were used:
a
υ
B = −ω
2
1 · AB
a
τ
B = ε 1 · AB
(10)
a
υ
C B = −ω
2
1 · BC
a
τ
C B = ε 1 · BC
(11)
The relations between the accelerations are:
a Bx
a By
=
cos θ − sin θ
sin θ cos θ
·
a Bυ
a Bτ
⇒
a Bx = a
υ
B cos θ − a
τ
B sin θ
a By = a
υ
B sin θ + a
τ
B cos θ
(12)
a C
0
=
a Bx
a By
+
cos ϕ − sin ϕ
sin ϕ cos ϕ
·
a
υ
C B
a
τ
C B
⇒
a C = a Bx + a
υ
C B cos ϕ − a
τ
C B sin ϕ
0 = a By + a
υ
C B sin ϕ + a
τ
C B cos ϕ
(13)
a Mx
a My
=
a Bx
a By
+
cos ϕ − sin ϕ
sin ϕ cos ϕ
·
−ω
2
2 · B N − ε 2 · N M
−ω
2
2 · N M + ε 2 · B N