4569846498

Modelling and analysis of suspension systems 223
C 6 on Body 6 and C 7 on Body 7, all located at point C. Note that we
already have
⎡ 210.
614 ⎤
{ AC3}
1{ AC7} 1 { AC} 1
⎢
28
476.707
⎥
mm/s
⎢
⎥
⎣⎢
3455.690 ⎦⎥
We can also calculate the acceleration {A C6 } 1 from
(4.228)
{A C6 } 1 {A C6I } 1 { 6 } 1 {V C6I } 1 { 6 } 1 {R CI } 1 (4.229)
where
{V C6I } 1 {V C6 } 1 {V C6C7 } 1 {V C7 } 1 (4.230)
2
⎡ 13.
628 ⎤ ⎡120.
555⎤
⎡ 134.
183 ⎤
{ V C6I
}
⎢
41.
045
⎥
⎢
435.
157
⎥
⎢
476.
202
⎥
mm/s
⎢ ⎥ ⎢ ⎥ ⎢ ⎥
⎣⎢
1988.
378⎦⎥
⎣⎢
1979.
499 ⎦⎥
⎣⎢
3967.
877⎦⎥
therefore {A C6 } 1 is given by
⎡A
⎢
⎢
A
⎣⎢
A
C6x
C6y
C6z
⎤ ⎡ 0 1. 159 0.
245 ⎤ ⎡ 134.
183 ⎤
⎥ ⎢
⎥ ⎢
⎥
1. 159 0 0.
904 476.
202
⎥
⎢
⎥ ⎢ ⎥
⎦⎥
⎣⎢
0. 245 0.
904 0 ⎦⎥
⎣⎢
3967.
877⎦⎥
⎡ 0
⎢
⎢
⎢
⎣
6z
6y
6z
6x
0
6y
6x
0
⎤ ⎡ 3 ⎤
⎥ ⎢
⎥ 9
⎥
mm/s
⎢ ⎥
2
⎥
⎦ ⎣⎢
436⎦⎥
(4.231)
(4.232)
⎡A
⎢
⎢
A
⎣⎢
A
C6x
C6y
C6z
⎤ ⎡420.
212⎤
⎡96z
436
⎥ ⎢ ⎥ ⎢
⎥
3742.
479 z 436
⎢ ⎥ ⎢36
⎦⎥
⎣⎢
463.
361⎦⎥
⎢
⎣
3 6y
9
(4.233)
If we now consider the relative acceleration vector {A C6C7 } 1 we can see that
this involves the relative acceleration between points on two bodies where
relative rotation and sliding occurs. Referring back to Chapter 2 we can
now identify the four components of acceleration associated with the combined
rotation and sliding motion as the centripetal acceleration {A p C6C7} 1 ,
the transverse acceleration {A t C6C7} 1 , the Coriolis acceleration {A c C6C7} 1
and the sliding acceleration{A s C6C7} 1 :
{A p C6C7} 1 { 6 } 1 {{ 6 } 1 {R C6C7 } 1 } (4.234)
{A t C6C7} 1 { 6 } 1 {R C6C7 } 1 (4.235)
{A c C6C7} 1 2{ 6 } 1 {V s } 1 (4.236)
{A s C6C7} 1 |A s C6C7| {l CI } 1 (4.237)
Since the C 6 and C 7 are coincident points it follows that {A p C6C7} 1 and
{A t C6C7} 1 are zero. It also follows that the sliding velocity {V s } 1 is equal to
6y
6x
6x
⎤
⎥
⎥ mm/s
⎥
⎦
2