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Modelling and analysis of suspension systems 167
A
B
Centre line
Instant centre
C
D
Roll centre
y
z
Roll centre height
Wheel base (WB)
Fig. 4.28 Instant centre and roll centre positions for a double wishbone
suspension. (This material has been reproduced from the Proceedings of the
Institution of Mechanical Engineers, K2 Vol. 213 ‘The modelling and simulation
of vehicle handling. Part 2: vehicle modelling’, M.V. Blundell, page 123, by
permission of the Council of the Institution of Mechanical Engineers)
B
A
WC
C
D
Z
X
Y
Fig. 4.29
Position of instant centre construction points on wheel centre YZ plane
It should be noted that the two-dimensional representation shown in Figure
4.28 is a simplification of the three-dimensional system and the graphical
construction that takes place in a YZ plane passing through the wheel
centre as shown in Figure 4.29.
Since it cannot be assumed that the axes through the wishbone mount
points are parallel to the x-axis the positions of points B and D will need to
be obtained by interpolation to the YZ plane passing through the wheel
centre. Positions A and C are found simply by projecting the upper and lower
ball joints on to the same plane.
In order to program this construction algebraically the first step is to set up
expressions for the gradients GR1 and GR2 of the upper and lower arms:
GR1 (BZ AZ)/(BY AY) (4.32)