Analytical solution for the roll center calculation

4. Ic point is (-850.99,239.1127)

Roll center point is (800,-224.7854)

Roll center height 224.7854 downwards from ground plane.

Explanation

solving the all equations by analytical geometry.

slope of upper control arm=7/36

Equation of upper control arm`implies``z=7/36y+4855/12`-(1)

Slope of lower cntrol arm=-3/53

Equation of lower control arm`implies``z=-3/53y+10120/53`-(2)

Solving equation (1)&(2)

y=-850.99

z=239.1127-Instantaneous center coordinates

Euation of line joining ic and tyre contact patch`implies``z=-2391127/8509900y`-(3)

Equation of vehicle centerline`implies``y=800`-(4)

Solving (3)&(4)

y=800

z=-224.7854-Roll center coordinates

Roll center height =`modz`=224.7854

Picture for the above question

https://drive.google.com/file/d/15bEZTOWFXy0TBwECchgrEUEDLOakoZ9G/view?usp=sharing

This can also be done by plotting the given coordinates in graph and extend the lines to find ic and roll center