# Distance travelled at articulation point of turning vehicle

## Problem outline:

I'm trying to figure out the distance travelled at the articulation point of a turning vehicle with 4 driven wheels (each wheel houses a motor and can all rotate at different RPMs). If this isn't a suitable place for such a question, please let me know if there's a better exchange/forum for it.

## Motivation:

This is a work-related odometry calculation problem used in a larger analytic, not something "just for the sake of doing it" (I wish!), so I unfortunately don't have anyone academic to turn to for assistance/grading etc.

## Known:

• The distance from the articulation point to the front axle, $$l_1$$,
• The distance from the articulation point to the rear axle, $$l_2$$ ($$l_1$$ != $$l_2$$),
• The length of each axle, $$l_a$$,
• The articulation angle, γ,
• The RPM of each wheel, and
• The diameter of each wheel.

I have a timeseries of RPM/articulation angle data with a 2Hz sampling rate, but if I can get some help with the general equations, I'm more than comfortable doing this bit.

I've done similar instant centre problems with non-articulated vehicles in the past, but my uni years are now a fair bit behind me and these days I spend most of my time programming, so my engineering skills are a bit rusty. Unfortunately, "reasonable" accuracy is important here (still making allowable assumptions such as disregarding slip, etc) so I can't use the assumption of linear distance. Any help would be very much appreciated!

Rough idea:

• Don't you also need to know the steering angle of each wheel/axle? Mar 25, 2019 at 10:02
• @am304 - since it's an articulated vehicle, the axle is solid with no steering angle for each wheel. The angle is all at the articulation point.
– ReyL
Mar 26, 2019 at 23:02