Arocs (Lego 42043)

Steering

Geometry

On the Eurobricks forum Technic Moderator “Jim” posted an excellent and exhaustive review of the 42043.  In it he wrote: “Using different links results in different steering angles for both axles.”

Yes, and that is desired.  I repeat here most of what I replied, plus more.

In steering any multiple-wheeled vehicle, there is at any moment a single point around which it rotates.  All wheels have to be oriented so that their axes go through that point.  It's perhaps easiest to see that in a top view of a bicycle:

O

The bike is turning left around point O.  Note that the circle of the front wheel does not have the same radius as the one of the rear wheel.

For the truck, similarly draw a top view, with rectangles for the wheels. Then draw a line extending one of the two rear axles.  Choose the point of rotation O on that line. From that point, draw lines to the centres of all other wheels.  Then rotate the rectangles that represent the wheels so that each is perpendicular to the line that goes through it.  Those are the only positions of the wheels that will make the truck steer a circle around the point of rotation without making the tyres slip and therefore wear out.

O

(I have put thin red rectangles over the last pair of wheels to show how they should turn too)

When I decided to buy the 42043 I was wondering how Lego would deal with the problem of making all wheels point to the same centre of rotation.  So the front wheels do a good job, though unfortunately the rear wheels do not turn, and at the front axles the wheels in each pair are always kept parallel whereas they should not be.  The latter problem is easy to solve in Meccano and almost impossible in Lego.

You will notice that the first pair of wheels must turn a little more than the second pair and that at least some of the rear wheels should also turn.  I have seen real platforms with four rear axles, all of which turn correctly as well as the double front axle.

You will also notice that in each pair the wheel closer to the point of rotation needs to swivel a little more than the wheel on the other side.  I know of no Lego set in which steering wheels do that (but there may be some).

In cars the usual geometry is like this: (and thanks to “750ACE” on the Eurobricks forum for telling me its name: “Ackerman steering”)

First draw a triangle (dashed red line) that connects the front wheels and the centre of the real axle.  Then construct a steering linkage that is a trapezium (green) corresponding to that triangle.

The rack of the rack-and-pinion steering mechanism is fixed to the bottom parallel line of the trapezium, and when it is shifted the wheels turn approximately as they should.  I say approximately, because the desired angles are transcendental functions of the turning radius; any simple mechanical linkage is not really good enough.

In Meccano rods are fixed with nuts and bolts, so any angle can be obtained.  In Lego it is very difficult to make that trapezium and even more difficult to set the wheel at an angle to the rods.

I hesitated to have a go at this problem, but finally did.  It resulted in a pretty lousy model, the only purpose of which was to show that it is possible though not very well.