Bicycle model kinematics towed trailer during normal forward driving

December 2023

During a normal forward/reverse towing, the front truck pulls/pushes on the front fifth wheel of the trailer, and the wheels of the trailer pivot about another point (separate from the pivot point of the front truck), as shown below.  The net result is that the towing truck leads the rear of the trailer through a turn.

Bicycle model kinematics towed trailer during tank turn

December 2023

I demonstrated earlier that the Mover truck can perform a tank turn.  In kinematic model, the front truck tank turns exactly the same even with payload on its 5th wheel, as you can see in the schematic diagram below, where the ❌ represents the kingpin locked into a 5th wheel.

As t he front truck executes the tank turn, the container on top of the rear truck gets pushed backward by approximately d (cos𝛳 – 1).  See this Jupyter notebook for the a more precise derivation.  The container also rotates during the tank turn, but by a much more attenuated angle η, as you can see below.

Bicycle model kinematics of single truck

December 2023

I begin with a bicycle model of a Ackermann front steered car with wheelbase L (200 cm) and front track width W (105 cm), which is at an arbitrary heading 𝛳 relative to the arbitrary chosen "forward" direction, which in this diagram is vertical, but can easily be horizontal as well.  The L and R wheel steering angle is capped to 30˚ in this analysis.  See a Jupyter notebook for detailed derivation.  Here's the resulting simulation for the case where the steering angle is oscillated with 1 cosine function, with the rear wheel speed ramping up to and down from 3 rad/s.

Model pivots about the rear axle

1/4 scale tank turn

November 2023

Here's a demo of the tank turn envisioned with a manually operated 1/10 scale model, but this time on a 1/4 scale model, and mechanized with a DC motor mounted directly on the front axle–just as I envisioned it.  The only discrepancy of this simplified 1/4 scale model is that the front axle is not independent of the frame (i.e. it is NOT suspended) but that is irrelevant for the purpose of the demo.  Note that the tank turn mechanism can still move well even with moderate weight placed on the frame.

1/10 scale model sensor mount

An autonomous truck needs to place sensors as high up above the ground, to see farther out than passenger cars, since the heavier truck needs longer stopping distance.  A unique problem for the Mover is that it needs to crawl under a trailer and dock to the rear of the trailer.   Clearly, a tall sensor mount will get in the way; so I need to fold it into the truck when the rear truck begins the docking maneuver.

I took inspiration from aircraft landing gear (shown on. the side), and came up with a design for the folding sensor mount, shown in the video below.  See how compactly it folds into truck's front top space.  If you imagine the top bar is a stereo camera base, it will have a stereo baseline of ~70 cm, and sit 7.5' above the ground (because the 1/10 scale model's camera height is 23 cm above the ground), which is at or slightly higher than traditional  driver's eye level.

The design has one shortcoming: it is locked into extreme poses; the solution I propose is a spring loaded hinge in the middle of the sensor mount beam (shown at the bottom), so that the spring's restoring force alone can spring the mount beam out of the extreme poses.

1/10 scale model tank turn

The reason why the Mover is more of a robot than a truck is that it can crawl under a rHom.me trailer during docking maneuver (see the concept video on the Home page), which is unlike any traditional parking maneuver.  Since there is very little space under a trailer, especially between the landing gears, the Mover needs to resort to tank turns.

To pull off a tank turn, the wheels need to toe-in ~60˚ and driven by a motor to turn the wheels directly.  The rear wheels (which are on traditional differentials) are left in neutral.  Since front L and R wheels need to be rotated in opposite directions during a tank turn, a single motor driving both the L and R wheels through a tensioned chain should work well for this purpose, as shown on the side (I ran out of gears so showing only the L side, but the R side can be driven with the same motor (different chain).

When the wheels toe in completely (and kept there with some kind of locking mechanism), the front pinion gear should mesh with internal gear on the inside of the front wheels.

1/10 scale model suspension

Since I want to carry 5000 lbs on each truck, coil spring+damper commonly used in passenger cars was out of the question.  Originally, I tried to fit the traditional leaf spring used in heavy duty trucks, but leaf springs are traditionally mounted on  ladder style frames whereas my frame is a trapezoid shaped.  It became clear that I would need an adapter to take out the slant of my frame, so rather than deal with the complexity of 3D printing a novel structure for this 1:10 model, I decided to just hang the front and the rear suspensions from the vertical tubes hanging down from the axial beam, as you can see on the side.

To keep the Mover short, I am going to use air springs instead of the traditional leaf springs, as you see on the side (the pink blobs are models of air springs).

2022 Nov-1/10 scale frame stiffened with outrigger cables

I propose a simple method to mount the front and rear suspensions to the main axial beams formed from two 8mmx8mm square tubes: hang vertical tubes (almost as wide as the main axial beam; 5.3 mm diameter here) that go through the top and bottom flanges of the beam, as shown on the side. 

If you are eagle-eyed, you can see the fish-mouth soles I drilled out in the vertical tubes, to affix the cross tubes.  Observe the relatively large manufacturing error (I am hand-drilling) and angular distortions in the initially assembled frame: the bottom cross tube is twisted by as much as 10˚ , but I correct it after the initial assembly by stringing diagnonally, much like the outriggers in early biplanes.  The cable tension can be adjusted with turnbuckles, but for the 1:10 model, there is no turnbuckle small enough, so I just pull the string sufficiently taught and tighten down with the Halyard Knot.  The result is far from perfect, as you can see on the side.  But in theory, the frame can be adjusted this way.

For the full scale truck, this level of poor of manufacturing error should be prevented at the design stage.  We'll see if all cables (e.g.  the cross cables at the front and the middle section of the truck–where there is little room for thick tubes) can be removed for the full scale prototype.

With a sufficiently stiffened frame, I can continue onto suspensions.

2022 Oct–Start of 1/10 scale model

I finally have a rough 3D design of my autonomous truck.  To test the basic sanity of the design, I am starting with a tenth scale mockup from mostly plastic components–either off-the-shelf or 3D printed.  Step 1: make truck frame from 8mm x 8mm square tube. 


A heavy duty truck usually has a body-on-frame structure: all important components hang off the frame, so it's important to have a stiff frame.  Both the L/R axial frames, and the cross members that connect the axial frames are of steel C-beams as you can see on the right.


For the 1/10 scale mockup, a steel C-beam is an overkill and instead off-the-shelf ABS plastic modeling tubes and rods will do, but the ABS tube I can buy from eBay was way too compliant, so here's an easy way to stiffen up the frame.