Kinematics of wheel loaders

[Jundis]

Hi guys&gals,

while discussing the 42209 in the corresponding thread, we stumbled upon the kinematics behind the arm and bucket movement. As this theme applies to all wheel loaders, I'd like to follow the idea of @jorgeopesi and create a seperat thread to discuss this in more detail.

The basics so far:

There are different kinematics, the main ones are Z-kinematics (Z represents the appearance of the linkage) , P-kinematics (parallel) and TP-kinematics (torque-parallel, so far Volvo exclusive).

Z-Kinematics

With Z-kinematics, the tipping movement of the bucket is actuated when pressure is applied to the push-side of the cylinder. The piston rod extends and pushes the reversing lever forwards. This lever is rotatably mounted on the lifting arm and so the movement is transferred to the mounted coupling rod which causes the bucket to start tipping in. 
This kinematic system has a very high break-out force due to the pressurization of the push-side (we come to that later in the pic with the cylinder). When tipping out, very short tipping times are possible.

P-Kinematics

The parallel kinematics enable goods to be lifted and lowered in parallel according to their layered design. This is particularly advantageous when operating with a loading fork, as the driver does not have to manually adjust the cylinders during the lifting process. The connecting linkages, the cylinders and the lift arms together form a parallelogram. They are controlled in the opposite direction to the Z-kinematics. The system is primarily used in wheel loaders for the agricultural sector and construction.

This results in lower break-out forces and longer tipping times but higher linear stability. Here is a short video which compares the Z and P-kinematics on a Liebherr Wheel Loader and a picture (P-kinematic on left, Z-kinematic on right side)

TP-Kinematics

The torque-parallel-kinematics combine the advantages of Z-kinematics and P-kinematics. Its like an inverted Z-kinematics.

The design results in a high break-out force with parallel guidance during the lifting process as well as controlled tipping in the upper lifting position. As far as I know, only Volvo uses this system.

 

 

The main purpose of using a Z-kinematic instead of a P-kinematic is the difference in the force of a hydraulic or pneumatic cylinder for push and pull. The piston rod reduces the surface area of the pull side (orange) by the cross-sectional area of itself (green). Therefor, the cylinder has a higher push-force (yellow area) and a lower pull-force (orange = yellow minus green).

Coming back to Lego: At least from my understanding, there shouldn't be any difference in force when using a linear actuator --> can someone confirm or disprove this assumption?

 

Linkage System 

The linkage system itself is way more complicated and so far I found this source from Stefan Segla from 2018 published in the Journal of Manufacturing Technology called: "Kinematic Analysis and Optimization of a Wheel Loader Mechanism"

It is only for Z-kinematics, but should also be adaptable to PT kinematics. It describes the optimization by seperating the differen linkages and given movement and geometrical constraints. He then optimized them via an analysis of the desired and the actual value of the bucket angular position.

I put together the initial picture and included the virtual point J he introduces in the abstract view of the mechanism and also coloured the lines in the image below.

Depending on the scale of the Lego model, an initial value should be used instead of meters. I would suggest using the yellow line BG, which for example is 2 studs for the new bucket of the 42209. By replacing the line BG of 0.35 m with 2 stud we get the measurement of 1 stud equals 0.175 m. We then can calculate back the other values, which are the following:

BG = 2 studs
GD = 4.68 studs
DC = 3.84 studs
CE = 1.92 studs
JC = 5.06 studs
AJ = 5.53 studs

While some value may be round up well to suitable numbers for available bricks, others are kind of hard to achieve...

To be continued...

Edited June 10 by Jundis
Added content to linkage system and spelling.

[mpj]

Very simple and clear explanation, good job!
As you pointed out, Volvo uses a different linkage than the classic Z-linkage used in set 42209, so that could be a good challenge to mod. 

[Paul B Technic]

Well done for explaining this so well.

[Jundis]

  On 6/10/2025 at 8:50 AM, mpj said:

Very simple and clear explanation, good job!
As you pointed out, Volvo uses a different linkage than the classic Z-linkage used in set 42209, so that could be a good challenge to mod. 

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Thanks, guys. Looks like the L120 has both systems: Z and PT

[mpj]

Mmm I don't think so, the L120 electric and L120H looks to be only available with TP. Do you have any picture of a L120 with Z?

[Jundis]

  On 6/10/2025 at 2:31 PM, mpj said:

Mmm I don't think so, the L120 electric and L120H looks to be only available with TP. Do you have any picture of a L120 with Z?

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Link

[jorgeopesi]

Cool explanation  .

[mpj]

  On 6/10/2025 at 2:34 PM, Jundis said:

Link

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Super! Thank you.

[Stereo]

  On 6/10/2025 at 8:20 AM, Jundis said:

Coming back to Lego: At least from my understanding, there shouldn't be any difference in force when using a linear actuator --> can someone confirm or disprove this assumption?

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I believe that's the case in theory, it's just a worm drive inside it.  There could potentially be friction differences though, since one will be under tension and the other compression so they'll be on different bearing faces.  Compression should be an internal one, tension might be external (ish) where the orange axle goes into the body.