# Linear actuator behind lifting boom

This is a follow-up on my previous question here: Sizing a motor for a floor jack-like mechanism

The floor jack setup is clearly inefficient when it comes to electric actuators. Something similar to a mobile crane would work better, as I'd benefit from the mechanical advantage of the lever formed between point of rotation and actuator.

My question is: can the actuator be anchored behind the point of rotation of the lifting arm, e.g.

NB: 400 mm is the linear actuator's install length. The stroke is 300mm.

If my understanding is correct, the system should have significant mechanical advantage?

EDIT Would this setup be similar to what you see on skip trucks? E.g.

• There are no pivots marked on your drawing. It's not clear what's supposed to happen. – Transistor Mar 20 '20 at 19:55
• @Transistor Ah, good point. Sorry for the vagueness, I've updated the diagram. – John Lane Mar 20 '20 at 22:58
• Much better - including addition of the ram. – Transistor Mar 20 '20 at 23:00
• The design you have made looks to me like it would just lock up, but clearly you can adjust pivot points to trade motion for mechanical advantage. Existing machines won't help because they will use hydraulics for their advantage. You need to think in terms of reversing your mechanisms so that the input has a larger stroke than the output. It i the nature of simple machines, just a lever. – Tiger Guy Mar 22 '20 at 18:14

Initial thoughts? I'm not a mechanical engineer but I think you'd be disappointed.

Figure 1. A quick pictorial analysis shows that there is almost no reason for the lift arm to move up.

Also, most of the effort in the linear actuator would be taken up by a force vector from C to A with very little of the effort going into rotation.

Figure 2. An online structural analysis program such as that offered by http://structural-analysis.com may be useful.

This quick little mock-up uses a pin (1) at the left end of your 400 mm lifting arm with 1 kN applied to the arm offset by 100 mm. The rotation is constrained by a roller joint (2). We can see that only 1/3 of the force is going to do any useful work.

You'll have to play around with the scaling on this. It's not optimised for sub-meter parts so you may need to scale up for good visibility.

Figure 3. At the start of the lift the ram is pulling the crank (green) with a starting angle of 45° or so - and the chains aren't even tight yet. This isn't too bad.

Figure 4. The situation appears to be worse when lifting off the truck as the crank (green again) angle is very low. Note, however, that the lift has been flattened against the skip to minimise height and that again the chains are slack. There is no load initially and by the time the chains are taut the crank will be at about 45°.

The skip truck design seems to be well thought out.

• Very thorough, much appreciated. – John Lane Mar 21 '20 at 9:04
• See the update. – Transistor Mar 21 '20 at 12:31
• Excellent! Thank you so much for your time, this clarifies thing a lot. – John Lane Mar 21 '20 at 12:40

Let's call the point where the hinge is welded to the boom D.

Scaling CD from your diagram we pick 30mm.

That means the mechanical leverage of this gadget is approximately

$$F_{boom}= F_{actuator}\frac{30}{400}= 0.075F{actuator}$$

This gets even worse because we need to consider the reduction of leverage due to the location of D, a nearly ratio of 1/20 efficiency.

And on top of that, the boom will lock up after a small rotation where the actuator will hit the boom $$\theta=\arctan(30/144)= 11.7degrees$$

By increasing the length of CD and changing the location of the pivots we can improve the leverage.

• thanks for the explanation. I've edited my question. In the context of the above, how does a skip truck operate? Is it at such a mechanical disadvantage as well, just compensated by really beefy hydraulics? – John Lane Mar 21 '20 at 9:20