Learning from Torque Curves

Introduction

Welcome to our deeper dive into Torque Curves. It is advised to read our ‘Introduction to Torque Curves’ page first if you are not yet introduced to Torque Curves. The button below will take you there.

As written on the ‘Specifying Exoskeleton Support’ page, exoskeleton support specifications in the current market generally go no further than specifying an ‘up to’ value generally expressed in 'kg', which are all measured or calculated using different definitions, making it impossible for potential buyers to compare support specifications between different exoskeletons. And the worst thing is because the definitions are also not specified by manufacturers, most potential buyers do not even know they are comparing apples to oranges.

Torque Curves specify the support of the exoskeleton over the entire exoskeleton bending range. This is where Laevo identifies a lot of differences between brands and types of exoskeletons and that is why we think it is good to have torque curves as a standard specification for exoskeletons. Torque curves make comparing exoskeleton support clear, so it becomes easier to select the right exoskeleton for the application.

The chapters below will give even more information and useful applications of torque curves. The information is a bit more advanced level than the 'Specifying Exoskeleton Support’ page, so get ready to get technical.

It is broken down into the following chapters:

1.     Torque Curve Measurement

2.     Reading Torque Curves

3.     Torque Curve Adjustments

4.     Energy

5.     Conclusion

1. Torque Curve Measurement

Torque curves at the core of Laevo exoskeleton design: The Laevo its ‘Smart Joints’ are designed to be able to output any given torque curve and Laevo has been optimizing its torque curves iteratively with many users for years to get the most effective and comfortable support.

Laevo designed its exoskeleton to generate torque around the user’s hip joint. This is one of the reasons why our exoskeleton Smartjoints axles are aligned with the user its hip joint. Because of this, it is easy for us to specify the torque curve around the hip joint. But torque curves can also be specified for exoskeletons that do not have any parts next to the hip joint, like soft exoskeletons or so-called exo-suits. Read about our torque curve measurement setup below.

Laevo Torque Curve Measurement Setup

Years ago, Laevo designed an exoskeleton to output a specific torque curve, but did it actually do so? For verification, Laevo invested in designing and building a measurement setup that replicates a simple bending motion around the hip. The setup connects to our calibrated universal testing machine which we have been using, before Laevo even existed, to measure conceptual mechanisms and springs, next to quality checks on specific incoming goods.

Of course, to be a standard specification for all exoskeletons, a machine like this should be standardized so every manufacturer can measure their exoskeleton in the same way. Laevo knows this is by no means a perfect representation of a bending human. The main point we are trying to make is that by using this relatively simple device and measurement that only takes a minute, you can get a support specification that gives far more insight into the exoskeleton support behavior than just a single ‘up to’ support value.

In the pictures below you can see the Laevo FLEX in our torque measurement setup.

Measuring torque around the hip

Why did we choose to measure torque around the hip joint? A lot of research about heavy lifting looks at the lower end of the spine, and to be more specific, the L5S1 disc. This is the name of the disc in between the lowest two vertebrae of our spine and is most often the victim of people with lower back disorders. Therefore scientists are also interested in supporting torque values at the L5S1 disc. So why don't we provide torque curves around the L5S1 disc?

First, an exoskeleton has a far larger range of motion than the L5S1 disc alone. Measuring the torque curve for the bending range of the spine alone would provide an incomplete picture of the support characteristic of the exoskeleton. So, for measuring the complete torque curve of the exoskeleton the measuring mannequin needs to bend around the hip joint.

Second, we could still measure the torque around the hip and calculate the torque curves around L5S1. However, this would require additional anthropometric data about the location of the position of the L5S1 disc relative to the hip joint. Not only are these dimensions different between people while standing straight, but these dimensions also vary during the motion based on the flexibility of the user and the specific posture the user chooses to make. So yes, it is possible to calculate a torque curve around L5S1, but this curve will be dependent on additional variables which are different between users, which is unpreferable for a standard specification. It would also be a mechanical challenge to create a measuring setup that varies the L5S1 location relative to the hip joint in a realistic way during the bend.

Third, in reality, humans will use a combination of bending their spine and rotating their hip relative to their legs when bending forward. Our test setup does not bend its spine during bending. Similar to what was mentioned in the second point, the bending of the human spine varies during the motion based on the specific user's spine shape, the flexibility of the user, and the specific posture the user chooses to make. Taking bending of the spine into account will therefore again be dependent on additional variables that are different between users, which is unpreferable for a standard specification. Some exoskeletons even restrict spine bending altogether, which makes designing some kind of universal bending of the spine during the measurement even more complex.

Therefore, Laevo thinks it is best to measure the torque of a trunk-supporting exoskeleton purely based on a rotation of the trunk around the hip relative to the legs. Not only to be less reliant on additional variables that are different between users but also because it is very practical. It does not require very advanced and hard-to-operate sensors and machinery and the measurement can be done in a minute. This method will not exclude any trunk-supporting exoskeletons that we know of. For a select few exoskeletons, the torque curves will not exactly correspond to what a user will experience when using the exoskeleton because of some slight dependence of the support on spine curvature, but still, it will give a lot of information about the global support characteristic.

We are not alone

Laevo recently discovered a scientific paper 'A Novel Approach to Quantify the Assistive Torque Profiles Generated by Passive Back-Support Exoskeletons’. First, like us, they propose to use torque curves to quantify the exoskeleton support. And second, the researchers came to the same conclusion to use only the rotation of the trunk around the hip relative to the legs because of the universality and practicality. The researchers are using a computerized isokinetic dynamometer to generate torque curves of trunk-supporting exoskeletons. This high-end device would probably result in even more qualitative results than with our self-built measurement setup. They even investigated the difference between a torque curve generated by a human and a mannequin and found similar results.

Measuring other exoskeletons

Our measurement setup proved to be helpful in the verification of our own work but also proved to be helpful to exoskeleton research. Laevo exoskeletons are often used in research projects from universities or companies. Researchers have been asking for exoskeleton torque curves since the beginning, and Laevo has always been one of the few (if not the only) manufacturer that was able to provide detailed information about our exoskeleton torque curves. When Laevo presented closely matching designed vs. measured torque curve output, multiple researchers immediately asked how we did this, and if the measurement of other trunk-supporting exoskeletons would be possible. Laevo made some changes to the measurement setup to allow the mounting of a broader range of trunk-supporting exoskeletons. This way, Laevo has had the chance to facilitate torque curve measurement of other brands and types of exoskeletons, including soft exoskeletons, by independent external researchers.

All researchers involved have been delighted to finally have torque curves available for all exoskeletons in their research and, just like Laevo, hope this will be a standardized specification for all exoskeletons on the market.

Are you curious to see actual exoskeleton torque curve measurements? Laevo has written a compact white paper about torque curve measurement using the Laevo and several other exoskeletons. If you are new to this topic, it might be a good idea to finish reading this page before reading the white paper, so you have better insight into reading torque curves and understanding the results.

2. Reading Torque Curves

A torque curve will tell you a lot about the support of the exoskeleton. The following chapters will take you through reading torque curves step by step.

2.1 The shape of the curve

The curve will tell you at what bending angle you can expect which support torque. As mentioned on the ‘Specifying Exoskeleton Support’ page, the exoskeleton with the red curve will not offer a lot of support at small bending angles. Examples like a surgeon bending over the operating table, or a factory worker assembling products over a desk-high conveyor belt: in these cases, the green torque curve, with its high support at lower bending angles, will alleviate the user a lot more.

2.2 The bending range

The example torque curves both show a bending range of 120 degrees. It is important to know this is the bending angle of the complete exoskeleton, so the angle between the torso and the upper legs around the hip joint. So, the amount the user bends his torso forward relative to his upper legs.

There are a few exoskeletons that have a mechanism that starts exerting torque at a specific bending angle relative to the vertical plane or hip angle, and not relative to the upper legs. But after the engagement, these exoskeletons will still follow a torque curve based on the angle relative to the legs.

In the figures below you can see bending angle B (beta) = a0 - a. You can see after 115 degrees of exoskeleton bending, the front of the chest and the front of the upper legs, almost touch. Therefore 120 degrees of exoskeleton bending should be enough for most workers.

Some exoskeletons have a mechanical stop at the end of the bending range, like the Laevo. Some exoskeletons will have a shorter range, limiting your bending motion up to a certain point. Others have no limit on the bending range. Therefore, it is good to inform yourself about what bending range your work requires.

But also note, a job might not generally need a large bending range, but if the user accidentally drops an object on the floor, a too-short bending range or too much support might prevent the user from picking it up.

2.3 The amount of support

It is good to ask yourself: How much support do I need? Because torque values are new to most people, users will just have to try and find out. Because when you do not know what a kg feels like, you do not know if 25kg is heavy or not. Users will have to experience different amounts of torques to experience what is comfortable for them. Of course, Laevo can advise a comfortable and effective support strength based on weight, body size, and task, and our extensive experience in the market. Laevo can also supply customers with a pack containing all gas spring strengths, so users can experience different amounts of torque. Torque curves for our products can be found at the bottom of the corresponding product pages (Laevo FLEX and Laevo V2.5).

It is good to understand that more support is not always better. There can definitely be too much support. Especially in passive exoskeletons, like the Laevo, it is important not to have too much support. Because in passive exoskeletons, we are storing energy in the exoskeleton when we increase our bending angle and get the energy back when we come back up, like a spring.

It is important to know that the energy that is stored in a passive exoskeleton when bending forward is not our own energy. Laevo has seen exoskeleton ‘experts’ make this mistake. Passive exoskeletons do NOT cost the user energy, as long as the amount of support is not too much. Technically speaking: The energy we store in the exoskeleton when bending forward is potential energy from the mass of our upper body that is being pulled down because of earth its gravity. Simply said: Our upper body ‘falls’ down when we bend forward. This ‘falling’ down of the upper body does not cost the user energy. When you drop a rock on the floor, this rock is not tensioning any muscles to do so, right? As long as the weight of the upper body of the user is enough to bend the exoskeleton, bending the exoskeleton will cost the user no additional energy!

If someone would be able to perfectly match the support of the exoskeleton to the weight of the user its upper body in all bending angles, the torso would feel weightless (like in space). Although this would be a fun experiment, this would also not be a good idea because our back muscles are also being used by our bodies to stabilize our spine when lifting heavy loads. Lifting a heavy load without tensioning the back muscles might cause the spine to buckle under the vertical load. Of course, this is hypothetical because no one has been extensively working in an exoskeleton with that high support, but researchers are warning us in advance.

Summarizing: Exoskeletons are not in a support specification race like who has the most horsepower like cars. For exoskeletons: more support is not better. Users have to find an exoskeleton with a torque curve that fits their personal size, weight, and usage requirements.

2.4 Hysteresis

Hysteresis does not necessarily need to be shown in the torque curve, but the torque curve is the best way to explain what hysteresis in exoskeleton support is. Hysteresis in exoskeleton support is the amount of energy that is lost during a supported bend of the exoskeleton due to mechanical losses in the exoskeleton. It is a variable that defines the efficiency of the exoskeleton when it comes to storing energy and giving it back to the user. Therefore, it is especially relevant for passive exoskeletons such as the Laevo where no external energy source is present.

Below, the dashed lines show example hysteresis curves below our example torque curves, and arrows are added to show the direction of the hysteresis loop. Effectively, hysteresis causes the exoskeleton to provide less support when coming back up, compared to bending down. Looking at the graph, the solid lines represent bending down, and the dashed lines represent coming back up. Hysteresis is generally expressed as a percentage defined by the energy that is lost due to friction, compared to the total amount of energy stored. You can read more about the ‘Energy Specification’ in a further chapter on this page.

Exoskeleton hysteresis mainly comes from friction. This friction can have multiple sources:

2.4.1 hysteresis In The spring

The physical part where most of the energy is stored can have a considerable amount of hysteresis. Below are a couple of spring types often encountered in exoskeletons.

• Gas springs

  Gas springs feature a relatively high amount of hysteresis because there is a lot of friction in the gas spring seals that are trying to keep the pressurized gas inside the gas spring while still allowing movement of the piston rod. The advantage is that these are relatively light for high amounts of energy storage.

• Steel springs

  Steel springs have very low hysteresis because there is only a single part that is bending. The disadvantage is their weight for high amounts of energy storage.

• Solid ‘Rubber’ springs

  Solid rubber springs have very different hysteresis properties because the material properties can be very different.

• ‘Woven’ elastic springs

  Woven springs usually are straps or cords and have relatively high hysteresis. Because when stretched, all the woven fibers slide over each other in which every sliding contact is a source of friction. 

2.4.2 hysteresis in The mechanism

A lot of exoskeletons feature a certain kind of mechanism using revolute joints and/or sliders. Every physical location where two parts are in contact while moving relative to each other is a source of friction and therefore hysteresis. Therefore, using correct bearings and lubrication can help reduce hysteresis.

2.4.3 hysteresis in the Materials used

The mechanical structure of the exoskeleton also makes a difference in hysteresis. Stiff parts can pass through forces and torques without noticeable hysteresis. Materials like fabrics always have some stretch in them, and again, because of the fabric fibers sliding over each other, fabrics that are stressed and relaxed during bending can be a source of hysteresis. Selecting the right fabrics with the correct stiffness in the correct direction can help reduce hysteresis.

2.4.4 hysteresis due to Sliding of the exoskeleton on the body

The biggest source of hysteresis can also be outside of the physical exoskeleton. If parts of the exoskeletons are sliding on the user’s body this will be a major source of friction. Therefore, it is important to design exoskeletons for minimal sliding parts on the body. For soft exoskeletons, this is a difficult task, since the entire exoskeleton is wrapped around the body, making contact everywhere and subtle sliding of parts is present everywhere when loading the exoskeleton. On the other hand, soft exoskeletons enjoy the lack of hysteresis in mechanisms, which can be a major source of friction in hard exoskeletons.

Summarizing: Showing the torque curve including hysteresis is the most honest thing an exoskeleton manufacturer can do when specifying support.

3. Torque Curve Adjustments

Most exoskeletons come with ways built in to modify their support, mainly to increase or decrease the amount of support. What is often not realized by potential users is that very different types of adjustments are used to achieve this. As will be shown in this chapter, a lot of types of adjustments have side effects that can influence the comfort and support of the user.

Modifying support means modifying the torque curve, so below some general exoskeletons adjustments are visualized through torque curves. For clarity’s sake, the hysteresis curves are not shown.

3.1 Pre-tension

Pre-tensioning is often seen in exoskeletons, especially soft exoskeletons which generally have a torque curve with a relatively linear shape like the red torque curve below. Pre-tensioning shifts the torque curve to the left, as shown in the figure below.

Pre-tensioning is almost always done to get more support at a specific bending angle. As you can see from the red torque curve, the torque has increased by about 10Nm for every bending angle. The downside is, that there is also 10Nm of torque at the 0-degree bending angle, so while standing straight. This could be experienced as uncomfortable as the user is effectively being pulled backward while standing straight. The user needs to tension his abdominals to keep the body straight or keep leaning forward a bit.

The top end of the torque curve is also shifted left, so in some exoskeletons pre-tensioning also shortens the bending range, and in others, the peak torque just increases.

3.2 Slack

The other way around is what Laevo calls ‘slack’. This is seen more in hard exoskeletons which can have more freely designed torque curves like the green one below. Introducing slack shifts the torque curve right, as shown in the figure below.

Slack can be introduced for multiple reasons. For a simple linear curve such as the red one, it decreases torque at all angles. But the most popular reason to introduce slack is to make walking with the exoskeleton easier because most trunk-supporting exoskeletons use the upper legs for support. Walking can move the upper leg upward 20 degrees, which feels very heavy if the exoskeleton is pushing the leg back down using the support torque at a 20-degree bending angle. The simplest way of getting rid of this is just starting the support after 20 degrees of bending. The downside is, you are not supported for the first 20 degrees of bending, which for a lot of users can be most of the work.

Luckily, some exoskeleton manufacturers also found the differential mechanism, which is also present in the Laevo V2 and optimized further in the Laevo FLEX. The differential allows for free walking, but also provides support at small bending angles. Ask us, if you want to know more about this mechanism.

3.3 Stiffening springs

Some exoskeletons have the option to change to stiffer springs or add additional springs to the exoskeleton. Depending on the type of mechanism this can have a stiffening effect on the torque curve, meaning the torque increases at a higher rate when going through the bend. For linear torque curves this is a great adjustment, as the torque curve effectively scales, and standing straight remains free of torque. For a more freely designed torque curve, the effect of changing spring characteristics can have very different effects on the torque curve, as the mechanisms are very different, therefore it is not shown in the graph below.

3.4 Scaling

In Laevo’s opinion, the optimal way of adjusting the amount of support is to scale the torque curve. Scaling the torque curve to the correct amount for a specific user will make the support experience the same for every size and weight of the user. Some exoskeletons use pre-tensioning or slack to change the amount of support for different users, but this changes far more than the amount alone, as described above. A heavy user might be forced to use a lot of pre-tension so he is being pushed back while standing straight, and a light user might be forced to use a lot of slack so having no support during the first degrees of bending.

The Laevo FLEX uses its Smartjoint technology to scale its torque curve when changing the gas spring to a different strength as shown below. Laevo can provide 5 different strength gas springs so everyone can find a well-suited amount of support.

4. Energy

Knowing the torque curve of an exoskeleton unlocks a further specification that Laevo feels is very important when comparing exoskeletons: The amount of potential energy that can be returned by the exoskeleton during each bend.

Exoskeletons are saving the user’s energy by relieving the muscles of the user. But what is generally unknown is that we can also specify the amount of energy saved during each bend. In engineering, energy is expressed in Joules. Using the torque curves, we can calculate the number of Joules that are saved for each bend. Even better, torque curves visualize the amount of energy returned in a very nice way.

This is because the surface in between the torque curve and the bottom axis of the graph is an accurate representation of the amount of energy that can be returned by the exoskeleton. We will skip explaining why and how to calculate the amount of energy precisely because it requires some more advanced physical and mathematical knowledge and understanding it fully does not really contribute to the point we are trying to make in this chapter but do not hesitate to contact us if you would like to learn how to do this.

We can see that the total surface below the green line is bigger than the surface below the red line, indicating a larger amount of energy can be returned by the green exoskeleton.

The difference becomes even larger when we consider a user making only small bends. Comparing the surfaces when limiting the bend angle to 40 degrees, the green surface is about 4 times bigger than the red one. So, for a 40-degree bend, the green exoskeleton will save the user 4 times more energy than the red exoskeleton while the torque is only 3 times bigger!

We should remember that saving energy is an important goal of exoskeletons and applying torque to the human body is a method to do so. Therefore, the amount of energy returned during each bend might just be an even better specification for exoskeleton support. The energy curves for the torque curves above would look like the graph below.

Just like in the torque curve graph, the bending angle in degrees is on the bottom axis, and the total amount of energy returned by the exoskeleton in Joule is shown on the vertical axis. You can see what we just noticed by looking at the size of the surface below the torque curve lines: there is about 300% more energy returned by the green system at 40 degrees, and after a full 120-degree bend there is about 50% more energy returned. This is very important to understand because both exoskeletons have a peak torque of 60Nm and a 120-degree bending range. The numbers are the same, but the torque and energy curves show an immense difference in support.

So, the torque curve is not the only specification to look at when evaluating exoskeleton support: potential energy storage also is. Again, exoskeletons are trying to reduce the energy consumption of the back muscles, and checking the surface below the torque curve is the closest we can get to the amount of energy a user can save by using an exoskeleton. Because all energy returned by the exoskeleton is energy the user does not have to put in using his back muscles.

While the energy curves show the energy being saved while using the exoskeleton, torque curves provide more comprehensible insight into the actual support behavior of the exoskeleton. Laevo believes torque curves are more valuable to know for potential users.

Again, the hysteresis curves were left out in this chapter for clarity, but hysteresis is (very) important when fully investigating an exoskeleton and its potential energy storage because the energy lost to friction is energy not used to support the user. In our torque curve measurement whitepaper, we show results of torque curve measurements on the Laevo and other exoskeletons, including energy calculations that take hysteresis into account.

5. Conclusion

Thanks for reading! If you do not have a technological background, we understand it is a lot to take in. If something is unclear, or if you have suggestions to improve this page, do not hesitate to contact us.

An exoskeleton is a product that needs to cooperate with the user's body in such a close manner that every detail matters. Laevo is also convinced that there is no universal exoskeleton. There is, however, a most suited exoskeleton for every task. Torque curves can be an important tool in selecting the right exoskeleton for a certain task, but it does not end there. The support characteristic is only one of many specifications that needs improvement. Providing clear information to potential buyers about all sorts of exoskeletons specifications is crucial to get exoskeletons accepted and adopted by all workers that need physical support.

Laevo is already working with organizations to set up exoskeleton standards and is open to collaborating with other exoskeleton manufacturers. To, for example, find ways for everybody to measure torque curves in a standardized way, fix a standard list of exoskeleton specifications everybody should use, and most importantly, find ways to select the right exoskeleton for every potential user.