This is a case study that shows how important it is to understand the basics of Physics when you are designing IoT devices. In addition to electronics, we are actually integrating with electro-mechanical devices. It is here that we need to understand concepts such as Torque, Force, etc.

The Author

Srinivasan holds a Bachelor’s Degree in Electronics and Communication Engineering from Anna University-Chennai, a Master’s Diploma in Business Administration [MDBA] from Cambridge University, and has received his Indian Management Fellowship [IMF] from Cambridge University as well. An Embedded product design strategist and technology evangelist at heart, Srini heads the Industrial Automation Center of Excellence at Sosaley Technologies.

Sosaley Torque Calculation

As we mentioned elsewhere, we have started a long term association with one of India’s leading kitchen appliances manufacturer. The objective is to introduce IoT in as many kitchen appliances as possible, and help the client design and manufacture new products that are IoT ready and compatible with mobile phones.

One of the first projects we have begun is to introduce IoT to the ubiquitous domestic gas stove. Even assuming that just 10% of the Indian population uses these stoves, we are looking at a user base of nearly 100 million!!

The Beginning

As we start this project, one of the first needs of the hour is to introduce a motor that can replace the knob that is manually turned to increase or decrease the gas flame.

There are a large number of other factors such as power, a spark to light the gas, heat dissipation, etc. In this article, we will focus on introducing the motor. We will write about others as we work on them.

The Objective

The objective is to remove the manual knob and use the smartphone to control the flame size. On the smartphone, a simple slider control image will be displayed. As you slide your finger clockwise, the flame on the gas stove will increase. When you slide your finger anti-clockwise, the flame will die down. The communication between the smartphone and the gas stove will be either Bluetooth or WiFi.

On the gas stove, the motorized knob will ape the smartphone control action and, in reality, increase or decrease the gas flame.

The Challenge

The challenge is quite simple actually but proved to be tough to resolve. The challenge is to estimate the amount of rotational torque needed to turn the valve that controls the gas flow. The degree of rotation will be provided by the app on the smartphone.

Additional Challenges

As we started working with the client, he threw a few more googlies at us. He has set up a number of conditions that will have an effect on the design.

  1. Low cost. The final cost of the IoT hardware and software has to be kept as low as possible. The idea is to make this revolutionary change available to every household. Today, literally everyone uses a smartphone. So why not a gas stove that can be controlled by the smartphone?
  2. To be sized to fit the existing stove frame(s) without any modifications to that.
  3. Highly degree of accuracy and precision allowing the user to set the flame level at his or her choice.
  4. Should have manual control in case of failure of the IoT system.
  5. To attempt at retrofitting. It should be possible for an existing stove owner to get the IoT system retrofitted at a service station.

Design Methodology

Usually, one would speak theory first and then, look at the practical aspects of the theory. But, here, we are going to do just the opposite. Based on experiments conducted in the office, we suggested a small range in torque needed for the motor. This was contested by the client based on his long experience. We then had to necessarily get down to basic theory and arrive at a figure that was fairly accurate and acceptable to the client.

The Practical Analysis

In the first trial and error on the workbench, we programmed a low-cost DC motor with a torque of 1.37 Newton meter (1.37Nm) at roughly 3000 rpm. We realized this was unable to rotate the valve knob. So we coupled a gearbox to understand the exact torque needed. With the gearbox, the motor delivered a torque of 1.6Nm – roughly 16kg to the centimetre. This proved just enough to rotate the valve’s knob.

But the motor also decided to throw a googly at us. When we applied power multiple times, we saw the motor rotating to different angles (as one position to another in a 180-degree table). As we said before, accuracy was paramount. The motor simply had to deliver the exact same degree of rotation for the same power applied, irrespective of how many times we did it.

Another issue we faced was that the rotation did take place when driven by the motor. But when we tried to use the manual knob, the whole motor started turning. We were forced to introduce a loop holder between the shaft and the manual knob. This was more a mechanical headache that is not too relevant to this discussion on torque requirements.

The Stepper Motor

After a lot of tinkering, the DC motor with the gearbox and loop holder did do its job. But we were unhappy with its accuracy, noise, and the possibility of sparks coming from the motor.

We decided then to try out a stepper motor. This meant a tradeoff in terms of cost. What we were looking for was a motor that could move 1.8 degrees clockwise or anti-clockwise for a certain quantum of power supplied to the motor. In other words, we were looking at breaking the 180 degrees movement of the valve shaft to 100 possible positions.

We began our quest with a commonly available stepper motor. This had a low torque of 0.26Nm. This refused to move the valve knob.

After doing some simple maths on torque, cost, accuracy, and size factors, we concluded we needed a stepper motor that could deliver roughly 2Nm of torque.

The Shock

At this juncture, just when we were happy that we had the results, we did not realize we were in for a shock.

We took our calculations and results to the client. After all, his concurrence is mandatory, is it not? He came back to us that we do NOT need a torque of more than 0.5Nm as that is what they have been using and measuring all their lives.

What? 1/4th of what we concluded we needed? This left us scratching our heads in frustration. This was when we decided a theoretical understanding of Physics was essential that could support our claim of 2Nm.

Before we move into the theory part, let us state our conclusions based on the simple experiments we did.

Sosaley’s Practical Measurements & Conclusions

  1. A geared DC motor of 1.5Nm (or 16Kg-cm) was capable of rotating the knob.
  2. A commonly available stepper motor with a torque of 0.25Nm cannot rotate the knob.
  3. The ideal stepper motor should have a torque of 2Nm. Even though 1.5Nm is sufficient, a higher value would mean longer life for the whole system. We are assuming that the motor’s energy delivery would degrade with time.

Theoretical Analysis

We first decided we must understand the system the client was using for measuring the torque. We saw that they were using a long tool to hold and rotate the knob during measurements. This was surprising to us. The long tool was acting as a lever and reducing the input force needed at the fulcrum. In our case, the fulcrum is the centre of the axis of the shaft mounted on the valve.

For understanding this in simple terms, let us take the case of a door. Try opening and closing the door using the handle at the end of the open side. Now try opening and closing the door using force nearer the hinge. You will see that you need a much higher input force to open and close the door.

In our case, we are connecting the motor directly to the ‘hinges of the door’. The coupling is the motor equivalent to the hinges of the door.

Defining and Calculating Torque

What is torque? Torque is the force that rotates an object on its axis. Torque may also be called a moment of force. Force is generally understood as the amount of energy need to push or pull. In a circular motion, the energy is needed to twist or turn, and this is called torque.

Mathematically, Torque is defined as the product of the force (F) and the displacement vector (r)

T = r F SinA


T represents Torque
r represents the distance (or displacement) vector
F represents the force
A represents the angle between the displacement and force vectors.

In our case, we will replace A with Sinθ

T = r F Sinθ


r represents the radius or length (the same as displacement vector). This is a constant factor.
F represents the force
Sinθ is calculated for any value of θ from 0 to 360 degrees. This value is also considered as constant. Let us call this as ‘c’.

Now let us use this formula and introduce lever as a factor. The equation explained above has multiple values, some of which are known and some unknown. Let us extrapolate the equation to place the value we need on the left-hand side.


F = T / r sinθ
T/F = r Sinθ

We had originally defined Sinθ as ‘c’, a constant between 0 to 360 degrees.


r Sinθ = r*c = C where C is a factor between torque (T) and force (F)

T = C times (F)

Now, C becomes directly proportional to torque & inversely proportional to force.

If C increases, F decreases. If C decreases, F increases.

F = T / C

If C increases, T increases.  If C decreases, T decreases.

Torque = T = FC

In our particular case, the client uses a lever (r) that is 170mm long.

C = rsinθ and r = 170mm

Torque = 170FSin90



We calculated and created a table where we inserted the known values to arrive at the unknown values.

We first kept the lever at a constant of 170mm. We then calculated the force needed for three angles of turn of 5, 10, and 15 degrees. For each of these angles of turns, we started with 0.2Nm and increased the torque to 0.5Nm in steps of 0.1Nm. With these input values, we calculated the force needed.

r or L in mmAngle Of Turn (θ)SinθTorque (Tau)Force Needed
1705 degrees0.087155780.20.01349848
1705 degrees0.087155780.30.020247721
1705 degrees0.087155780.40.026996961
1705 degrees0.087155780.50.033746201
17010 degrees0.1736482510.20.006775021
17010 degrees0.1736482510.30.010162532
17010 degrees0.1736482510.40.013550042
17010 degrees0.1736482510.50.016937553
17015 degrees0.2588191530.20.004545531
17015 degrees0.2588191530.30.004545531
17015 degrees0.2588191530.40.004545531
17015 degrees0.2588191530.50.004545531

With C (rSinθ) being constant, as torque is increased, the resultant force also goes up.

Now we come to the interesting part. Let us keep all factors constant, and decrease the lever length.  With that, let us see what happens to the torque and force requirements.

What we did in the following table was to, first, take the row containing a torque of 0.2Nm from the above table for each angle of turn. With all factors constant including force needed, we reduced the lever length or displacement vector to 100, 50, and 2. We then recalculated and looked at the resultant torque and C values.

Angle of turn (θ)Sin(θ)R or L in mmFTT/F (or C)T Ratio


It is abundantly clear that as you reduce the displacement vector, the resultant torque goes down dramatically. In the table above, using the first row as the base, when we reduced the displacement vector from 170mm to 2mm, the resultant torque falls to just 4%.

In other words, when you go closer to a displacement vector of zero, you do a need much higher torque to turn the knob to the same degree.

The client had arrived at a max torque of 0.5Nm using a displacement of 170mm. Our stepper motor has to have a displacement of zero as it is mounted directly on the valve shaft. Using gears to enhance the energy delivered by the stepper motor, our conclusion of 2.5Nm is perfectly correct.

We have convinced the client of this calculation, and we are now moving forward in fine-tuning the stepper motor mounting and the connection methodologies. We reckon we will need to use a torque anywhere between 2.0 to 2.5Nm to achieve a uniform and dependable movement of 1.8 degrees clockwise and anticlockwise. That is our target.

In school and college, I used to spend a lot of time understanding every formula in detail. I used to be mocked by my classmates. But that did not stop me from working on understanding the basics of Physics. Today, it feels nice to know that all that hard work is getting implemented on patentable and commercial products.

Kudos to science and technology that give us an adrenaline rush when we solve such issues.