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28 April

Tensegrity Explained

04 Forces, Demonstrations, IP3 04 Forces, Lego 0 Comments

There is a new internet trend called “tensegrity” – an amalgamation of the words tension and integrity. It is basically a trend of videos showing how objects appear to float above a structure while experiencing tensions that appear to pull parts of the floating object downwards.

In the diagram below, the red vectors show the tensions acting on the “floating” object while the green vector shows the weight of the object.

The main force that makes this possible is the upward tension (shown below) exerted by the string from which the lowest point of the object is suspended. The other tensions are downward and serve to balance the moment created by the weight of the object. The centre of gravity of the “floating” structure lies just in front of the supporting string. The two smaller downward vectors at the back due to the strings balance the moment due to the weight, and give the structure stability sideways.

This is a fun demonstration to teach the principle of moments, and concepts of equilibrium.

The next image labels the forces acting on the upper structure. Notice that the centre of gravity lies somewhere in empty space due to its shape.

Only the forces acting on the upper half of the structure are drawn in this image to illustrate why it is able to remain in equilibrium

These tensegrity structures are very easy to build if you understand the physics behind them. Some tips on building such structures:

  1. Make the two strings exerting the downward tensions are easy to adjust by using technic pins to stick them into bricks with holes. You can simply pull to release more string in order to achieve the right balance.
  2. The two strings should be sufficiently far apart to prevent the floating structure from tilting too easily to the side.
  3. The centre of gravity of the floating structure must be in front of the string exerting the upward tension.
  4. The base must be wide enough to provide some stability so that the whole structure does not topple.

Here’s another tensegrity structure that I built: this time, with a Lego construction theme.

Apart from using Lego, I have also 3D-printed a tensegrity structure that only requires rubber bands to hold up. In this case, the centre of gravity of the upper structure is somewhere more central with respect to the base structure. Hence, 3 rubber bands of almost equal tension will be used to provide the balance. The STL file for the 3D model can be downloaded from Thingiverse.com.

The main challenge in assembling a tensegrity structure is the adjustment of the tensions such that the upper structure is balanced. One way to simplify that, for beginners, is to use one that is supported by rubber bands as the rubber bands can adjust their lengths according to the tensions required.

3D-printed tensegrity table balanced by rubber bands

Another tip is to use some blu-tack instead of tying the knots dead such as in the photo below. This is a 3D printed structure, also from Thingiverse.

3D-printed tensegrity table held up and balanced by nylon string

(This post was first published on 18 April 2020 and is revised on 24 August 2022.)

28 April

Using Google Spreadsheet to obtain best-fit line

21 Practical / Planning 0 Comments

I am taking the opportunity (since my students are all doing home-based learning) to teach them how to use spreadsheets to do calculations and to obtain a best-fit line. While they can still submit graph work using PDF scanning apps such as Office Lens and Camscanner into Google Classroom for me to mark, they can make use of the spreadsheet-generated graph to check their results.

Even though for exams, we still require them to plot the points on paper and obtain the gradient and intercept from points on the best-fit line, nobody is going to do so when they start working. So I might as well teach them now.

Due to the lack of face-to-face time, I made this step-by-step video showing them how to do so.

28 April

Best-fit Line

21 Practical / Planning 0 Comments

For lab work, students often have to estimate a line of best fit for their data points manually. It takes a bit of practice to get it right. With this app, students can generate data points with varying types of scatter and predict their own best-fit line before comparing it with a computer generated one based on the least mean square method.

25 April

Hydraulic Press Simulation

IP3 05 Density, Pressure and Upthrust 1 Comment

This simulation can be used for O-level Physics, for the topic of Pressure. I created it as it was relevant to our school’s IP3 physics as well.

It demonstrates the working principle of a hydraulic press. By adjusting the cross-section areas (A) of the two cylinders, you only need a small amount of force at the narrow piston to exert a large amount of force at the wider piston. This is how, when driving, the force applied by one’s foot is enough to supply a large force to apply the brake pads on a car’s wheels.

The advantage of using GeoGebra is that one can create such simple simulations within a couple of hours and it can be readily embedded into SLS – a wonderful tool to have during this period of full home-based learning.