Scraps and Physics of a Tensegrity Structure

TABLE OF CONTENT

Scraps and physics of a Tensegrity System

INTRO: Scraps and physics of a Tensegrity System

STEP 1: A little history

STEP 2: Materials

STEP 3: Copyrights

STEP 4: Two conditions of equilibruim

STEP 5: How it works

STEP 6: Construction

STEP 7: SIzing up and inspection

STEP 8: Rope making

STEP 9: First prototype

STEP 10: Abandoning the status quo

STEP 11: Final thoughts

Scraps and physics of a Tensegrity System

Floating tables are quite awesome especially with an illusion effect. They look crazy because at first glance, it seems like the table is standing up on nothing, more or less levitating in space but a closer look its on strings instead of on solid legs. Which is impossible, seems impossible, sounds impossible and looks damn outright impossible, right?

There is nothing magical about it, it’s just plain physics. A floating table is an example of a tensegrity system

Step 1: A Little History for Clarification

The word TENSEGRITY is a design principle that applies when a discountinous set of compression elements is opposed and balanced by an internal prestress that stabilizes the entire structure. This was a term coined by Buckminster Fuller an iconoclastic architect, engineer and poet to describe his vision of a new kind of architecture one that looked like it was built by nature instead by humans

Step 2: Materials

this build is actually tailored as an educational experimental work repurposing left overs into useable stuff we will be using:

• left over wood 1by1 inch (9 inches in length)
• scraped out hot glue from electronic boards
• left over nylon cable
• soldiering iron
• tape
• thumb pin
• hammer

Step 3: Copyrights

I WANT TO STATE HERE THAT MY INSTRUCTABLE IS BASED AND BUILT AROUND THE WORK OF RHETT ALLAIN . ALL THE WRITE UP AND THE PICTURES OF STEP 4 AND 5 HEREIN ATTACHED ARE ALL WORKS OF THE AUTHOR IT IS NOT MINE AND I DO NOT CLAIM OWNERSHIP OF HIS WORK PICTURES AND INTELLECTUAL PROPERTIES SITED HEREIN. ALL WORKS OF THE AUTHOR EXPRESSED HERE ARE FOR KNOWLEDGE AND LEARNING.

STEP 4 and 5(Rhett allain 2020)

Step 4: Two Conditions of Equilibrium

If an object is at rest (meaning that it’s not accelerating), we say it’s in a state of equilibrium. This means that the following two conditions must be true..... FIG 1

The first equation says that the total force on the object (Fnet) must add up to the zero vector. Yes, force is a vector meaning that it’s defined in more than one dimension), as indicated by the arrow over the symbol. Same for the zero vector, which just means that the total force has to be zero in all directions.

The second equation is a little more complicated. It says that the total torque (τnet ) about some point o (whatever point you want) must add up to the zero vector. These two zero vectors are different in that they have different units—newtons for force and newton-meters for torque.

Torque is complicated, but here you can just think of it as a "twisting"
force. The value of a torque depends on the value of the force applied and where it’s applied. Here is a simple example. Suppose you are pulling on the handle of a wrench to tighten a bolt, like this....... FIG 2

This would produce a torque (around the bolt) in the clockwise direction with a magnitude of FIG 3

Here F is the force applied, r is the distance from the axis of rotation, and θ is the angle at which you pull. (If you pull straight down here, sin 90° = 1 and this simplifies to τ = Fr.)
So, there you have it. That's torque. If an object is in equilibrium, then the sum of the clockwise twisting torques must be equal to the counterclockwise torques.

Step 5: ​How It Works

Now, let's see how this idea of equilibrium works with the floating table. Here is a simplified side view of the structure, along with a separate diagram of the forces just on the top part FIG 4

You can see three forces acting on the table. The first is the downward-pulling gravitational force (mg). Although the gravitational force interacts with all parts of the tabletop, it turns out it's equivalent to having just one force located at the center of gravity (derivation here).

The next force is labeled T1. This is the upward-pulling tension from the blue bracket. The upward tension in this string in the middle is what holds the whole thing up. Finally, there is another tension, labeled T2. This is a downward-pulling force.

Yes, you have to pull down here to keep the table upright; otherwise it would tip over to the left. (Really, there is another downward-pulling string on the right side that you can't see in this view, but we can just combine the two for the analysis.)

Now, we want the top piece to be stationary, so we can put these forces into our equilibrium equations. Since these three forces are all in the vertical (y) direction, we can ignore the horizontal (x) dimension. That simplifies things. Here are the total forces in the y direction.....FIG 5

Really, this doesn't tell us much. All it says is that the upward-pulling tension has to be equal to the two downward forces (gravity and the other tension). But what about the sum of the torques? If the object is in equilibrium, you can pick any point on the object to calculate the torque. I'm going to pick point o, where the upward-pulling string is attached. And I’ll say clockwise torques are negative values and counterclockwise are positive.

To get the torque resulting from each force, remember that τ = Fr. But since the distance (r) for T1 is zero, this tension results in zero torque. So now, with only two other forces, the only way for their torques to offset is for one to pull clockwise and the other to pull counterclockwise. T2 is pulling down on the right side, which creates a negative torque around point o of T2 r2.

But the gravitational force mg also pulls down—we can’t change that. That means the center of gravity of the top platform has to be on the other side of the central support string. So here’s our equilibrium torque equation......FIG 6

That’s the key to the whole thing: The center of gravity of the “floating” tabletop and the downward force T2 need to be on opposite sides of the central suspension string.

Step 6: Construction

The construction was quite simple and straight forward. Armed with the understanding of the previous chapter The piece of woods were virtually arranged to simulate the final build and before being glued together.

PROCESS:

Using my soldiering iron i melted the scraped out glue to join the wood together. The process involves heating the glue till its all liquid then attach the parts together applying a little pressure to remove air pockets and ensure proper surface to surface bonding. The excess glue that overflowed as i applied pressure was later melted around the joints to serve as a brace.

since i didnt have a plum or set square i used the remaining pieces of wood as a rig to ensure proper positioning. And it turned out pretty well.

Step 7: Sizing Up and Inspection

I must say that there is no official measurement or proportion used here besides the length of the left over woods. I decided to work on a free hand with out conformity to show how one can easily replicate a tensegrity structure with out much stress.

It would be nice to note that from my images i made the base alot bigger for balance, since i was not working with any measurement or ratio.

Step 8: Rope Making

The rope i used for this instructable was the remaining rope from my cloth hanger. Untwine the bunch and test the tread for its tensile strength.

PLEASE DO NOT PULL OR TUG ON A NYLON ROPE IT CAN CAUSE SERIOUS INJURES. I SHALL NOT BE HELD RESPONSIBLE FOR ANY INJURY CAUSED BY THIS ACT. WEAR PROTECTIVE EQUIPMENT.

The single strands did not hold up, 2 strands held but strained as i reached the elastic limit so I decided to bunch 4 strands tied of at the two ends to avoid fraying to form my ropes.

Step 9: First Prototyping

Assembling the tensegrity structure with out an extra pair of hands can be quite difficult and since i used glue any fall can mean a broken arm at this stage.

i used the thumb pin to create attachement points for the thread based on the original layout and other possible atleration points.

since i did not have more wood to build a scafold for the structure to rest on i had to improvise.Hanging the center piece and balancing the top, i put some of the remain bits of wood under the top arm tied up the frist rope before securing the second rope.

N/P i didnt tie off the ropes since i was planning to alter the basic structure as we know it. i used tape to hold the ropes after harnessing on the thumbpin.

Step 10: Abandoning the Status Quo

I also tried out other possible construction of the tensegrity structure making sure the center of gravity is on one side while the force is on the other side. I attached thumb pins to many points were i observed could serve as the point of force application to balancethe structure.

I will like to state here that i found out quite a few points to alter the structure effectively.

using my hand drill box to apply a significant stress on the system, i observed that the structured held and didnt buckle with some touch and shakes.

OBSERVATION: i did notice that the forces at work her can be categorised into three. The first two are the anticlock wise force which is located at the arms in the center while the clocwise are located at the forks. the third force is more like a stability force which helps to maintain inertia and structural intergrity.

Any attempt to alter the position of the force acting in the clockwise direction transfers the line of the force fron the strings of the acting force to the strings of the inertia force on the system

any attempt to focus the line of forces (clockwise and inertia force) acting on the structure to a point leads to unstability. the two forces counteracting the anticlockwise force can not me made to have a single point of origin at the same time but can happen alternately

Step 11: Final Thoughts

You can pull strings to make something happen............, but everyone agrees that pushing on a string is futile. ---RHETT ALLAIN

Its very interesting toying around with the tensegrity structure. A better structure can be made using screws as fasteners. I used up alot of the scrap glue which i had slavaged from circuit boards and a single fishing rope can also be used for easy attachment and above all for estatic purposes.

if you like my work i will surely appreciate a vote also feel free to ask any question in respect to the alterations i made to the structures. stay safe................

Step 12: Possible Modes

i have some scraps from the xmas hat and a broken liquid soap dispenser. the plan is to disassemble the dispenser attach a rope to the pump. the idea is for the unit to rock as soon as you try to touch it and the lights will also flicker