A theme that keeps coming up in any discussion of motion is the flow of force and energy. Sometimes this is surprising, because our conscious minds tend to focus on task oriented and position oriented aspects of motion – “I’m going to reach over here, grab the cup by the handle, and carry it over the table on the other side of the room.” Yet, given these high level positional and task level goals, the ultimate execution of these actions is entirely dependant on the management and control of forces, both internal (how force flows through your body to the ground) and external (the force of contact between your hand and the cup.) And, of course, these two aspects interact – the weight of the cup imparts a force into your hand that must flow through your body to the ground.
This last point is critical! Any force applied to your body – be it something pushing on you, or you pushing on the world (lifting a box, pushing a door, etc) must flow through your structure to the ground. The total amount of incoming force has to equal the total out-flowing force. Any imbalance between these two will cause motion. While motion is often the goal, it is important to understand the static flow of force in your body. It is this physical reality of forces needing to ground out in contact with the environment in some way that leads to the study of long kinematic chains of muscles in the body. If you have really strong arms, but weak stomach muscles, you might be able to bench press a heavy weight, but when you try to lift a similar weight while standing you could hurt your back due to your inability to control the forces that need to flow from your upper body through your core and legs and out to the ground.
I once saw an excellent visual example of this when I was visiting my Masters Advisor at Stanford, Oussama Khatib. He at the time he was working on a simulation environment to study how multi-point contact dynamics and forces propagated through humanoid robots. He showed me a simulation of a humanoid where you could drag the robot around into any pose you wanted and then “push” on it. As you did so force vectors at the feet would show you the reaction force from the ground. This was great! Playing with it you could see how leaning the robot one way or the other would cause more force to flow through the left or right foot. Likewise, push on its arm and you could see in real-time how the forces at the feet would shift. Every part of the body between the applied force and the ground contact has to be strong enough to transmit that force, or damage occurs. Good motivation to go out and get some exercise!
So, how do forces flow through a structure? At the end of the day, there are really only two types of forces that exist: compression and tension – or push and pull. All other mechanical forces (shear, bending, etc) are made up of a combination of compression and tension forces. As a simple example, hold a rod in your hands and bend it slightly. That bending action is actually the result of compressing one side of the rod, while putting the longer side in tension.
A lot of structural engineering focuses on the compression forces. Think of a medieval cathedral with the flying buttresses – those buttresses are placed to provide support to hold the walls and roof up. You can look at them and just “see” how the forces are flowing out towards the ground.
Most houses are built with framing and posts and beams that pass the force along in a compressive manner. This makes sense since houses are (normally) always in a single relationship with gravity, so you can predict where the forces will flow. But this gets more difficult to do for some structure that will experience a wide range of forces. If you built a sailboat with a mast that could withstand all the forces that the sail will impart on it as it is blown from many directions, you would have to build a very think and heavy mast to avoid it bending with the wind. Many sailboats are built with stays – high-tension lines that run from the mast down to the deck at an angle. This is an example of separating the compression and tension forces into separate structures. This allows the mast to experience just the compressive force, while the stay lines carry the tension. By separating the structure this way, the mast does not experience as much bending and can be built in a lighter and more efficient manner.
The fullest expression of this separation between tension and compression forces is called a Tensegrity Structure. What is unique about the tensegrity structure is that every structural element experiences either pure tension or pure compression, without any bending or shearing forces. Another interesting quality is that there is no continuous chain of compression elements. The flying buttress is a continuous chain of compression. Even the sailboat, which has some similarity, experiences a line of compression from the mast into the deck of the boat, which itself anchors the endpoints of the stays. Rather, in a tensegrity structure, the continuous chain of forces is held in the tension elements and the compression components are separate islands in the network, not touching each other. In fact, this is where the name comes from as coined by Buckminster Fuller: a combination of ‘Tension’ and ‘Structural Integrity.’ This gets at the root concept that the stability of the structure ultimately derives from the integration of the tension members. The result? Beautiful and odd art where metal rods just float in space, held in place by cables under tension.
You can see here that there is no continuous chain of compression like you see in a cathedral with flying buttresses. You also find elements of tensegrity structures throughout many large modern buildings that take advantage of tension lines to suspend and support large span domes and buildings which need to survive the wild forces of earthquakes. In general though, the concept is surprisingly new having first been explored by Buckminster Fuller and artist Kenneth Snelson in the 1960’s. Fuller is best known for his geodesic domes, which he developed based on concepts explained and demonstrated by Snelson through sculptures such as his 18 meter high Needle Tower built in 1968.
I’ll be going into much more depth about tensegrity structures in future posts, because they turn out to be very valuable tools in understanding and modeling the exact geometric distribution of pure compression/tension forces in a structure. Tensegrity structure analysis will help to visualize that earlier question of how exactly the forces in a human body propagate from the hand holding the box all the way down to the feet where they ground out. But it gets even more exciting than just modeling tools! It turns out that tensegrity structures are an excellent design choice for a structure that must move and exist in a complex dynamic environment, where the experienced external forces can come from any direction and must be handled robustly. And, there is a growing body of evidence that biological systems are built around tensegrity principals, starting at the cellular level. In fact, it turns out that the bones on humans and mammals don’t pass compressive force to each other; rather, they are suspended in a tension network of muscles and fascia in a tensegrity design. This concept is called Biotensegrity, and was first put forth by Dr. Stephan Levin and advanced deeply in collaboration with Tom Flemons. There is a lot more to be said about their work, and the implications to our understanding of human motion, healing (body work), and the design of future robots and control systems.
UPDATE Oct 2012 To see some of my recent work on tensegrity robotics, see my post on a robotic tensegrity snake, development of a tensegrity based planetary lander, and a video of a lecture I gave in Switzerland.