Mittwoch, 4. November 2020

Closed kinematic Chains

It's a long text about,
  • what closed kinematic chains (ckc) are
  • why the ckcs in the horses hocks (Spannsägenkonstruktion) as well as those in the human body are not part of a lever system. 
  • how a new perspective shows the integration of ckcs in the tensegral structure.
  • what indicates that Newton's laws according to mechanical functioning have been misapplied in respect to ckcs in a living body for a long time.
  • how closed kinematic chains act and interact in planar and omnidirectional movements in tensegrity models
  • how to understand, grasp and feel the physics* of lever-free movement, even if the associated mathematics is a mystery to you.
  • how the motor safety systems in the body can be supported or interfered, activated or suppressed.

1 What is it all about?

A kinematic chain is a power transmission system that in its simplest form consists of bars and joints, some fixed somewhere and some not.

A closed kinematic chain is created when the first and last links of the chain are also connected to each other.

In a closed kinematic chain, the movements of the individual elements regulate each other. The limitation in one joint automatically limits the range of motion of the other joints. Effect on one element acts on all elements according to their arrangement.

Figure 1.1
A closed kinematic chain with three elements (3-bar-chain, Figure 1.1) is a stable, rigid triangle. The shape is determined by the length of the bars, but even with free joints it's configuration doesn't change. It is wonderful to build a model from children's toys.

Figure 1.2a
A closed chain of five or more elements (multi-bar chain) is hypermobile, so to speak, and there is no controlled mutual limitation. This can be observed well on a bicycle chain, but can also be tested on children's toys. (Figure 1.2a&b)

Figure 1.2b

Figure 1.3
In a closed kinematic chain with four elements, there is mutual control, because each element limits the movement of the other elements. This regulation results from the structure and not from an active application of force! The structure-immanent control systemof a 4-bar ckc thus offers a certain degree of movement security and protection against "erratic" movements (Figure 1.3a-c).

Figure 1.3b
Figure 1.3c
This mutual limitation refers, as mentioned above, to planar movement, which means that each element remains on its own plane (in children's toys, the elements move in different parallel planes, but do not switch or rotate them).

The heart painting pantograph shows a closed kinematic chain in action, the video shows the children's toys in motion:

2 What happens during spatial observation?

The closed 4-bar model, now with spatial joint freedom (Figure 2.1), suddenly gains a lot of mobility and the widened range of motion weakens the system-immanent control. The rods can twist against each other in such a way that the rods touch each other and, if there is enough energy in play, can also damage each other (Figure 2.2) or collapse, as shown in Figure 2.3.

Figure 2.1
Figure 2.3

Figure 2.2

The closed 3-bar chain also gains mobility by moving in space, but retains its shape. If one wanted to make the 4-bar system controllable by restricting the joint angles while allowing free spatial mobility, shear forces would be generated by external influences (the child's toy would break if the appropriate force was applied).

3 Closed kinematic chains in tensegrity models

Figure  3.1                                                 (c) Maren Diehl 2020

Figure  3.2           (c) Maren Diehl 2020

Figure  3.3             (c) Maren Diehl 2020

At  first sight  Figures 3.1 and 3.2 consist of a combination
of 3- and 4-bar elements.

However, a closer look reveals that the 4-bar module is none,
because the rod in the middle turns the 4-bar module into two
3-bar ones (Figure 3.3).

Figure  4                                                   (c) Maren Diehl 2020

4 The volume

As hopefully can be seen in figure 4, the change of the whole is mainly achieved by changing the spatial position (rotation) of the 3-part modules. These do not change their size (if the model is properly made with cord rather than rubber band), but they are able to change their orientation in relation to each other. This changes the volume of the model, which thus can expand and contract omnidirectionally.

The volume of the body changes without any of its parts changing their length or area! 

These models are not models of biological structures, but tangible, graspable representations of the forces acting in biological structures. In natural living structures the same principles are found and the same forces are at work, but in an unmanageable variety.

The infinite variability of the geometry holds an enormous potential for change and reaction with minimal stress on the material. No levers, no strain, no shear stresses.

5 Stable or unstable? - The theory of stability

"Mathematical stability theory deals with the development of disturbances that occur as deviations from certain states of dynamic systems. (...) A system is unstable when a small disturbance leads to large and resounding deviations." (Wikipedia)

An open kinematic chain can be compared to the  flicking tail of a horse, where a spatially limited energetic movement at one end produces a high deflection at the other end. An open kinematic chain represents an unstable system.

Closed kinematic chains, and in particular the spatially interconnected kinematic 3-chains in tensegral structures, form a self-controlling system that always returns to its energy-efficient normal state or switches between two equal (in respect to the energy-efficiency) states. Although it can move as a whole in space and change its shape and orientation, it does not lose itself in the amplitudes of movement.

The description of the (human) body as an open kinematic chain, which is common in the literature of human biomechanics, ignores the fact that the tensgral structure of the body consists of very, very many nested and interconnected closed kinematic chains. By this arrangement, an energy-efficient control of all parts, their relation to each other and their movement in space is possible.

An unstable system is uncontrollable and erratic in its reactions to the forces acting on it. This can be seen, for example, in the hypermobile horse that becomes justifyable anxious about the loss of control over its own body. A system that is unstable as a whole is is unsustainable for any organism. 

A functional system, maintaining suitable stability and flexibility in any situation  must be able to switch/change the interactions and configurations of its internal ckc-system holistically.

Degeneracy, the possibility of different solutions to the same problem... Patterns, switch without effort...

Himmel und Hölle

LEVERS? Where are the levers?

6 Action

Here we enter the realm of experience and observation, of experimentation.

If, after all, all people are constructed in the same way, if all horses consist of approximately the same parts, where do the big differences in stability, resilience, motor control and movement competence come from?

If it cannot be due to the architecture, then what is the reason? My observations always lead to the point that the "right spirit", the active and joyful confrontation with external forces, the will to survive or to save others, the ability to "get the whole team to the start" make the difference.

According to Gerald Hüther, the brain researcher, "attitude", i.e. the right spirit, is a meta-concept that has evolved from experience. The physical system also requires a wide range of experiences to develop a healthy attitude towards life and is certainly also a metaconcept

According to my observations, the chains can be switched on by the "Call for ACTION" and switched off by blind confidence, putative security and the absence of need for action.

The chains are switched off by the illusion we know what is next, we know how the world goes and how it will go. They are switched off by the illusion of safety and stability that doesn't exist in real life.

The longer we live with these illusions, the harder the impact of the wake-up call will be!

Whoever or whatever gives a good reason to become active, sets a training stimulus. Those who demand "the right thing" in the sense of a doctrine that tries to create stability by creating stability usually short-circuit the system. In the cage of "trying to do everything right", the body seems to stand on the accelerator and brake at the same time or work with a burning slipping clutch.

7 Antifragility

In his book on antifragility, Nassim Nicholas Taleb describes the ability to grow in resistance, to win by failure and to become stronger under pressure. 

According to him, the opposite of fragility is not robustness, because it cannot be impressed by external influences. Therefore, he invented the term antifragility to describe systems that become stronger, more flexible, more capable of action, more efficient, etc. due to stress, unforeseen events and the unpredictability of life. The book is very comprehensive, I have only half read it, but the insights it provides are already priceless.

Antifragility is a characteristic not only of individuals, but also of societies, companies, states, associations. Antifragility thrives on unpredictability, as opposed to fragile systems that are based on security and predictions based on past events. 

The try to make fragile systems stable leads to a final breakdown, while training antifragility works with small incidents and failures, which makes the system able to handel even "black swans".

Those who, like me, consider antifragility a desirable quality apprechiate real life as a training stimulus. Mostly.

8 No end in sight

With this I have covered a wide range of topics from kinematic chains to tensegrity models, stability theory, movement competence and antifragility. All these aspects lead to numerous other questions that we can regard as antifragility training for the brain:

  • IF tensegrities are composed of closed kinematic chains...
  • IF this way of construction is one of the foundations of the "wisdom of the body"...
  • IF our didactic approaches short-circuit these links...
  • IF blind trust and detachment break these links...
  • IF modern horse dressage creates an unstable system that can only be controlled with a lot of force...
  • IF the body is forced by general ideas of movement to provide levers where nature has not provided any...
  • IF in the system of dressage training the inherent safety and control system of the body is replaced by external control...
  • IF, in the pursuit of security and stability, we unfortunately create fragility...
... then we have once again opened a box that can no longer be closed.


* Physics: The working method of physics consists of a combination of experimental methods and theoretical modelling. Physical theories prove their worth in application to systems in nature by allowing predictions of later states when their initial states are known. Progress in knowledge results from the interaction of observation or experiment with theory. A new or further developed theory can explain known results better or even explain them for the first time and, in addition, stimulate new experiments and observations whose results then confirm or contradict the theory. Unexpected results of observation or experiment give rise to theory development in various forms, from gradual improvement to the complete abandonment of a theory that has been accepted for a long time. (Wikipedia)

Keine Kommentare: