Eight segment kinetic chain

With some doubting / fighting the existence of kinetic chains it is perhaps useful to simply look at nature and see what it has to teach us mortals often so readily enthralled by our knowledge and technology. To that end I can conveniently use a program I have developed some time ago, simulating flexible beams with multiple linked segments.

I have arbitrarily chosen segments of equal length of 1m, connected with revolute joints. Overall maximum length hence 8m. The mass for the inner segment is arbitrarily chosen to be equal to 1.28 kg, with each segment half the mass of the previous one. Hence, successively, 1.28, 0.64, 0.32, 0.16, 0.08, 0.04, 0.02, and 0.01 kg for the most distal mass.

As shown in Fig1 the ensemble is simply dropped from the position shown, no external torques applied, just letting nature do its own thing and hence having gravity do its job on the ensemble of segments. Notice how the inner segments race ahead initially but then progressively wait for the the more distal segment to catch up to them to eventually form an almost perfect in-line position.

Notice how nicely the segments reform almost a straight line, corresponding to maximum distal end speed, similarly as in a golf swing when left arm and club align. It is truly remarkable the very high velocity obtained by the tip, 329 miles/hour - with only gravity force acting on the eight segment pendulum, see Fig2.

From Fig3 one can readily observe some essential features -

- A sequential motion where starting form the center sequentially elements reach a certain maximum velocity, and hence a maximum kinetic energy, and subsequently giving it up mostly to the next adjacent segment.

- The amount of kinetic energy flowing down to a more distal segment increases steadily till there is a very large transfer to and an almost explosive action of the most distal segment - a rather whip like behavior.

Notice that deceleration occurs in sequence for each segment without any external braking force applied. Some seem to have the impression that an external braking force/torque is required to initiate/maintain the sequential kinetic energy transfer. But is clear from above that all this takes place here automatically.

A golfer also consists of various linked segments but forming a complex ensemble in 3D, with the additional complexity of torque motors throughout. The main problem however is that each golfer is unique and therefore basic notions universally valid for ALL golfers are likely difficult to establish.

Nevertheless nature's inherent DNA seems to show clearly that it knew about kinetic chains long before it became a matter of existential debate between posters on various golf forums. The concept of kinetic chain seems to me to be a matter of common sense. You crawl before you walk and walk before you run and similarly nature seemingly invites us to progressively build up distal speed.

mandrin