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Flow of trigonometric calculation for the formula of the voluntary movement

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Published on Sep 19, 2014

I share the flow of trigonometric calculation for the mathematical formula of basic mechanical linkage for the voluntary movements of animals in the nature.

## Flow of trigonometric calculation for the formula. ###

A = 1.0

α1β1 = A * 0.5

α2δ1 = A
α2γ1 = A

β1γ1 = A

α1δ1 = (A - α1β1)
α1α2 = sqrt(α1δ1**2 + α2δ1**2)

B = (α2γ1**2 + α2δ1**2)

γ1δ1 = sqrt(B)
β2γ2 = sqrt(B)

C = B

γ2δ2 = sqrt(C)
β3γ3 = sqrt(C)
γ1γ2 = C + sqrt(C)
β2δ1 = C + sqrt(C)
γ2γ3 = C + sqrt(C)
β3δ2 = C + sqrt(C)
γ3γ4 = C + sqrt(C)

deg_α2α1β1 = - rotation.x*180/math.pi

rad_α2α1β1 = deg_α2α1β1/180*math.pi

deg_B = deg_α2α1β1
rad_B = deg_B/180*math.pi

α2β1 = sqrt((α1α2**2) - 2*α1α2*α1β1*cos(rad_α2α1β1) + (α1β1**2))

### α2 ###
α2 = mathutils.Euler((0.0, 0.0, 0.0), 'XYZ')
###

### α1 ###
α1 = mathutils.Euler((α1α2, 0.0, 0.0), 'XYZ')
###

### β1 ###
β1 = mathutils.Euler(((α1α2 - α1β1*cos(rad_α2α1β1)), (α1β1*sin(rad_α2α1β1)), 0.0), 'XYZ')
###

### γ1 ###
rad_γ1α2β1 = acos((α2β1**2 + α2γ1**2 - β1γ1**2) / (2*α2β1*α2γ1))
deg_γ1α2β1 = rad_γ1α2β1*180/math.pi

α2γ1_X = (cos(rad_γ1α2β1)*(β1.x - α2.x) - sin(rad_γ1α2β1)*(β1.y - α2.x) ) * α2γ1 / α2β1 + α2.x
α2γ1_Y = (sin(rad_γ1α2β1)*(β1.x - α2.x) + cos(rad_γ1α2β1)*(β1.y - α2.x) ) * α2γ1 / α2β1 + α2.x

γ1 = mathutils.Euler((α2γ1_X, α2γ1_Y, 0.0), 'XYZ')
###

### δ1 ###
deg_γ1α2δ1 = 90
rad_γ1α2δ1 = deg_γ1α2δ1/180*math.pi

α2δ1_X = (cos(-rad_γ1α2δ1)*γ1.x - sin(-rad_γ1α2δ1)*γ1.y) * α2δ1 / α2γ1
α2δ1_Y = (sin(-rad_γ1α2δ1)*γ1.x + cos(-rad_γ1α2δ1)*γ1.y) * α2δ1 / α2γ1

δ1 = mathutils.Euler((α2δ1_X, α2δ1_Y, 0.0), 'XYZ')
###

### γ2 ###
deg_β1γ1γ2 = 135
rad_β1γ1γ2 = deg_β1γ1γ2/180*math.pi

γ1γ2_X = (cos(-rad_β1γ1γ2)*(β1.x - γ1.x) - sin(-rad_β1γ1γ2)*(β1.y - γ1.y)) * γ1γ2 / β1γ1 + γ1.x
γ1γ2_Y = (sin(-rad_β1γ1γ2)*(β1.x - γ1.x) + cos(-rad_β1γ1γ2)*(β1.y - γ1.y)) * γ1γ2 / β1γ1 + γ1.y

γ2 = mathutils.Euler((γ1γ2_X, γ1γ2_Y, 0.0), 'XYZ')
###


### β2 ###
rad_γ2γ1δ1 = acos(((γ2.x - γ1.x)*(δ1.x - γ1.x) + (γ2.y - γ1.y)*(δ1.y - γ1.y))/(γ1γ2 * γ1δ1))
deg_γ2γ1δ1 = rad_γ2γ1δ1*180/math.pi

γ2δ1 = sqrt((γ1γ2**2) - 2*γ1γ2*γ1δ1*cos(rad_γ2γ1δ1) + (γ1δ1**2))
#γ2δ1_2 = sqrt((γ1γ2 - γ1δ1*cos(rad_γ2γ1δ1))**2 + γ1δ1*sin(rad_γ2γ1δ1)**2)




rad_β2γ2δ1 = acos((γ2δ1**2 + β2γ2**2 - β2δ1**2) / (2*γ2δ1*β2γ2))
deg_β2γ2δ1 = rad_β2γ2δ1*180/math.pi

β2γ2_X = (cos(-rad_β2γ2δ1)*(δ1.x - γ2.x) - sin(-rad_β2γ2δ1)*(δ1.y - γ2.y) ) * β2γ2 / γ2δ1 + γ2.x
β2γ2_Y = (sin(-rad_β2γ2δ1)*(δ1.x - γ2.x) + cos(-rad_β2γ2δ1)*(δ1.y - γ2.y) ) * β2γ2 / γ2δ1 + γ2.y




β2 = mathutils.Euler((β2γ2_X, β2γ2_Y, 0.0), 'XYZ')
###

After, repetition of the same triangle calculation method continue.

--

The next generation of da Vinci

I discovered that there exists a mathematical theorem and formulas that integrates every voluntary movement of natural animal bodies. This is also the invention of a universal biomechanical link mechanism to create artificial animals. It's the first universal perfect machine element in human history which surpass the conventional functions such as rotating elements like wheels and propellers invented in ancient times or robotics joint torque control.

This technological innovation which brings the infinite applications was born through the historic intangible cultural heritage and the esoteric education in Romandy of Switzerland where has a high perspective overlooking the whole world and is active in alternative medicine and sustainability of global environment.

That is, I made this technological innovation by the agglutination of the theories of two traditional intellectual properties that are related to medical technologies in the east and the west such as European mechanical arts called Automata - Horology and Chinese internal martial arts called Kung Fu.

We now have reached the one of singular point.

Then I also discovered the fundamental theory which is able to explain well this technological innovation among the philosophy advocated by Abraham-Louis Breguet the Horologist - Mechanician at two hundred years ago.

In order to demonstrate the infinite applications, divided the holistic work plan in the 10 work packages, I designed the basic applications of voluntary movement, introduced it visually.

Holistic Work Plan organised into the following ten work packages :
« http://varipon.com/index.php/art-work... »

Over the past few years, while introducing application examples in the world, I've gained global understanding little by little.

Producer's résumé
« http://varipon.com/index.php/producer... »

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