Mathematics behind the Lawsin Linkage

The Lawsin Linkage Mathematics :

Triangulation is one of the techniques used in designing the Lawsin Linkage. Triangular structures are the most stable figure in geometry especially when it comes to load distributions and stress reductions. In a typical truss structure, various stress exists in every joint. When forces are pulling away from the center it is called Tensile or Expansion Stress. When they are pushing toward the center it is called Compression Stress. When stress reaches its maximum it is now called Strain. Usually, rods twist, buckle under stress in the weakest joint. To prevent this, slide some bushings tightly in every rod of your lego structure.

Triangles are made up of 3 sides and 3 angles. In a 90 degrees triangle, also known as a right triangle, each side has a special name. The side perpendicular to the ground is called the altitude or adjacent side. The side parallel to the ground is called the base or opposite side. The diagonal side, which is the longest line and across the right angle, is called the Hypotenuse. The angles inside the right triangle are 30, 60, and 90; which in total is equal to 180 degrees. These 3 sides and 3 angles are trigonometrically related by the Pythagorean Theorem and the Soh-Cah-Toa Ratios.

On the other hand, when a triangle has 3 unequal sides and 3 unequal angles, it is called Scalene. When it has 2 sides of equal length and 2 equal internal angles, it is called Isosceles. If it has 3 equal sides and 3 equal angles, it is called Equilateral. The internal angles of an equilateral triangle are all equal to 60 degrees. Remember that all these equations, theorems, functions are not simply mathematical principles but they are all-natural laws. These forms of embedded intelligence, or E.I., existed before the human minds evolved.

Aside from the triangles, the Lawsin, Klann, Jansen linkages are also made up of other geometrical figures, such as the square, circle through rotational motion, and pentagon or hexagon depending on how your imagination perceives their structural links. From here, you can use the Pythagorean theorem, the trigonometric functions, kinematics, and other relevant equations in solving for the forces, loads, structures, and designs of your creation.

"The intelligence of mathematics existed first before the human minds evolved".

 ~ Joey Lawsin

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