Síntesis de un mecanismo de cuatro eslabones para una silla de descanso usando el método de Newton-Raphson - Cribillero Zevallos, Deyvis Irving (2019)
The present work entitled "Synthesis of a four-link mechanism for a rest chair using the Newton-Raphson method", was developed using the Freudenstein equation to obtain the optimal dimensions of a four-bar mechanism in a rest chair, and ensure stability in the extreme positions of the chair. The angles 1, 2 and 4 of the links of the mechanism were taken based on the ergonomics of a resting chair and taking into account the anatomy of the human body (back, legs and arms) The synthesis of the mechanism was proposed in the Freudenstein equation for a fourlink mechanism, to which the least-squares method was applied to minimize the error in the desired positions (2 and 4) of the links. A system of non-linear equations is obtained by applying the partial derivative with respect to the k constants of Freudenstein to the function that defines the positions of the mechanism. This system of nonlinear equations was solved with the Newton Raphson method. The roots of this system of non-linear equations (1, 2 and 3) are the lengths of the links of the four-bar mechanism. To use this method in a system of nonlinear equations Taylor series were used because they are what allow us to arrive at the iterative equation that will solve system of nonlinear equations. The Newton Raphson method was applied at 2 = 110°, 125°, 140°, 155° , 165° ; 4 = 97°, 116°, 134°, 153°, 165° and 1 = 10° to determine the values of 1, 2 y 3. The programming code was made in Matlab of the Newton Raphson method. We took 5 angular positions for 2 and 4. A tolerance or error of 0.0001, a maximum of iterations of 100 (c = 100) and starting from an initial vector k0 = (1, 1, 1) that are initial values of the constants k with which the process is going to start of iteration. The program converged to the 12 iterations resulting in the optimum lengths of the four-link mechanism for a rest chair (r1 = 52 cm), (r2 = 15.3787 cm), (r3 = 55.4466 cm), (r4 = 11.5684 cm). The selected profile is an ASTM 513 pipe with a thickness of 1.2mm and a diameter of ¾ ". A stability analysis was made to support the weight of a 100kg person. The safety factor obtained is 1.5