On the synthesis of the spherical four-bar

A novel and efficient kinematic synthesis approach of the spherical 4R function generator for five and six precision points

“…Firstly, a novel approach for the exact kinematic synthesis of SFGs involving five precision points is proposed. This approach offers the advantage of leading directly to a 3rd degree univariate polynomial, while requiring fewer computations than other similar procedures [7][8][9][10]. Secondly, an exact kinematic synthesis process of SFGs including six precision points is also presented.…”

“…[2][3][4][5][6][7][8][9]. However, studies regarding the exact kinematic synthesis of SFGs for five [6][7][8][9][10][11] and six [8,9,11] precision points are indeed scarce.…”

Some improvements on the exact kinematic synthesis of spherical 4R function generators

“…2 In these works, a wide variety of synthesis procedures have been proposed. However, a careful and detailed examination of these contributions allows us to extract some concluding remarks: (1) some of the proposed techniques are lengthy and/or include polynomials of second and higher order; which usually increment the number of required arithmetic operations, and, consequently, increment the error involved into the numerical computations, and (2) several design procedures lead to algorithmic problems, i.e., the synthesis problem was formulated in such a way that it may not admit real solutions.…”

“…As it will be shown later, for the function generation with spherical four bar linkages, intended for three and four precision points, it is possible to find suitable design coefficients that allow to obtain the exact solution of the corresponding nonlinear equations, as if they were a system of linear equations. However, when five precision points are desired, the synthesis problem becomes highly nonlinear [2][3][4][5], and, consequently, the resulting equations cannot be rearranged and solved as linear equations.…”

“…The kinematic synthesis of spherical 4R function generators (SFG, in short) has been investigated extensively in the literature [2][3][4][5][6][7][8][9][10][11][12][13][14]. 2 In these works, a wide variety of synthesis procedures have been proposed.…”