Analytical synthesis of function generating spherical four-bar mechanism for the five precision points

This paper presents an analytical method for synthesis of function generating spherical 4R mechanisms for the five precision points. For the design requirements an additional parameter, reference value of output angle, ψ0, was added to angular link length parameters, αi(i = 1, … , 4). In the dimensional synthesis procedure, a novel approach of polynomial approximation method was proposed to determine these five design parameters. Using this method, a set of five non-linear equations was easily transformed into a set of fifteen linear equations. Hence, the problem was reduced to the solution of a cubic polynomial equation. Moreover, a graphical method in a CAD environment is proposed to verify the solutions.