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

It is shown that a careful definition of the design coefficients may improve the kinematic synthesis of spherical 4R linkages – intended for function generation – for three and four precision points. As a result, the design process is based on a simple system of linear equations whose solution is obtained in closed form. Moreover, the synthesis process does not lead to algorithmic problems during the determination of the link lengths. Furthermore, useful discussions for obtaining positive link lengths are also provided. Finally, several application examples are presented to prove the feasibility and the validity of the proposed method.