The Algebraic Solution to The Spherical 4R Function Generator for Six Precision Points

This paper presents an algebraic solution procedure for six precision points function generation of the spherical 4R linkage. First of all, a set of six design equations with thirteen linear homogeneous design coefficients are formulated based on the input-output equation and six compatibility equations are reduced according to the definition of design coefficients. Then, three kinematic synthesis equations are derived from the aforementioned equations by the variable substitution and the linear elimination. Finally, a 7th-degree univariate polynomial equation is yielded from the 8 by 8 Sylvester resultant matrix. At last, two numerical examples are provided to validate the procedure.