Motion generation of spherical four-bar mechanism using harmonic characteristic parameters

In an earlier work, we presented a method to address the path generation problems associated with spherical four-bar mechanism. In this paper, we seek to extend this approach to the synthesis of spherical four-bar linkages for motion generation. Through harmonic analysis, the output characteristics of a spherical four-bar mechanism is observed to be dependent on the rigid body rotation angle operator μp(t). Subsequently, a database that contains 221,968 sets of basic rotation angle dimensional types for a spherical four-bar mechanism was constructed. The theoretical formulas to calculate the actual dimension and installation parameters of spherical four-bar mechanism are deduced from the harmonic parameters for position output and the harmonic parameters for the rigid body rotation angle operator. On the basis of the theoretical formulas and the numerical atlas database, the motion generation problem for a spherical four-bar mechanism was solved. Finally, two examples are provided to demonstrate the validity of this method.