The synthesis of an RPS serial chain to reach a given set of task positions

The number of task positions and constraint equations can be reduced by specifying some of the dimensional parameters. For the cases of six through eight task positions, analytical solutions are provided using both a resultant elimination strategy as well as a generalized eigenvalue elimination procedure. The generalized eigenvalue method has been implemented using Java and integrated into our design software. A numerical example of the solution for eight design positions is presented.