Type synthesis of four-degree-of-freedom parallel mechanisms using valid arrays and topological graphs with digits

The type synthesis of four-degree-of-freedom parallel mechanisms using valid arrays and the valid topology graphs with digits is studied. First, the 12 contracted graphs without any binary links for type synthesis of the four-degree-of-freedom parallel mechanisms are constructed. Second, a complicated derivation of topology graphs with digit is transformed into a simple derivation of array, many valid arrays are derived, and many invalid arrays and invalid topology graphs with digit are determined and removed from the arrays using a compiled program. Third, many valid topology graphs with digit with various basic links are derived from the valid arrays, and the 46 different four-degree-of-freedom parallel mechanisms are synthesized using the valid topology graphs with digit and arrays, in which eight existing four-degree-of-freedom parallel mechanisms are included. Finally, the degree of freedoms of synthesized parallel mechanisms are calculated to verify the correction and effectiveness of type synthesis approach using valid arrays and the valid topology graphs with digit.