Sajad H. Abdali - Department of Mechanical Engineering, University of Al-Qadisiyah, Diwaniyah, ۵۸۰۰۱, Iraq
Essam L. Esmail - Department of Mechanical Engineering, University of Al-Qadisiyah, Diwaniyah, ۵۸۰۰۱, Iraq

Planetary gear trains (PGTs) with one or more degrees of freedom (DOFs) have numerous uses in PGT-based mechanisms. The majority of the currently available synthesis methods have focused on ۱-DOF PGTs, with only a few investigations on multi-DOF PGT synthesis. The method for synthesizing ۷-link ۳-DOF PGMs is outlined. All possible link assortments are produced, labeled spanning trees are generated, and potential geared graphs are constructed. The guidelines for including geared edges and how to synthesize geared graphs are outlined. Vertex-degree arrays are generated to validate the geared graphs. Isomorphic geared graphs are identified by comparing the isomorphic identification numbers of geared graphs with the same spanning tree. Fractionated geared graphs are identified using the reachability matrix method. The new method has a straightforward algorithm. In contrast to what is reported in the literature, the results of the synthesis of ۷-link ۳-DOF PGMs show that there are seven non-fractionated mechanisms. MATLAB programs are used to acquire the vertex-degree arrays.

Fractionated, Isomorphic, Link assortment, Planetary gear trains, Structural synthesis, spanning tree