Epicyclic gear trains (EGTs) are used in the mechanical energy transmission systems where high velocity ratios are needed in a compact space. It is necessary to eliminate duplicate structures in the initial stages of enumeration. In this paper, a novel and simple method is proposed using a parameter, Vertex Incidence Polynomial (VIP), to synthesize epicyclic gear trains up to six links eliminating all isomorphic gear trains. Each epicyclic gear train is represented as a graph by denoting gear pair with thick line and transfer pair with thin line. All the permissible graphs of epicyclic gear trains from the fundamental principles are generated by the recursive method. Isomorphic graphs are identified by calculating VIP. Another parameter “Rotation Index” (RI) is proposed to detect rotational isomorphism. It is found that there are six nonisomorphic rotation graphs for five-link one degree-of-freedom (1-DOF) and 26 graphs for six-link 1-DOF EGTs from which all the nonisomorphic displacement graphs can be derived by adding the transfer vertices for each combination. The proposed method proved to be successful in clustering all the isomorphic structures into a group, which in turn checked for rotational isomorphism. This method is very easy to understand and allows performing isomorphism test in epicyclic gear trains.

Detection of isomorphism in planar and geared kinematic chains (GKCs) is an interesting area since many years. Enumeration of planar and geared kinematic chains becomes easy only when isomorphism problem is resolved effectively. Many researchers proposed algorithms based on topological characteristics or some coding which need lot of computations and comparisons. In this paper, a novel and simple algorithm is proposed based on graph theory by which elimination of isomorphic chains can be done very easily without any tedious calculations or comparisons. A new concept “Net distance” is proposed based on the graph theory to be a quantitative measure to assess isomorphism in planar kinematic chains (PKCs) as well as GKCs. The proposed algorithm is applied on nine-link two-degrees-of-freedom (DOF) distinct kinematic chains completely and the results are presented. Algorithm is tested on examples from eight-link 1-DOF, ten-link 1-DOF, 12-link 1-DOF, and 15link 4-DOF PKCs. The algorithm is also tested on four-, six-link 1-DOF GKCs to detect isomorphism. All the results are in agreement with the existing literature.

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The Artificial Neural Network (ANN) techniques were utilized to predict wear rate and CoF of the Ti-5Al-2.5Sn matrix reinforced with B 4 C particle manufactured by the powder metallurgy. TMCs and wear test samples were characterized by the Scanning Electron Microscope (SEM). Dry sliding wear narrative of the composites was estimated on a pin-on-disc machine at various loads of 20-60N, sliding velocity of 2-6m/s and sliding distance from 1000m-3000m. The wear rate of the composite was reduced by augmentation in weight fraction of boron carbide from 3-9%. The benefits of interfacial TMCs with B 4 C are: increase in strength, wear-resistance, and volume fraction. ANN was planned and utilizes a Levenburg-Marquardt program algorithm to reduce the mean squared error using a back-propagation technique. The input parameters are considered to include load, sliding velocity, and sliding distance. The experimental results of an ANN model and regression model are compared. ANN replicas have been urbanized to foreshow experimental rate of wear and CoF of TMCs and examined that ANN predictions have exceptional concord with deliberated values. Accordingly, the prediction of wear rate and CoF of TMCs using ANN in earlier actual manufacture will significantly save the manufacturing time, exertion, and expenditure.

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