Topology Synthesis of SingleDOF Epicyclic Gear Trains Based on Graph Theory * The research shows that the topology structure of gear kinematic chains can be represented by graphs. The topological synthesis of epicyclic gear trains based on graph theory is an effective system synthesis method. In this paper, a topology synthesis method is developed for single degree of freedom (DOF) epicyclic gear trains. A new effective identification method Linkage Characteristic PolynomialFundamental Circuit Polygon (LCPFCP) is proposed to solve isomorphism and rotationally isomorphism problem generated in topology synthesis process. The basic idea of proposed topology synthesis is to enumerate all candidate singleDOF gear train kinematic chains first. Then use the LCPFCP algorithm to identify the isomorphism of the graphs and the rotation graphs respectively, and finally synthesize the kinematic chains that meets the corresponding fundamental requirements. All of the above steps can be automated by a computer program.

Topology optimization with accessibility constraint for multiaxis machining Abstract   In this paper, we present a topology optimization (TO) framework to enable automated design of mechanical components while ensuring the result can be manufactured using multiaxis machining. Although TO improves the partxe2x80x99s performance, the asdesigned model is often geometrically too complex to be machined and the asmanufactured model can significantly vary due to machining constraints that are not accounted for during TO. In other words, many of the optimized design features cannot be accessed by a machine tool without colliding with the part (or fixtures). The subsequent postprocessing to make the part machinable with the given setup requires trialanderror without guarantees on preserving the optimized performance. Our proposed approach is based on the wellestablished accessibility analysis formulation using convolutions in configuration space that is extensively used in spatial planning and robotics. We define an inaccessibility measure field (IMF) over the design domain to identify nonmanufacturable features and quantify their contribution to nonmanufacturability. The IMF is used to penalize the sensitivity field of performance objectives and constraints to prevent formation of inaccessible regions. Unlike existing discrete formulations, our IMF provides a continuous spatial field that is desirable for TO convergence. Our approach applies to arbitrary geometric complexity of the part, tools, and fixtures, and is highly parallelizable on multicore architecture. We demonstrate the effectiveness of our framework on benchmark and realistic examples in 2D and 3D. We also show that it is possible to directly construct manufacturing plans for the optimized designs based on the accessibility information.