A decomposition Method for Modular Dimensional Synthesis of Planar Multiloop Linkage Mechanisms

MARTÍN PUCHETA; ALBERTO CARDONA

Santa Fe

Congreso; 15 Congreso sobre Métodos Numéricos y sus Aplicaciones, ENIEF 2006; 2006

Asociación Argentina de Mecánica Computacional

The essence of mechanism synthesis is to find the mechanism for a given motion or task. There are three customary tasks for kinematic synthesis: function generation, path generation and rigidbody guidance. The task is often defined by a number of prescribed displacements and orientations called precision points. Conceptual design of mechanisms has two main stages: (i) Type Synthesis, where the number, type and connectivity of links and joints are determined, and (ii) Dimensional synthesis, where the link lengths and pivot positions at the starting position are computed. From the first stage we already get a mechanism represented by a graph (Pucheta and Cardona, In Mec´anica Computacional, volume XXVI, proc. of MECOM 2005, Buenos Aires, Argentina). To evaluate its feasibility to fulfill a given task it must necessarily have dimensions. To this purpose, we implement a strategy developed by Sandor and Erdman (Advanced Mechanism Design: Analysis and Synthesis, vol. 2, Prentice-Hall, 1984). This strategy consists in: (a) decomposing the complex mechanism topology into Single Open Chains (SOCs), (b) solving dimensionally each SOC using complex numbers and the analytical Precision Point Method, and (c) reassembling the solutions. Decomposition of complex multiloop linkages into single subsystems was deeply studied for automated kinematic and dynamic analysis. However, its use in automated synthesis applications is less addressed in the literature. The proposed SOCs Decomposition algorithm uses the graph structure, the geometry of the prescribed parts and the motion constraints data imposed on them. The resultant order of SOCs is not unique, there could be many valid orders. The optimal order will be a compromise between what best satisfies the solvability (number of equations for linearization required by analytical methods) and what best matches the number of prescribed motion constraints given by the precision points. In spite of the complexity of this method, it produces multiple good initial guesses for subsequent optimization stages based on gradient methods which often fail because of the bifurcating and highly non-linear nature of this inverse problem. The method was programmed in C++ language under the Oofelie environment (Cardona et al., Engng Comp, 11:365–381, 1994). The method was programmed in C++ language under the Oofelie environment (Cardona et al., Engng Comp, 11:365–381, 1994). precision points. Conceptual design of mechanisms has two main stages: (i) Type Synthesis, where the number, type and connectivity of links and joints are determined, and (ii) Dimensional synthesis, where the link lengths and pivot positions at the starting position are computed. From the first stage we already get a mechanism represented by a graph (Pucheta and Cardona, In Mec´anica Computacional, volume XXVI, proc. of MECOM 2005, Buenos Aires, Argentina). To evaluate its feasibility to fulfill a given task it must necessarily have dimensions. To this purpose, we implement a strategy developed by Sandor and Erdman (Advanced Mechanism Design: Analysis and Synthesis, vol. 2, Prentice-Hall, 1984). This strategy consists in: (a) decomposing the complex mechanism topology into Single Open Chains (SOCs), (b) solving dimensionally each SOC using complex numbers and the analytical Precision Point Method, and (c) reassembling the solutions. Decomposition of complex multiloop linkages into single subsystems was deeply studied for automated kinematic and dynamic analysis. However, its use in automated synthesis applications is less addressed in the literature. The proposed SOCs Decomposition algorithm uses the graph structure, the geometry of the prescribed parts and the motion constraints data imposed on them. The resultant order of SOCs is not unique, there could be many valid orders. The optimal order will be a compromise between what best satisfies the solvability (number of equations for linearization required by analytical methods) and what best matches the number of prescribed motion constraints given by the precision points. In spite of the complexity of this method, it produces multiple good initial guesses for subsequent optimization stages based on gradient methods which often fail because of the bifurcating and highly non-linear nature of this inverse problem. The method was programmed in C++ language under the Oofelie environment (Cardona et al., Engng Comp, 11:365–381, 1994).C++ language under the Oofelie environment (Cardona et al., Engng Comp, 11:365–381, 1994).