This paper presents the combined use of two systematic methods for the synthesis of planar linkage mechanisms satisfying multiple kinematic tasks. First, a Graph Theory-based method is used to exhaustively enumerate the topological alternatives for a given problem. Then each feasible alternative is automatically dimensioned using the Precision Position Method; this computation includes space and design constraints. The existing methods to synthesize multiple tasks solve, in sequence, a decomposition of the problem into single kinematic tasks. The task decomposition and the topology selection for each task are usually performed by hand. This process leads to topologies with a repeated pattern and could lead to ignoring potentially desirable topologies. This paper analyzes a design strategy for the simultaneous solution of multiple kinematic tasks. This strategy has two advantages: (i) it eliminates the need for task decomposition, and (ii) it allows the exhaustive exploration of all non-isomorphic topologies up to a defined number of links. An example of simultaneous synthesis for a double rigid-body guidance task with application to a flap-tab mechanism is shown to illustrate the methodology.
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Hereafter, the term “type” embraces both the type and the number synthesis stages of design.
Genetic algorithms are suitable for problems where neither domain nor goal function and restrictions are known; or they are so complicated that gradient computation becomes difficult or impossible . Note that in this sizing problem, the system of (10) may not have a solution and it is difficult to compute the gradient of the space constraints.
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This work has received financial support from the following Argentinean institutions: Consejo Nacional de Investigaciones Científicas y Técnicas PIP2009 112-200801-02473, Agencia Nacional de Promoción Científica y Tecnológica PICT-2010-1240, and Universidad Nacional del Litoral CAI+D 2009 PI65-330.
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Pucheta, M.A., Cardona, A. Topological and dimensional synthesis of planar linkages for multiple kinematic tasks. Multibody Syst Dyn 29, 189–211 (2013). https://doi.org/10.1007/s11044-011-9294-3
- Planar linkage mechanisms
- Graph theory
- Number synthesis
- Modular dimensional synthesis
- Multiple kinematic tasks
- Synthesis strategies