A graph grammar scheme for representing and evaluating planar mechanisms

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Radhakrishnan, Pradeep, 1984-

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There are different phases in any design activity, one of them being concept generation. Research in automating the conceptual design process in planar mechanisms is always challenging due to the existence of many different elements and their endless combinations. There may be instances where designers arrive at a concept without considering all the alternatives. Computational synthesis aims to arrive at a design by considering the entire space of valid designs. Different researchers have adopted various methods to automate the design process that includes existence of similar graph grammar approaches. But few methods replicate the way humans’ design. An attempt is being made in the thesis in this direction and as a first step, we focus on representing and evaluating planar mechanisms designed using graph grammars. Graph grammars have been used to represent planar mechanisms but there are disadvantages in the methods currently available. This is due to the lack of information in understanding the details of a mechanism represented by the graph since the graphs do not include information about the type of joints and components such as revolute links, prismatic blocks, gears and cams. In order to overcome drawbacks in the existing methods, a novel representation scheme has been developed. In this method, labels and x, y position information in the nodes are used to represent the different mechanism types. A set of sixteen grammar rules that construct different mechanisms from the basic seed is developed, which implicitly represents a tree of candidate solutions. The scheme is tested to determine its capability in capturing the entire set of feasible planar mechanisms of one degree of freedom including Stephenson and double butterfly linkages. In addition to the representation, another important consideration is the need for an accurate and generalized evaluator for kinematic analysis of mechanisms which, given the lack of information, may not be possible with current design automation schemes. The approach employed for analysis is purely kinematic and hence the instantaneous center of rotation method is employed in this research. The velocities of pivots and links are obtained using the instant center method. Once velocities are determined, the vector polygon approach is used to obtain accelerations and geometrical intersection to determine positions of pivots. The graph grammar based analysis module is implemented in an existing object-oriented grammar framework and the results have found this to be superior to or equivalent to existing commercial packages such as Working Model and SAM for topologies consisting of four-bar loop chain with single degree of freedom.



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