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. / text

The challenges in automating the design of planar mechanisms are tremendous especially in areas related to computational representation, kinematic analysis and synthesis of planar mechanisms. The challenge in computational representation relates to the development of a comprehensive methodology to completely define and manipulate the topologies of planar mechanisms while in kinematic analysis, the challenge is primarily in the development of generalized analysis routines to analyze different mechanism topologies. Combining the aforementioned challenges along with appropriate optimization algorithms to synthesize planar mechanisms for different user-defined applications presents the final challenge in the automated design of planar mechanisms. The methods presented in the literature demonstrate synthesis of standard four-bar and six-bar mechanisms with revolute and prismatic joints. But a detailed review of these methods point to the fact that they are not scalable when the topologies and the parameters of n-bar mechanisms are required to be simultaneously synthesized. Through this research, a comprehensive and scalable methodology for synthesizing different mechanism topologies and their parameters simultaneously is presented that overcomes the limitations in different challenge areas in the following ways. In representation, a graph-grammar based scheme for planar mechanisms is developed to completely describe the topology of a mechanism. Grammar rules are developed in conjunction with this representation scheme to generate different mechanism topologies in a tree-search process. In analysis, a generic kinematic analysis routine is developed to automatically analyze one-degree of freedom mechanisms consisting of revolute and prismatic joints. Two implementations of kinematic analysis have been included. The first implementation involves the use of graphical methods for position and velocity analyses and the equation method for acceleration analysis for mechanisms with a four-bar loop. The second implementation involves the use of an optimization-based method that has been developed to handle position kinematics of indeterminate mechanisms while the velocity and acceleration analyses of such mechanisms are carried out by formulating appropriate linear equations. The representation and analysis schemes are integrated to parametrically synthesize different mechanism topologies using a hybrid implementation of Particle Swarm Optimization and Nelder-Mead simplex algorithm. The hybrid implementation is able to produce better results for the problems found in the literature using a four-bar mechanism with revolute joints as well as through other higher order mechanisms from the design space. The implementation has also been tested on three new challenge problems with satisfactory results subject to computational constraints. The difficulties in the search have been studied that indicates the reasons for the lack of solution repeatability. This dissertation concludes with a discussion of the results and future directions. / text