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This paper focuses on the kinematic and dynamic numerical simulation of mechanisms by applying a numerical method, and a complex simulation programme built on it, developed by the author. Described are mathematical principles of the numerical method used and also the programming progression of the important parts of the application and its optimization. The final part includes comparative measuring of the accuracy and performance.

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