INTRODUCTION One of the major problems in generating distinct planar kinematic chains is the detection of isomorphism A lot of time and effort has been devoted to developing a reliable and computationally efficient technique Structural analysis and synthesis is very important in the design of mechanisms Identifying isomorphism among kinematic chains is an essential step in kinematic mechanism synthesis Undetected isomorphism results in duplicate solutions and unnecessary effort and falsely identified isomorphism eliminates possible candidates for new mechanisms The study of mechanisms begins as early as the Iron age when people started building simple machines Today mechanisms are encountered everywhere from nano mechanical devices to the space shuttle Due to the great need for new mechanisms automated design of mechanisms from a given set of functional requirements is advantageous During the conceptual design phase some of the functional requirements can be transformed into structural requirements of the mechanisms The structural studies of kinematic mechanisms are broadly divided into structural synthesis and structural analysis
The structural synthesis of kinematic chains involves enumerating all possible kinematic chains having a specified number of links degrees of freedom and types of joints One of the important steps in this process is the detection of degenerate kinematic chains using Gruebler s degrees of freedom equation In structural analysis the major problems are isomorphism detection and identification of type of mobility Researchers in the mechanisms community follow different approaches to specify the non isomorphic kinematic chains However most of the existing methods are not computationally efficient and hence only generation of non isomorphic kinematic chains with fewer links was possible Furthermore there are several discrepancies in the results obtained by researchers in the mechanisms community Hence there is a need for an efficient and reliable method for the synthesis of kinematic chains and a re examination of the existing results on kinematic synthesis to validate the existing methods This forms the first objective of this work In the structural analysis of planar kinematic chains one common error is to assume that the graph of a planar kinematic chain is a planar graph It was pointed out recently that the main cause for this is the misuse of the word planar In mechanisms it means to lie in one or more parallel planes but in graph theory it means to lie on a single plane Several algorithms for structural analysis including the algorithms for degeneracy testing isomorphism testing and mobility type identification work under the assumption that the graph of a planar kinematic chain is a planar graph Mechanisms are created by the designer s intuition skill and experience
This approach however cannot ensure the identification of all feasible design alternatives nor does it necessarily lead to an optimum design During the conceptual design phase some of the functional requirements of a desired mechanism can be transformed into structural characteristics that can be employed for systematic enumeration of mechanisms The kinematic structure of a mechanism contains the essential information regarding connectivity of different links with different type of joints Depending upon the number and type of links joints and their connectivity the kinematic chains differ resulting in different output In the early stage of mechanism design it is helpful to determine all the distinct kinematic chains of the required number of links and degree of freedom in a systematic manner Once this is accomplished each mechanism structure can be then sketched and evaluated with respect to the remaining functional requirements This result in a class of feasible mechanism that can be subjected to dimensional synthesis kinematic and dynamic analysis design optimization and design detailing The study of kinematic structure of mechanisms is basic to an understanding of their function An understanding of this structure will lead to systematic development of identification classification and detection of isomorphism among kinematic chains and mechanisms It also leads selection of best suited mechanism to achieve a desired set of motion characteristics The kinematic structure is to be analyzed for better understating of a mechanism In mechanism analysis it is convenient to define one of the links as the fixed frame of reference All motion with respect to this link is then termed absolute motion The first step in the analysis of complicated mechanisms is to sketch the equivalent kinematic or skeleton diagram The study of structural aspects of kinematic chains is important for the invention and innovation of mechanisms Structure synthesis and analysis generally involves the study of following 1 Determination of all possible structurally distinct kinematic chains with a given number of links and degree of freedom i e testing isomorphism 2 Determination of all possible structurally distinct mechanisms that can be derived from a kinematic chain i e detecting inversions 3 Determination in case of multi degree of freedom kinematic chains whether the given chain has total partial or fractional freedom 4 For a given mechanism determining all possible locations for supplying input motion
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