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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. / text

This thesis comprises a study on the kinematic and force analyses of the overconstrained mechanisms. The scope of the overconstrained mechanisms is too wide and difficult to handle. Therefore, the study is restricted to the planar overconstrained mechanisms. Although the study involves only the planar overconstrained mechanisms, the investigated methods and approaches could be extended to the spatial overconstrained mechanisms as well. In this thesis, kinematic analysis is performed in order to investigate how an overconstrained mechanism can be constructed. Four methods are used. These are the analytical method, the method of cognates, the method of combining identical modules and the method of extending an overconstrained mechanism with extra links. This thesis also involves the force analysis of the overconstrained mechanisms. A method is introduced in order to eliminate the force indeterminacy encountered in the overconstrained mechanisms. The results are design based and directly associated with the assembly phase of the mechanism.

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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

This work discusses the dynamic predictions of compliant mechanisms using the Pseudo-Rigid-Body model (PRBM). In order to improve the number of mechanisms that can be modeled, this research develops and identifies several key concepts in the behavior of beam segments where both ends are fixed to a rigid body (fixed-fixed flexible segments). A model is presented, and several examples are discussed. The dynamic behavior of several compliant segments is predicted using the PRBM and the results are compared to finite element analysis and experimental results. Details are presented as to the transient behavior of a typical uniform rectangular cross section beam. The results of this study are extended and applied to compliant planar mechanisms. It is shown by comparison with finite element analysis and experimental results that the PRBM is a good model of the physical system's dynamic behavior. The method is also demonstrated for use with compliant microelectromechanical (MEMS) systems.

The present work studies instantaneous motion of smooth planar and spatial objects in unilateral point contacts. The traditional first-order instantaneous kinematic analysis is found insufficient to explain many common physical scenarios. The present work looks beyond the velocity state of motion for a comprehensive understanding through higher-order kinematic analysis of the above system. The methodology proposed herein is a Euclidean space approach to second-order motion space analysis of objects in point contacts. The geometries of the objects are approximated up to second-order in the differential vicinity of the point of contact; meaning, up to curvature at the point of contact. The instantaneous motion is approximated up to second-order kinematics, i.e., up to acceleration state. The basic approach consists of impressing an instantaneous motion upon one object while holding the other fixed which is in a single point contact initially, and observing for one of the following three states: penetration, separation, and persistence of contact between the two objects. These three states are characterized by the interference between the geometries of the objects. Penetration and separation of two curves for rotation about points on the plane is geometrically studied based on the relative configuration of the osculating circles at the point of contact. It is shown that the plane is partitioned into four regions of rotation centers. Partitioning of the plane into motion space regions at a contact provided a geometrical framework compose the motion space for multiple contacts. The applications include second-order form-closure (SFC) and synthesis of kinematic pairs. To explore the consequence of a generic motion, an analytical scheme is formulated using the screw theoretic concepts of twist and twist-derivative. It is shown that the characteristics of second-order motions at a single contact depends only upon the geometric kinematic properties of the motion; meaning, the motion characteristics are time-independent. The geometric conditions for the second-order motion that will be admissible or restrained at a contact are not available in the existing literature on \second-order mobility". The classical Euler-Savary equation for enveloping curves is found to represent the condition which is both necessary and sufficient for the second-order roll-slide motion. An elegant generalized geometric characterization of second-order motions is derived. This is made use for deriving condition of immobilization of, planar mechanisms with up to 2-degrees-of-freedom (d.o.f.), with a single point contact. Illustrative examples of four-bar and 2R-mechanisms are presented. Rapid prototyped model of the four-bar mechanism is fabricated and the SFC theory is verified satisfactorily. Through a novel use of Meusnier's theorem, rotational motion characteristics of planar curves in a point contact is used to determine the patterns and distribution of admissible axes of rotation in space for two surfaces in a single point contact. In the generalized analytical method of motion space analysis, the surfaces are locally represented in Monge's form up to second-order terms and motion is represented using twist and twist-derivative. An analytical framework for the second-order motion space analysis of surfaces with multiple contacts has been developed. Using this procedure, pairs of objects are analyzed for SFC and equivalent lower kinematic pair freedom. Revolute and planar joints with two contacts, prismatic joint with three contacts, SFC of regular concave spherical tetrahedron and regular tetrahedron with four contacts are demonstrated. Although conventional first-order studies demand seven contact points for form-closure, within the context of second-order motion, the present study established that, under special geometric conditions relative immobilization of two smooth objects can be enabled with much fewer contacts. Conditions for immobilization using three and two smooth contacts have been derived. Using contact kinematics equations based on higher-order reciprocity, an instantaneous spatial higher pair to lower pair substitute-connection which is kinematically equivalent up to acceleration analysis for two smooth surfaces in persistent point contact is derived. An illustrative example of a three-link direct-contact mechanism is presented.