This thesis has developed an efficient methodology for automatic kinematic analysis of planar linkages using the concept of modular kinematics. Unlike conventional general purpose kinematic analysis packages where each joint in the mechanism is represented using a set of non-linear constraint equations which need to be solved by some iterative numerical procedure, modular kinematics is based on the original observation by Assur that kinematic state of a mechanism involving large number of links can be constructed out of the kinematic states of patterns of sub chains called modules taken in a given sequence called module sequence which in turn emulates the step by step construction procedure of traditional graphical methods. The position, velocity and acceleration analysis of modules are available in closed form. Kinematic analysis of modules later in the sequence is enabled by those of the ones earlier in the sequence, hence, the kinematic analysis of a mechanism is accomplished without any iterative endeavor by doing the kinematics of the modules as given in the module sequence. [102] classified all modules into three fundamental types namely input, dyad and transformation and also introduced the concept of constraint module for analyzing graphically non-constructible mechanisms within the paradigm of modular kinematics where a small step of numerical search was needed in an over all closed form kinematic formulation. Module sequence for a mechanism using the modules is not unique. Choice of a later module in the sequence depends upon the selection of modules earlier in the sequence. This thesis has presented a systematic approach of identifying all such methods for all the inversions of the mechanism and represented in the form of a module hierarchy or a module tree where each path from root to the leaf node represents a valid module sequence for the kinematic chain in hand. The work also extended the set of modules by adding eight new modules to what has already been used in literature to make it complete in the sense that all planar mechanisms involving revolute, prismatic and pin-in-slot (including circular slots) can be handled. The computational effort involved for analyzing these mechanisms thus depend on the number of constraint modules occurring in succession in the module sequence. However, maximum possible number of constraint modules in any mechanism with up to twelve links is only two. The derivative analysis also uses the same module sequence, but they are always devoid of any iterative steps. During the process of generation of a module sequence, at every stage multitude of modules could be identified for their potential placement in the sequence. But for every module sequence the difference between the number of input modules and that of constraint modules is constant and is equal to the kinematic degrees-of-freedom (d.o.f) of the mechanism. The algorithm presented in this thesis minimizes the number of generalized inputs (and hence extraneous constraints) and thus attempting to identify the simplest of the module sequences. In that sense the module sequences represented in the module tree are all optimal module sequences. The present work introduced the concept of multi phase modular kinematics which enables a large variety of mechanisms, conventionally identified as complex mechanisms, to be solved in closed form. This is achieved through the use of novel virtual link and virtual joints. Virtual link is slightly different from a normal rigid link in the sense that the joint locations on this are functions of some independent parameters. Since, the locations of joints are not fixed even in the local coordinate frame of the virtual link, the relative velocities between joints are not zero, they need to be appropriately accounted in kinematic analysis. The theory presented in the thesis is implemented in a computer program written in C++ on Windows platform and Graphics library (OpenGL) is used to display linkage configurations and simulations. The program takes the data of joints, input pairs, ground link in certain format through a file. Geometric models developed in any of the existing modeling softwares like ProE, Ideas, AutoCad etc. can be imported in VRML format to the links and in case of no geometric models a simple convex 2D geometry is created for each link for the purpose of visualization. Geometric import of links helps not only in understanding the simulations better but also in useful for dynamic analysis, dynamic motion analysis and interference analysis. A complete kinematic analysis (position, velocity and acceleration) is given for a four bar mechanism and illustrated the positional ( configuration) analysis using modular kinematics for several other examples like old-ham, quick-return mechanisms etc. in the current work. Multi-phase modular approach is illustrated using a five bar with floating input pairs, a back actor and a drafter mechanism and the Back actor configuration is shown with the imported link geometries. It is observed in practice that there are many apparently spatial Mechanisms, which are constructed out of symmetric dispositions of planar mechanisms in space. A pseudo spatial mechanism concept is proposed to solve this class of spatial mechanisms, which can actually be analyzed with the effort of solving only one such component. This concept is illustrated with Shaker and Umbrella mechanisms. Possible extensions of the concept for modeling and analysis of more general class of pseudo-spatial mechanisms are also indicated.

This work deals with addressing the issues related to design of double toggle switch mechanisms with emphasis on structural, dimensional and dynamic aspects. Currently, almost all the issues related to electrical switches are dealt from electromagnetic point of view; the operating mechanism is hardly touched. It is observed that kinematic parameters influence electrical performance of switch significantly. Therefore, there is a need to develop methodologies for supporting exploration of diverse kinematic chains (KCs) for this purpose. Visual inspection is tedious and error prone even when a complete list of design criteria is available, hence, the work presented in the thesis contributes towards automated design of toggle switch mechanisms. In this context, in house modular kinematics data structure is found useful for using it as a tool in the design of toggle switch. Modular kinematics, typically used for kinematic analysis, works on the principle of finding the configuration of a mechanism using a given set of modules by a procedure called module sequence. This module sequence is used and interpreted in a number of ways for its effective use in various design stages. Structurally, a set of seven conditions must be satisfied by a KC to exhibit double toggle. These conditions are broadly classified into three categories: criteria for KC, function assignment criteria and criteria for stoppers. These three criteria are to be checked automatically by use of module sequence in the same order as mentioned. In the criteria for KC, one of the conditions is that, the KC should not have fractionated degrees of freedom (d.o.f.). Hence, detection of fractionation in a KC is inevitable. In literature, is was found that the algorithms for detection operate at their worst case complexity, O(n4), and some of them do not report joint fractionation. Thus, the algorithms are not only robust but also computationally expensive. Therefore, a frugal and comprehensive method O(n2) is implemented to detect fractionation using modular kinematics. Also, inherent structural pattern embedded in fractionated KCs is hardly studied in literature. It is found that the way body and joint fractionation is defined in fractionated KCs is inconsistent. So, fractionation is interpreted as symbolic partitioning of joints and links in the traditional body and joint fractionation types respectively. Based on the number of ways of partitioning, simple and multiple types of fractionation are recognized. Valid partitions are identified using the notion of fractionating and non-fractionating subchains. Relative locations of these subchains influence distribution of d.o.f. across the fractionated KC. Conventional representation of KCs as links and joints or graphs is difficult to comprehend this distribution. For this, a novel concept of fractionation graph is introduced that gives d.o.f. distribution information and the relative locations of the constituent subchains across the KC. Modular kinematics gives a constructive description of fractionated KCs. Characterization of fractionated KCs, based on presence of multiple separation links, is introduced as order of fractionation. Uniqueness for a given order of fractionation is also justified. After the criteria for KC, a KC is tested for feasibility for function assignment criteria. This requires recognition of active and passive subchains of the KC with respect to input and output pairs. For this, module sequence is characterized for recognition of the subchains. Based on these subchains, locations of stoppers are derived. Using this information, an algorithmic approach to assign functions (functions like spring, ground link, input link, etc.) to derive distinct driving mechanisms provided isomorphic elements (links and joints) of the KC are known beforehand, is introduced. The design parameters influencing dimensional synthesis have been identified as dimensions of links, spring anchor points and stopper locations. Sub-problems associated with each parameter are analyzed. It is found out that optimum location of stoppers for selecting operational range of motion is necessary by taking into account the considerations of timing of switch and impact velocity. Based on the analysis, an algorithmic way to design single toggle switch mechanisms is introduced. Timing for closing or opening of a switch is one of the critical measure that determines its performance. Timing should be as low as possible without exceeding the impact velocity at the instant contacts meet each other. Timing of a switch depends on the dimensions of the links, inertial parameters, spring stiffness etc. For a given timing for a mechanism, dynamic synthesis, in this thesis, deals with finding the inertial parameters of the links using Quinn's energy distribution method, modular kinematics, and Nelder and Mead's downhill simplex method for optimization. This thesis helps the designer to use modular kinematics as a potential automated tool to select a valid design to make the solution space more meaningful in the design of toggle switch mechanisms.