The decomposition of a linkage into minimal components is a central tool of analysis and synthesis of linkages. In this paper we prove that every pinned d-isostatic (minimally rigid) graph (grounded linkage) has a unique decomposition into minimal strongly connected components (in the sense of directed graphs), or equivalently into minimal pinned isostatic graphs, which we call d-Assur graphs. We also study key properties of motions induced by removing an edge in a d-Assur graph -defining a stronger sub-class of strongly d-Assur graphs by the property that all inner vertices go into motion, for each removed edge. The strongly 3-Assur graphs are the central building blocks for kinematic linkages in 3-space and the 3-Assur graphs are components in the analysis of built linkages. The d-Assur graphs share a number of key combinatorial and geometric properties with the 2-Assur graphs, including an associated lower blocktriangular decomposition of the pinned rigidity matrix which provides modular information for extending the motion induced by inserting one driver in a bottom Assur linkage to the joints of the entire linkage. We also highlight some problems in combinatorial rigidity in higher dimensions (d ≥ 3) which cause the distinction between d-Assur and strongly d-Assur

No abstract

We introduce the idea of Assur graphs, a concept originally developed and exclusively employed in the literature of the kinematics community. The paper translates the terminology, questions, methods and conjectures from the kinematics terminology for one degree of freedom linkages to the terminology of Assur graphs as graphs with special properties in rigidity theory. Exploiting recent works in combinatorial rigidity theory we provide mathematical characterizations of these graphs derived from 'minimal' linkages. With these characterizations, we confirm a series of conjectures posed by Offer Shai, and offer techniques and algorithms to be exploited further in future work.

No abstract

Many methods that support human creativity by manual or computational means have been proposed in the past. They rely on the assumption that following a certain process of reasoning might lead to generating ideas considered creative. We start by defining creativity as a capability that enables the creation of systems that are patentable. We review the state-of-the-art of creative conceptual design and organize it with a framework. Subsequently, we present a method called infused design that guarantees generating design solutions by transforming systems and methods from remote disciplines. In many cases, these solutions would be deemed creative. Finding these systems and their transformations is done through a process based on the underlying discrete mathematical representation. This process is partially supported by a computer tool.We describe the method of infused design and illustrate its operation through part of the results achieved until now, including designing a new active torque amplifier system. We 2 further demonstrate its benefits through other examples. We discuss the relation of infused design with other creativity or design methods and conclude with future developments of the method."A well-directed imagination is the source of great deeds." Chinese proverbKeywords: creativity; conceptual design; graph representation; collaborative design; design support systems; framework; analogy INTRODUCTIONConceptual design is a central stage in product design; it determines the principles that govern the product. Decisions made in this stage have major impact on the final product quality, cost, and market success (Pahl and Beitz, 1996). But even high quality conceptual design leading to high quality products does not guarantee product success. If a company wishes to capture or maintain its market leadership, it must do better than that; it must develop breakthrough or radical innovations (McDermott and O'Connor, 2002).Our position in this paper is that creative conceptual design (CCD) is central to developing innovative products. Therefore, studying and improving CCD is an important undertaking.However, creativity and innovation are elusive concepts; to some it is mysterious. There are more than 80 definitions of creativity in the literature (Dasgupta, 1994). A common definition of creativity is that creativity is the ability to generate new useful things that are characterized by being original and imaginative. The meaning of these properties is open to interpretations; therefore, for the purpose of this study we adopt a particular definition: CCD outputs a description of a device or a system that is or judged to be patentable. This definition concentrates on the engineering functionality of products rather than on their industrial design or 3 esthetics. We also focus on determining the principles that govern the product rather than a precise description of its structure and its detailed embodiment.In section 2, we review the state-of-the-art of creative conceptual design. We provide a framework that ...