Compliance Vectors Research Articles

Shape Optimization Framework for the Path of the Primary Compliance Vector in Compliant Mechanisms

AbstractThe primary compliance vector (PCV) captures the dominant kinematic behavior of a compliant mechanism. Its trajectory describes large deformation mechanism behavior and can be integrated in an optimization objective in detailed compliant mechanism design. This paper presents a general framework for the optimization of the PCV path, the mechanism trajectory of lowest energy, using a unified stiffness characterization and piecewise curve representation. We present a meaningful objective formulation for the PCV path that evaluates path shape, location, orientation, and length independently and apply the framework to two design examples. The framework is useful for design of planar and shell compliant mechanisms that traverse a specified mechanism trajectory and that are insensitive to load perturbations.

多層シェルの多目的設計問題に対する形状－トポロジー同時最適化

This paper describes a new approach for creating the optimal shape and topology of a multi-layered shell considering multi-objective design. By implementing topology optimization in the variable design domain which is optimized by shape optimization at every iteration, the optimal topology and shape is simultaneously determined. The free-form optimization method and the SIMP method for multi-layered shells are applied to shape and topology optimization, respectively. The compliance vector minimization problem is formulated and its sensitivity functions for shape and density variations are theoretically derived. Both the optimal shape and density variations are determined by using the H1 gradient method, where the sensitivity functions are applied to vary the shape and density. The results show that the proposed simultaneous optimization method provides stiffer and lighter structures with less numerical instabilities while maintaining smooth surface and density distribution.

Geometric metrology I. Separation functionals in tolerance assessment

Geometric metrology represents a fundamental shift in viewpoint in regard to the analysis and interpretation of measurement data sets associated with metrological analysis. Geometric metrology is based on the notion of a separation functional and provides a unifying and conceptual framework to describe the shape variability of manufactured artefacts. The methodology is simple and intuitive, provides a complementary perspective to normal metrological analysis, enlarges the class of shapes that can be accommodated in terms of minimum zone separation, and provides a means to classify, categorize and quantify manufactured objects. Geometric metrology allows dimensional tolerances to be generalized and evaluated in a geometric framework, and includes the normal “one-number” compliance test as a first-order approximation in shape differences. The separation functional is the basic object of interest in geometric metrology, and is useful to visualize, interpret, and analyze the measurement data, as well as to extract (additional) information from the measurement process not available using normal techniques. The minimum zone separation functional for a metrological artefact is computed for a simple planar region representing the measurement data and an arbitrary convex polygon as the perfect form. The zone separation functional for a perfect form is then introduced and computed in closed-form for several special cases. The perfect form functional allows several new measures associated with the manufactured artefact to be computed and compared with its nominal form. An equivalence class of artefacts is defined using the separation functional, and a description of form based on a compliance vector generalizes the usual tolerance inspection test. A global measure of shape difference between the actual and nominal artefact is described using the separation functional.