Structural-Parametric Synthesis of the RoboMech Class Parallel Mechanism with Two Sliders

This paper addresses the structural-parametric synthesis and kinematic analysis of the RoboMech class of parallel mechanisms (PM) having two sliders. The proposed methods allow the synthesis of a PM with its structure and geometric parameters of the links to obtain the given laws of motions of the input and output links (sliders). The paper outlines a possible application of the proposed approach to design a PM for a cold stamping technological line. The proposed PM is formed by connecting two sliders (input and output objects) using one passive and one negative closing kinematic chain (CKC). The passive CKC does not impose a geometric constraint on the movements of the sliders and the geometric parameters of its links are varied to satisfy the geometric constraint of the negative CKC. The negative CKC imposes one geometric constraint on the movements of the sliders and its geometric parameters are determined on the basis of the Chebyshev and least-square approximations. Problems of positions and analogues of velocities and accelerations of the considered PM are solved to demonstrate the feasibility and effectiveness of the proposed formulations and case of study.

Enhanced geometric constraint-based phase unwrapping algorithm in binocular stereo vision fringe projection system

Phase unwrapping plays an important and central role in phase-based digital fringe projection profilometry. The unwrapping quality directly influences the three-dimensional measurement accuracy. Recently, an effective geometric constraint-based phase unwrapping algorithm has been proposed to obtain the continuous absolute phase map and the unwrapped phase accuracy was found to be high. However, in this technique the virtual depth plane at z = zmin is often created empirically, which increases the manual measurement error. For this reason, this paper proposes a method for accurately constructing the virtual plane and further applies it to phase unwrapping of objects with a larger depth range. In this method, a binocular stereo vision system is used as the measurement set-up for the virtual depth plane construction and a series of virtual depth planes at z = zimin (i ≥ 2) is automatically built using a computational framework. Then, the phase is unwrapped for each region according to the continuity of the unwrapped phase and a complete absolute phase map is obtained by merging the unwrapped phases in all regions for 3D reconstruction. In this process, the virtual depth planes are created automatically and quantitatively by the measurement system. No human intervention is required and it greatly reduces the manual measurement error. Experiments show that the artificial virtual planes can be built accurately and the phase is unwrapped correctly and readily.

An Efficient Surrogate-Based Optimization Method for BWBUG Based on Multifidelity Model and Geometric Constraint Gradients

Performing shape optimization of blended-wing-body underwater glider (BWBUG) can significantly improve its gliding performance. However, high-fidelity CFD analysis and geometric constraint calculation in traditional surrogate-based optimization methods are expensive. An efficient surrogate-based optimization method based on the multifidelity model and geometric constraint gradient information is proposed. By establishing a shape parameterized model, deriving analytical expression of geometric constraint gradient, constructing multifidelity surrogate model, the calculation times of high-fidelity CFD model and geometric constraints are reduced during the shape optimization process of BWBUG, which greatly improve the optimization efficiency. Finally, the effectiveness and efficiency of the proposed method are verified by performing the shape optimization of a BWBUG and comparing with traditional surrogate-based optimization methods.

An Intrinsic Geometric Constraint on Morphological Stomatal Traits

A strong negative non-linear relationship exists between stomatal density (SD) and size (SS) or length (SL), which is of high importance in gas exchange and plant evolution. However, the cause of this relationship has not been clarified. In geometry, SD has an intrinsic relationship with SS−1 or SL−2, which is defined as a geometric constraint here. We compiled global data to clarify the influence of this geometric constraint on the SD-SS relationship. The log-log scaling slope of the relationship between SD and SS and between SD and SL was not significantly different from −1 and −2, respectively. Although the non-geometric effect drove the SD-SS curve away from the power function with −1, a larger influence of the geometric constraint on SD was found. Therefore, the higher geometric constraint possibly causes the SD-SS relationship to be inevitably non-linear and negative. Compared to pteridophyta and gymnosperms, the geometric constraint was lower for angiosperm species, possibly due to most of them having smaller stomata. The relaxation of the geometric constraint seems to extend the upper range of SD in angiosperm species and hence enable them to exploit a wide range of environments.