Flat Knitting Loop Deformation Simulation Based on Interlacing Point Model

In order to create realistic loop primitives suitable for the faster CAD of the flat-knitted fabric, we have performed research on the model of the loop as well as the variation of the loop surface. This paper proposes an interlacing point-based model for the loop center curve, and uses the cubic Bezier curve to fit the central curve of the regular loop, elongated loop, transfer loop, and irregular deformed loop. In this way, a general model for the central curve of the deformed loop is obtained. The obtained model is then utilized to perform texture mapping, texture interpolation, and brightness processing, simulating a clearly structured and lifelike deformed loop. The computer program LOOP is developed by using the algorithm. The deformed loop is simulated with different yarns, and the deformed loop is applied to design of a cable stitch, demonstrating feasibility of the proposed algorithm. This paper provides a loop primitive simulation method characterized by lifelikeness, yarn material variability, and deformation flexibility, and facilitates the loop-based fast computer-aided design (CAD) of the knitted fabric.

Inverse kinematics for the variable geometry truss manipulator via a Lagrangian dual method

This article studies the inverse kinematics problem of the variable geometry truss manipulator. The problem is cast as an optimization process which can be divided into two steps. Firstly, according to the information about the location of the end effector and fixed base, an optimal center curve and the corresponding distribution of the intermediate platforms along this center line are generated. This procedure is implemented by solving a non-convex optimization problem that has a quadratic objective function subject to quadratic constraints. Then, in accordance with the distribution of the intermediate platforms along the optimal center curve, all lengths of the actuators are calculated via the inverse kinematics of each variable geometry truss module. Hence, the approach that we present is an optimization procedure that attempts to generate the optimal intermediate platform distribution along the optimal central curve, while the performance index and kinematic constraints are satisfied. By using the Lagrangian duality theory, a closed-form optimal solution of the original optimization is given. The numerical simulation substantiates the effectiveness of the introduced approach.

Asymptotic Analysis of the Curved-Pipe Flow with a Pressure-Dependent Viscosity Satisfying Barus Law

Curved-pipe flows have been the subject of many theoretical investigations due to their importance in various applications. The goal of this paper is to study the flow of incompressible fluid with a pressure-dependent viscosity through a curved pipe with an arbitrary central curve and constant circular cross section. The viscosity-pressure dependence is described by the well-known Barus law extensively used by the engineers. We introduce the small parameterε(representing the ratio of the pipe’s thickness and its length) into the problem and perform asymptotic analysis with respect toε. The main idea is to rewrite the governing problem using the appropriate transformation and then to compute the asymptotic solution using curvilinear coordinates and two-scale asymptotic expansion. Applying the inverse transformation, we derive the asymptotic approximation of the flow clearly showing the influence of pipe’s distortion and viscosity-pressure dependence on the effective flow.

A generalized space curve meshing equation for arbitrary intersecting gear

This article derives the space curve meshing equations for arbitrary intersecting gear mechanism, which could achieve continuous and smooth transmission between arbitrary angle intersecting axes, and then establishes the central curves equations of the driving and driven tines on the basis of space curve meshing equations. According to the equations, a calculation example is given and material prototype samples are made to experimentally validate the kinematic performance. The result shows that if the central curve of the driving tine is a circular helix, the central curve of the driven tine is close to a conical helix. This article will supply a basic theory for the application of the arbitrary intersecting gear mechanism in various areas.

On isolated singularities of surfaces which do not affect the conditions of adjunction (Part II.)

In the first part of this paper I investigated the nature of the isolated singular points which can appear on an algebraic surface without affecting the conditions of adjunction and the arithmetic genus of the surface. It appeared that such points have neighbourhoods analysable into connected chains or trees of curves, each rational and of virtual grade − 2, and arranged either in a single chain (giving a binode, or a conic node if there is only one curve) or in three chains of, say, n, p, q curves respectively, one end curve of each chain meeting one which we may call the central curve of the tree. The values of n, p, q are not arbitrary, but satisfy either p = q = 1, or n ≤ 4, p = 2, q = 1; the unodes given by the former case we call U, those given by the latter case U, with a suffix indicating the reduction in class in each case. I pointed out the similarity between these results and Coxeter's enumeration of groups generated by reflexions, there being a one-one correspondence between these singularities and Coxeter's groups, with the restriction that the only groups with which we are concerned are those in which any two primes of symmetry are inclined at either π/2 or π/3. In fact, the curves which make up a complete neighbourhood correspond to the bounding primes of a fundamental region, two curves which do not meet corresponding to mutually perpendicular, primes, and two which do to primes inclined at π/3.