Triangular Principle Research Articles

Linear and nonlinear analytical equations for fast design of three types of triangular-amplified compliant mechanisms

Compliant amplification mechanisms based on the triangular principle have attracted considerable applications in precision and other engineering fields due to their compactness and efficient amplification capacity. However, a fast engineering design for geometric nonlinearity of large strokes is still much challenging. We report herein a series of analytical equations of nonlinear amplification ratio, input and output stiffness for three commonly-used triangular-amplified compliant mechanisms, namely the rhombus, diamond and bridge types. The pronounced geometric nonlinearities of axially-loaded stiffening and kinematics-arching effects are explicitly formulated. The proposed nonlinear formulas can be directly degenerated as the linear models by vanishing the nonlinear terms, which enables a comprehensive analysis of linear and nonlinear kinetostatics, and hence offers a straightforward way for the fast performance evaluation and size synthesis/optimization. This relieves an engineer's experience and knowledge for an ab initio modeling process. The prediction error is discussed and some insights into the linear and nonlinear characteristics of the three commonly-used triangular-amplified compliant mechanisms are outlined that confirms the advantage of analytical equations bringing to a fast engineering analysis and design.

The process of achieving the principles of the triangle area of middle school students through YouTube assisted learning during a pandemic

The purpose of this study was to describe the achievement of the triangular principle of junior high school students through YouTube-assisted learning during the COVID-19 pandemic. It is exploratory research. The subjects of this study were middle school students in Bengkulu City, Indonesia. We conducted task-based interviews with twenty-one people. The data from the completion of the task was analyzed early to determine their level of thinking. It was using its genetic decomposition. We classified them into five levels of schema development. We selected students who were at the trance level for further in-depth interviews. We use audio-visual recorders to get complete and accurate data. Data were analyzed by applying qualitative data analysis techniques. The results of this study were 19% of the research subjects were at the intra level, 33% were at the semi-inter level, 33% were at the inter level, and 10% of the subjects were at the inter level, and only one person who was at the trance level (= 5%). The conclusion of this study is that students who are at the highest level are able to build relationships between actions, processes, objects, and previous schemas so that a mature schema is formed about the area of the triangle.

CW range-resolved S-lidars: capabilities and limitations in range domain

CW Range-resolved S-lidars (the S symbol comes from Scheimpflug) have gradually evolved into a new class of laser sensors for remote environmental monitoring and a potential alternative to traditional atmospheric lidars. Based on the biaxial optical scheme, they sense the environment by continuous-wave laser emitters, implement the triangular principle of range control and use position-sensitive photodetectors. Providing range-resolved monitoring of the environment, they are grounded on low-power CW lasers and advanced technologies of nanophotonics. We examined characteristic features of this class of lidars in the range domain, analyzed the potential width and limitations of their depth of field, as well as achievable boundaries of the non-dimensional factor characterizing the range resolution quality. Based on an analysis of requirements for sensor capabilities, we combined a number of parameters and introduced dimensionless quantities to simplify the characteristics of systems with many interdependent parameters and influence factors. We proposed a way to evaluate the range-domain efficiency of S-lidars based on the introduced criterion of range resolution quality. Applied to S-lidars with infinite and finite depth of field, their actual range-domain efficiency can be quantitatively characterized by using the introduced criterion and taking into account the instrumental limitations. All of this made it possible to develop generalized algorithms for evaluating range-domain related characteristics of CW range-resolved S-lidars, which are easily adapted to specific applications, and also significantly simplify the procedure for selecting instrument parameters to satisfy tactical requirements. The disclosure and generalization of specific features of S-lidars will expand applicability of this promising class of laser remote sensing devices.

The triangular principle is equivalent to the triangular scheme

The triangular scheme is a diagrammatic characterization of congruence join-semidistributivity. The triangular principle is a variant of this condition, where one of the congruences is replaced by a tolerance. This paper contains two proofs showing that the triangular principle and the triangular scheme are equivalent for varieties. The first one is a routine argument using tame congruence theory, and works only for locally finite varieties. The second proof is an elementary, but nontrivial calculation with terms, which works for arbitrary varieties. This yields a stronger Mal’tsev-condition characterizing congruence join-semidistributivity than the one obtained from the triangular scheme.

A Note on Triangular Schemes for Weak Congruences

Some geometrical methods, the so called Triangular Schemes and Principles, are introduced and investigated for weak congruences of algebras. They are analogues of the corresponding notions for congruences. Particular versions of Triangular Schemes are equivalent to weak congruence modularity and to weak congruence distributivity. For algebras in congruence permutable varieties, stronger properties—Triangular Principles—are equivalent to weak congruence modularity and distributivity.

Machine Vision and Data Reconstruction for Measuring Free Form Surface

Reverse engineering of free-form surfaces is one of the most challenging technologies in advanced manufacturing. With the development of industry more and more sculptured surfaces, such as molds and turbine blades, are required to measure quickly and accurately. Optical non-contact probes possess many advantages, such as high speed, no measuring force, in comparison with contact ones. The ability of stereovision probe with CCD cameras in gathering a large amount of information simultaneously makes it the most popularly used one in sculptured surface measurements. So based on the laser triangular principle, a measuring and testing device with two CCD cameras was designed, and its accuracy was analyzed. With a virtual 3D target in form of a grid plate, all the intrinsic and extrinsic parameters of CCD camera including the uncertainty of image scale factor and optical center of camera can be readily calibrated. In order to obtain all the required data with high accuracy in a short time, the curvature-based adaptive sampling strategy is presented. Due to huge amount of arbitrary scattered points, the Delaunay triangular division and Bezier interpolation and NURBS interpolation are applied to get a continuous surface.

物理エージェントシステム(PAS)における遠隔操作ロボットのガイダンス(ネットワーク/メディアロボティクス2)

The purpose of this research is to provide a sensory feedback about distance information in the remotely controlled autonomous robot systems. The distance information to the target object, pointed by a laser pointer operated from remote place, is measured by triangular principle coupled with a CCD camera. In this research, force feedback is used, in order to display the distance information to an operator. As a result of this research, an operator can perform robot operation with a spatial feel. This paper evaluates and describes the relation between the force feedback patterns and distance recognition.

Triangulation or strangulation: managing the suicidal patient

The suicidal person is tortured by an internal dilemma to do with unbearable feelings of separation and loss which seem to be insoluble. The suicidal act is an attempt to resolve this by creating a phantasy in which the intolerable pain associated with a grievance is projected and obliterated by murdering the body that has become identified with it. This type of assault on the self reveals a major confusion between mind and body, affecting the capacity to think and resulting in two-dimensional, rather than three-dimensional, thinking, which can permeate therapeutic efforts, at both individual and systemic levels, in the way these patients are managed by their carers. It is suggested that a safety-net made up of mindful carers, based on a triangular principle, can provide a symbolic or mental space, and a containment for the patient's intolerable states of mind, which can be analogous to an ego-function that is lacking internally, and works well if the net can manage to function as a healthy parental couple. Two case studies are presented as an attempt to illuminate some of the dynamics and difficulties in maintaining the safety-net.

Development of a laser sensor for in-process guidance of an industrial robot

A pilot-type laser sensor for non-contacting distance measurement has been developed, which was aimed at application to in-process guidance of an industrial robot. A laser beam is emitted through a convex lens to an object and the reflected light is collected and focused by the lens. Diameter of its unfocused image is measured using one dimensional CCD-array, from which the distance is determined. Because the way of the beam emission and that of reflected light to the lens are the same, scanning of the beam to follow a path for robot guidance is easy and some geometric constraints, which may arise for a sensor using triangular principle, are removed. Geometric analyses for scanning the beam with a mirror are presented to determine the distance and position of an object point. A simple tracking control theory for the beam to follow a path and give informations about its position to a robot controller has been suggested and analyzed.