scholarly journals Formal Kinematic Analysis of a General 6R Manipulator Using the Screw Theory

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Aixuan Wu ◽  
Zhiping Shi ◽  
Yongdong Li ◽  
Minhua Wu ◽  
Yong Guan ◽  
...  

Kinematic analysis is a significant method when planning the trajectory of robotic manipulators. The main idea behind kinematic analysis is to study the motion of the robot based on the geometrical relationship of the robotic links and their joints, such as the Denavit-Hartenberg parameters. Given the continuous nature of kinematic analysis and the shortcoming of the traditional verification methods, we propose to use high-order-logic theorem proving for conducting formal kinematic analysis. Based on the screw theory in HOL4, which is newly developed by our research institute, we utilize the geometrical theory of HOL4 to develop formal reasoning support for the kinematic analysis of a robotic manipulator. To illustrate the usefulness of our fundamental formalization, we present the formal kinematic analysis of a general 6R manipulator.

Author(s):  
Ekaterina A. LOBANOVA

This article studies the cognitive features of the “power” frame and its gender implementation in the historical tragedy by W. Shakespeare “Macbeth”. Here, the author examines the concepts of “frame” and “gender” in linguistics, studying different approaches to their definition. The relevance of this work is determined by the close attention of the contemporary linguistics to these concepts, as well as their place in the contemporary academic paradigm. The academic affirmation of the “frame” and “gender” concepts designates a new step in understanding the ways and peculiarities of the language interaction, consciousness, and culture, and, consequently, it shows new aspects of the relationship of linguistics with other sciences. Nevertheless, the problems of both frame and gender are not yet fully understood. This study allows describing in detail the essence of the frame “power” and showing its meaning, use, and ways of its gender implementation in fiction, which explains the novelty of this article. The study’s methodology is based on the cognitive-discursive analysis of the text, as well as on an integrative approach to the discourse study, which combines methods of both cognitive and gender linguistics, as well as the discourse analysis. Common research methods were used along with private linguistic methods. The application of cognitive-discursive analysis has significantly increased the depth of understanding of the “power” frame that dominates Shakespeare’s historical tragedy. This historical text presents the central theme of political tragedy: the overthrow of the rightful ruler and the usurpation of power. The motive for the seizure of power forms a thematic core and is presented from the usurpers’ point of view. In this article, the author observes the gender shift and duality of the female and male beginnings: Shakespeare puts the female protagonist, hungry for power, among men, thus the images of Lady Macbeth and her husband come into conflict with the gender characteristics attributed to them. The play clearly traces the main idea of Machiavellianism: the goal justifies the means. The results conclude that the “power” frame is the leading one in Lady Macbeth’s monologue, thus setting one of the main themes of this tragedy.


Machines ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 41
Author(s):  
Tatsuya Yamamoto ◽  
Nobuyuki Iwatsuki ◽  
Ikuma Ikeda

The systematic kinematic analysis method for planar link mechanisms based on their unique procedures can clearly show the analysis process. The analysis procedure is expressed by a combination of many kinds of conversion functions proposed as the minimum calculation units for analyzing a part of the mechanism. When it is desired to perform this systematic kinematics analysis for a specific linkage mechanism, expert researchers can accomplish the analysis by searching for the procedure by themselves, however, it is difficult for non-expert users to find the procedure. This paper proposes the automatic procedure extraction algorithm for the systematic kinematic analysis of closed-loop planar link mechanisms. By limiting the types of conversion functions to only geometric calculations that are related to the two-link chain, the analysis procedure can be represented by only one type transformation function, and the procedure extraction algorithm can be described as a algorithm searching computable 2-link chain. The configuration of mechanism is described as the “LJ-matrix”, which shows the relationship of connections between links with pairs. The algorithm consists of four sub-processes, namely, “LJ-matrix generator”, “Solver process”, “Add-link process”, and “Over-constraint resolver”. Inputting the sketch of the mechanism into the proposed algorithm, it automatically extracts unique analysis procedure and generate a kinematic analysis program as a MATLAB code based on it. Several mechanisms are analyzed as examples to show the usefulness of the proposed method.


1988 ◽  
Vol 53 (3) ◽  
pp. 834-839 ◽  
Author(s):  
H. Andréka ◽  
W. Craig ◽  
I. Németi

Ordinary equational logic is a connective-free fragment of first-order logic which is concerned with total functions under the relation of ordinary equality. In [AN] (see also [AN1]) and in [Cr] it has been extended in two equivalent ways into a near-equational system of logic for partial functions. The extension given in [Cr] deals with partial functions under two relationships: a relationship of existence-dependent existence and one of existence-dependent Kleene equality. For the language that involves both relationships a set of rules was given that is complete. Those rules in the set that involve only existence-dependent existence turned out to be complete for the sublanguage that involves this relationship only. In the present paper we give a set of rules that is complete for the other sublanguage, namely the language of partial functions under existence-dependent Kleene equality.This language lacks a certain, often needed, power of expressing existence and fails, in particular, to be an extension of the language that underlies ordinary equational logic. That it possesses a fairly simple complete set of rules is therefore perhaps more of theoretical than of practical interest. The present paper is thus intended to serve as a supplement to [Cr] and, less directly, to [AN]. The subject is further rounded out, and some contrast is provided, by [Rob]. The systems of logic treated there are based on the weaker language in which partial functions are considered under the more basic relation of Kleene equality.


2014 ◽  
Vol 28 (9) ◽  
pp. 3785-3792 ◽  
Author(s):  
Jaime Gallardo-Alvarado ◽  
Albert L. Balmaceda-Santamaría ◽  
Eduardo Castillo-Castaneda

2007 ◽  
Vol 3 (10) ◽  
pp. 810-817
Author(s):  
Sa'ed Abed ◽  
Otmane Ait Mohamed ◽  
Ghiath Al Sammane

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