A diagram of the minimum necessary internal force required to resist external forces on two-point-grasped objects in two-dimensional space

Robotica ◽  
2011 ◽  
Vol 30 (5) ◽  
pp. 857-864
Author(s):  
Satoshi Ito ◽  
Kohta Tanaka ◽  
Minoru Sasaki
Keyword(s):  
External Force ◽  
Dimensional Space ◽  
Internal Force ◽  
Polar Coordinate System ◽  
Coordinate Frame ◽  
Two Dimensional ◽  
Force Diagram ◽  
Contact Points ◽  
Polar Coordinate ◽  
External Forces

SUMMARYThis paper considers the magnitude of the gripping power, i.e., the internal force that depends on the grasping posture or object orientation in a two-dimensional grasp by two contact points with friction. Expressing the effect of variations in the object posture as the direction of an external force, we propose an “internal force diagram.” The internal force necessary to create a statically stable grasp is depicted in the object coordinate frame. Then, a polar coordinate system is introduced in which the orientation represents the direction of the external force, while the distance from the origin represents the minimum necessary internal force. We demonstrate a method based on friction cone configurations to manually draw the internal force diagram, using only a ruler and a compass. The validity of this drawing method is confirmed by a comparison with computer-generated plots. Finally, the characteristics of the internal force diagram are discussed.

Averaging of a nonlinear bipolar model with phase transition and oscillating external forces

2015 ◽  
Vol 21 (2) ◽  
Author(s):  
Theodore Tachim Medjo
Keyword(s):  
Phase Transition ◽  
Small Parameter ◽  
Global Attractor ◽  
Bounded Domain ◽  
External Force ◽  
Two Dimensional ◽  
External Forces ◽  
Uniform Global Attractor

AbstractIn this article, we consider a non-autonomous nonlinear bipolar with phase transition in a two-dimensional bounded domain. We assume that the external force is singularly oscillating and depends on a small parameter ϵ. We prove the existence of the uniform global attractor 𝒜

A paradox of hovering insects in two-dimensional space

2008 ◽  
Vol 617 ◽  
pp. 207-229 ◽  
Author(s):  
MAKOTO IIMA
Keyword(s):  
External Force ◽  
Stokes Equations ◽  
Hydrodynamic Force ◽  
Dimensional Space ◽  
Exact Formula ◽  
Uniform Flow ◽  
Far Field ◽  
Two Dimensional ◽  
Field Representation ◽  
Whole Space

A paradox concerning the flight of insects in two-dimensional space is identified: insects maintaining their bodies in a particular position (hovering) cannot, on average, generate hydrodynamic force if the induced flow is temporally periodic and converges to rest at infinity. This paradox is derived by using the far-field representation of periodic flow and the generalized Blasius formula, an exact formula for a force that acts on a moving body, based on the incompressible Navier–Stokes equations. Using this formula, the time-averaged force can be calculated solely in terms of the time-averaged far-field flow. A straightforward calculation represents the averaged force acting on an insect under a uniform flow, −〈V〉, determined by the balance between the hydrodynamic force and an external force such as gravity. The averaged force converges to zero in the limit 〈V〉 → 0, which implies that insects in two-dimensional space cannot hover under any finite external force if the direction of the uniform flow has a component parallel to the external force. This paradox provides insight into the effect of the singular behaviour of the flow around hovering insects: the far-field wake covers the whole space. On the basis of these assumptions, the relationship between this paradox and real insects that actually achieve hovering is discussed.

Investigating the Polar Qualification System

1998 ◽  
Vol 6 (A) ◽  
pp. A191-A200 ◽  
Author(s):  
Károly J. Kaffka ◽  
László S. Gyarmati
Keyword(s):  
Infrared Spectroscopy ◽  
Coordinate System ◽  
Near Infrared Spectroscopy ◽  
Near Infrared ◽  
Polar Coordinate System ◽  
Base Line ◽  
Two Dimensional ◽  
International Conference ◽  
Polar Coordinate ◽  
Characteristic Features

A new, rapid qualification method was introduced at the 3rd International Conference on Near Infrared Spectroscopy according to which a “quality point” was defined on a two-dimensional “quality plane”. The quality point of the investigated material was given by the center of its spectrum represented in a polar coordinate system. The method was further developed, three interpretations were given for the “center” of the polar spectrum, resulting in three different formulas for determining the x and y coordinates of the quality point. The effect of the change in the amplitude of the absorption peaks, the effect of the noise of the spectrum, the effect of the shifting and tilting the base-line of the spectrum on the location of the quality point were investigated using the three formulas. The results of the investigation and the characteristic features of the three formulas are introduced.

Rapid and precise method to convert a two dimensional image from Cartesian to polar coordinate system

1997 ◽  
Vol 68 (9) ◽  
pp. 3490-3493 ◽  
Author(s):  
Weimin Wu ◽  
Yoshihiro Kato ◽  
K. Yamazaki ◽  
M. Yoshino ◽  
A. Danjo ◽  
...  
Keyword(s):  
Coordinate System ◽  
Polar Coordinate System ◽  
Two Dimensional ◽  
Precise Method ◽  
Dimensional Image ◽  
Two Dimensional Image ◽  
Polar Coordinate

scholarly journals The shape of space: Evidence for spontaneous but flexible use of polar coordinates in visuospatial representations

2021 ◽  
Author(s):  
Sami Ryan Yousif ◽  
Frank Keil
Keyword(s):  
Spatial Representation ◽  
Dimensional Space ◽  
Spatial Scales ◽  
Human Mind ◽  
Polar Coordinates ◽  
Polar Coordinate System ◽  
Coordinate Systems ◽  
Spatial Tasks ◽  
Polar Coordinate ◽  
Visual Matching

What is the format of spatial representation? In mathematics, we often conceive of two primary ways of representing two-dimensional space, Cartesian coordinates, which capture horizontal and vertical relations, and polar coordinates, which captures angle and distance relations. Do either of these two coordinate systems play a representational role in the human mind? Six experiments utilizing a simple ‘visual matching’ paradigm show that (1) representational format is recoverable from the errors observers make in simple spatial tasks; (2) human-made errors spontaneously favor a polar coordinate system of representation; and (3) observers are capable of using other coordinate systems when acting in highly structured spaces (e.g., grids). We discuss these findings in relation to classic work on dimension independence, as well as work on spatial representation at other spatial scales.

Research on improved hough algorithm and its application in lunar crater

2021 ◽  
pp. 1-9
Author(s):  
Lanfeng Zhou ◽  
Ling Li
Keyword(s):  
Coordinate System ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Detection Algorithm ◽  
Polar Coordinate System ◽  
Circle Center ◽  
Traditional Algorithm ◽  
Polar Coordinate ◽  
Cartesian Coordinate ◽  
Three Dimensional Space

Traditional Hough circle detection algorithm usually determines the center and radius of a circle by mapping points in cartesian coordinate system to polar coordinate system. Since it accumulates in the three-dimensional space, it requires more calculation consumption. In this paper, we solve the problem of high time complexity of Hough algorithm in judging circle radius and circle center from two aspects of circle angle and circle radius according to the geometric features of quasi-circles. A large number of experiments show that, compared with the traditional algorithm, this algorithm can not only identify quasi-circles, but also improve the detection success rate of circles by about 10%, with efficient running speed, and obtain good experimental results in the detection of craters.

Sign in / Sign up

Export Citation Format

Share Document