• Journal of the Korean Society for Precision Engineering
• /
• v.24 no.8 s.197
• /
• pp.50-57
• /
• 2007

In this paper, two types of novel planar Translational Parallel Manipulators (TPMs) by using parallelogram mechanism are conceived. One is made up of two Pa-P (Parallelogram-Prismatic) legs connecting the base to the moving platform. The other consists of two P-Pa legs, which is the kinematic inversion of the former. Since connecting links in a parallelogram mechanism are subject to only tensile/compressive load and all the heavy actuators are mounted at the base, the proposed manipulators can be applied for planar positioning/assembly tasks requiring high stiffness and high speed. The position, velocity, and statics are analyzed, and the design methodology using prescribed workspace and velocity transmission capability is presented. Finally, two types of prototype manipulators have been developed.

• The Pure and Applied Mathematics
• /
• v.16 no.1
• /
• pp.47-57
• /
• 2009

In this paper, we give some results which are in connection to the parallelogram law in G-inner product spaces and also prove some results related to Bohr's inequality in G-inner product spaces.

• Bulletin of the Korean Mathematical Society
• /
• v.33 no.1
• /
• pp.35-38
• /
• 1996

The aim of this paper is to present a characterization of Hilbert spaces in terms of the lengths of four sides and two diagonals of a parallelogram.

• Proceedings of the Korean Society of Precision Engineering Conference
• /
• 2007.06a
• /
• pp.385-386
• /
• 2007

• Journal of the Korean Institute of Telematics and Electronics T
• /
• v.36T no.3
• /
• pp.64-71
• /
• 1999

In this paper, two degree of freedom parallelogram link mechanism is used as DD(Direct-drive) robot mechanism. In parallelogram link mechanism, two motors being established in each base frame, the mass of motor itself is not loaded to anther motor; the number of links are increased, the mass of arm being lighter; with the estabilishment of link parameter, nonlinearity such as the centrifugal force disappears; at the same time anti-interference between motors can be realized. And to realize highy-accurate drive of parallelogram link DD robot manipulator, to improve the learning speed through the design of leaning control system using neural network, to raise adapting power to the varied work objects; the learning control algorithm is composed of neural network and feedback controller in this paper.

• Journal of Educational Research in Mathematics
• /
• v.13 no.4
• /
• pp.485-493
• /
• 2003

The purpose of this study is to suggest the alternative strategies for teaching mensuration of parallelogram raised by Max Wertheimer, a gestalt psychologist who was particularly concerned with mathematics learning and teaching. For this, 77 student teachers were paper and pencil tested and we could get the 7 interesting and useful ideas from their datas in spite of the fact that not many student teachers correctly responsed. Analysing the datas, it turned out all the 7 ideas are related to equivalent transformation and can make children more easily to see the structure of area of Wertheimer's parallelogram than traditional approach.

• Honam Mathematical Journal
• /
• v.39 no.3
• /
• pp.431-442
• /
• 2017

For a quadrilateral P, we consider the centroid $G_0$ of the vertices of P, the perimeter centroid $G_1$ of the edges of P and the centroid $G_2$ of the interior of P, respectively. We denote by M the intersection point of two diagonals of P. If P is a parallelogram, then we have $G_0=G_1=G_2=M$. Conversely, one of $G_0=M$ and $G_2=M$ implies that P is a parallelogram. In this paper, we show that $G_1=M$ is also a characteristic property of parallelograms.

• Journal of the Korean Society for Precision Engineering
• /
• v.32 no.1
• /
• pp.107-111
• /
• 2015

This paper proposes an optimal design for a precision motion stage employing a parallelogram flexure hinge. The voltage applied to the piezo element produces motion that is amplified through a 3-stage amplification structure. Especially, instead of the generally used conic section flexure hinge a parallelogram shaped flexure hinge is used that improves the flexibility of the lever. An Finite Element Analysis is performed on each motion stage lever where optimal design was achieved using Response Surface Methodology(RSM).

• Honam Mathematical Journal
• /
• v.39 no.1
• /
• pp.127-136
• /
• 2017

For a quadrangle P, we consider the centroid $G_0$ of the vertices of P, the perimeter centroid $G_1$ of the edges of P and the centroid $G_2$ of the interior of P, respectively. If $G_0$ is equal to $G_1$ or $G_2$, then the quadrangle P is a parallelogram. We denote by M the intersection point of two diagonals of P. In this note, first of all, we show that if M is equal to $G_0$ or $G_2$, then the quadrangle P is a parallelogram. Next, we investigate various quadrangles whose perimeter centroid coincides with the intersection point M of diagonals. As a result, for an example, we show that among circumscribed quadrangles rhombi are the only ones whose perimeter centroid coincides with the intersection point M of diagonals.

• Journal of applied mathematics & informatics
• /
• v.23 no.1_2
• /
• pp.321-327
• /
• 2007

We say that a triangle ${\Delta}$ tiles the polygon ${\rho}\;if\;{\rho}$ can be decomposed into finitely many non-overlapping triangles similar to ${\Delta}$. Let ${\rho}$ be a parallelogram with angles ${\delta}\;and\;{\pi}-{\delta}\;(0<{\delta}{\leq}{\pi}/2)$ and let ${\Delta}$ be a triangle with angles ${\alpha};{\beta},\;{\gamma}\;({\alpha}{\leq}{\beta}{\leq}{\gamma})$. We prove that if ${\Delta}$ tiles ${\rho}$ then either ${\delta}{\in}\;({\alpha},\;{\beta},\;{\gamma},\;{\pi}-{\gamma},\;{\pi}-2{\gamma})\;or\;dimL_{\rho}=dimL_{{\Delta}}$. We also prove that for every parallelogram P, and for every integer n $(where\;n{\geq}2,\;n{\neq}3)$ there is a triangle ${\Delta}$ so that n similar copies of ${\Delta}\;tile\;{\rho}$.