216 H. Stachel: On Arne Dür’s Equation Concerning Central Axonometries (2009)
Hellmuth Stachel, Ag Replacements O
Abstract. It is a classical Descriptive Geometry problem in the Euclidean nspace to characterize the central projections among collinear transformations with rank deficiency. Recently A. Dür...
THE GEOMETRY BEHIND THE NUMERICAL RECONSTRUCTION OF TWO PHOTOS (2009)
Abstract: The geometry of pairs of linear images has been a standard topic of Descriptive Geometry for more than 100 years [2]. During the last twenty years great progress has been made within the...
Giorgio Figliolini, Hellmuth Stachel, Jorge Angeles
The subject of this paper is a diagram due to Martin Disteli. The diagram, illustrating the relation between the angular velocities of a pair of skew gears, is intended for the analysis of the...
Guidelines for Preparing L ATeX Manuscripts for Journal of Geometry and Graphics (2009)
Hellmuth Stachel, Johannes Wallner
In order to achieve high printing quality and at the same time keep printing costs low, Journal of Geometry and Graphics accepts articles only if they are written in L ATeX, which is more or less...
TEACHING SPATIAL KINEMATICS FOR MECHANICAL ENGINEERING STUDENTS (2009)
Abstract. Spatial kinematics is a challenging field because of its real world applications at serial and parallel manipulators. However, it is not easy to teach as on the one hand the students ’...
Spatial involute gearing- a new type of skew gears (2009)
This is a geometric approach to spatial involute gearing which has recently been developed by Jack Phillips [4]. Due to Phillips ' fundamental theorems helical involute gears for parallel axes...
ISBN: 978-3-86780-042-6 COMMENTS ON HELICAL DEVELOPABLES (2009)
ABSTRACT: All normal lines of a helical developable Φ have the same distance to its axis a and make the same angle with a. This implies that on coaxial one-sheet hyperboloids of revolution or skew...
Gears and Belt Drives for Non-Uniform Transmission (2009)
Abstract Ordinarily, gears and belt drives are used for uniform transmission of rotations between parallel axes. Here we focus on the nonuniform case, i.e., with non-constant transmission ratio. We...
THE STATUS OF TODAYS DESCRIPTIVE GEOMETRY RELATED EDUCATION (CAD/CG/DG) IN EUROPE (2009)
ABSTRACT: The goal of my presentation is to explain what Descriptive Geometry is good for and in which way the Descriptive Geometry education is carried out in European countries. By definition,...
Abstract. Two problems from different areas are presented in order to demonstrate the applicability of geometry. In both cases the solutions are based on results that are beyond the topics we usually...
Sadi Abu-saymeh, Mowaffaq Hajja, Hellmuth Stachel
Abstract. Let ABC be a triangle with side-lengths a, b, and c. For a point P in its plane, let APa, BPb, and CPc be the cevians through P. It was proved in [1] that the centroid, the Gergonne point,...
Abstract. The geometry of multiple images has been a standard topic in Descriptive Geometry and Photogrammetry (Remote Sensing) for more than 100 years. During the last twenty years great progress...
Remarks on A. Hirsch’s Paper concerning Villarceau Sections (2008)
Abstract. When a surface of revolution with a conic as meridian is intersected with a bitangential plane, then the curve of intersection splits into two congruent conics. Conversely a necessary and...
What is Descriptive Geometry for? (2008)
This is a pleading for Descriptive Geometry. From the very first, Descriptive Geometry is a method to study 3D geometry through 2D images thus offering insight into structure and metrical properties...
On Spatial Involute Gearing (2008)
This is a geometric approach to spatial involute gearing which has recently been developed by Jack Phillips [2]. New proofs of Phillips ’ fundamental theorems are given. And it is pointed out that...
In the series of International Conferences on Geometry and (2008)
ABSTRACT This is a geometric approach to spatial involute gearing which has recently been developed by Jack Phillips (2003). After recalling Phillips ' fundamental theorems and other properties,...
Hans Dirnböck, Hellmuth Stachel
Abstract. Let two unit circles kA, kB in perpendicular planes be given such that each circle contains the center of the other. Then the convex hull of these circles is called Oloid. In the following...
On Martin Disteli’s Main Achievements in Spatial Gearing: Disteli’s Diagram (2008)
Giorgio Figliolini, Hellmuth Stachel
1. The relative axis for helical gears We treat the relation between the angular velocities of a pair of skew gears and the position and pitch of their relative PSfragscrew replacements motion. We...
216 H. Stachel: On Arne Dür’s Equation Concerning Central Axonometries (2008)
Hellmuth Stachel, Ag Replacements O
Abstract. It is a classical Descriptive Geometry problem in the Euclidean nspace to characterize the central projections among collinear transformations with rank deficiency. Recently A. Dür...
Napoleon's Theorem and Generalizations Through Linear Maps (2007)
Hellmuth Stachel, Recently J. Fukuta
Recently J. Fukuta and Z. Cerin showed how regular hexagons can be associated to each triangle, thus extending Napoleon's theorem. The aim of this paper is to prove that these results are...
A Remarkable Overconstrained Spherical Motion (2007)
: The motion under consideration is based on the fact that in the Euclidean space three pairwise orthogonal axes can simultaneously move on a so-called equilateral cone. This defines a non-rational...
Flexible Octahedra in the Hyperbolic Space (2007)
This paper treats exible polyhedra in the hyperbolic 3-space H . It is proved that the geometric characterization of octahedra being in nitesimally exible of orders 1 or 2 is quite the same as in the...
DESCRIPTIVE GEOMETRY MEETS COMPUTER VISION — THE GEOMETRY OF MULTIPLE IMAGES (2006)
ABSTRACT:The geometry of multipleimages has been astandard topic in DescriptiveGeometry and Photogrammetry (Remote Sensing) for more than 100 years. During the last twenty years great progress has...
Contact Areas of the Tibiotalar Joint (2006)
Gunther Windisch, Boris Odehnal, Reinhold Reimann, Friedrich Anderhuber, Hellmuth Stachel
ABSTRACT: The contact areas between the articular surfaces of the talus and tibia are essential for understanding the mobility of the ankle joint. The purpose of our study was to reveal the contact...
C2 popunjavanje praznina pomoću konveksne kombinacije ploha pod rubnim ograničenjima (2003)
Szilvási-Nagy, Márta; Department Of Geometry Budapest University Of Technology And Economics, Budapest, Hungary; Szilvasi@math.bme.hu, Vendel, Teréz P.; Department Of Mathematics University Of Pécs, Pécs, Hungary; Vendel@witch.pmmf.hu, Stachel, Hellmuth; Inst. Of Geometry Vienna University Of Technology, Vienna, Austria; Stachel@geometrie.tuwien.ac.at
Dane su dvije metode za izvođenje ploha. Jedna za povezivanje dviju ploha sa C2 neprekinutošću koja odgovara i dvjema graničnim linijama, a druga za G1 popunjavanje posebnog slučaja trostrane...
Instantaneous Spatial Kinematics and the Invariants of the Axodes (2000)
Hellmuth Stachel, Sir Robert, Stawell Ball
In this paper the dependencies between the instantaneous invariants of a spatial motion and the local invariants of the axodes are studied in a way that includes all types of ruled surfaces. New...
Instantaneous Spatial Kinematics and the Invariants of the Axodes (2000)
In this paper the dependencies between the instantaneous invariants of a spatial motion and the local invariants of the axodes are studied in a way that includes all types of ruled surfaces. New...
Higher Order Flexibility of Octahedra (1999)
More than hundred years ago R. Bricard determined all continuously flexible octahedra. On the other hand, also the geometric characterization of first-order flexible octahedra has been well known for...
Higher Order Flexibility of Octahedra (1999)
More than hundred years ago R. Bricard determined all continuously flexible octahedra. On the other hand, also the geometric characterization of first-order flexible octahedra has been well known for...
Higher-Order Flexibility for a Bipartite Planar Framework (1999)
Infinitesimally flexible frameworks are well known in kinematics, in particular recently as singular postures in robotics. The objective of this paper is to analyze a bipartite planar framework in...
Infinitesimal Flexibility of Higher Order for a Planar Parallel Manipulator (1999)
: The problems around rigidity and flexibility of geometrical structures have a long history in mathematics. Recently obtained results like the proof of the "Bellows Conjecture" have...
Higher Order Flexibility of Octahedra (1999)
More than hundred years ago R. Bricard determined all continuously flexible octahedra. On the other hand, also the geometric characterization of first-order flexible octahedra has been well known for...
On the Tetrahedra in the Dodecahedron (1999)
The 60 edges of the ten tetrahedra inscribed in a regular pentagondodecahedron form the so-called GR UNBAUM framework. It is already known that this structure is flexible. There are one-parameter...
This paper treats exible cross-polytopes in the Euclidean 4-space. It is shown that the examples presented 1998 by A. Walz are special cases of a more general class of exible cross-polytopes. The...
Almost-orthonormal Vector Systems (1996)
Dietrich Haase, Hellmuth Stachel, In R
. Particular systems of unit vectors e 1 ; : : : ; e n with rotational symmetry in R d , d = 2; 3 , d ! n , share some properties with orthonormal bases: The sum of dyadic products equals the...
Generating Solids by Sweeping Polyhedra (1996)
Ahmed Elsonbaty, Hellmuth Stachel
. Let a one-parametric motion fi and the boundary representation of a polyhedron P be given. Our goal is to determine the solid S 0 swept by P under fi : The complete boundary @S 0 of S 0 contains a...
What is Descriptive Geometry for?
This is a pleading for Descriptive Geometry. From the very first, Descriptive Geometry is a method to study 3D geometry through 2D images thus offering insight into structure and metrical properties...