Three-Dimensional Generalizations of Reuleaux’s and Instant Center Methods Based on Line Geometry

2010 ◽  
Vol 2 (4) ◽  
Author(s):  
Jasem Baroon ◽  
Bahram Ravani
Keyword(s):  
Rigid Body ◽  
Three Dimensional ◽  
Geometric Method ◽  
Two Dimensional ◽  
Line Geometry ◽  
Basic Form ◽  
Motion Reconstruction ◽  
Moving Body ◽  
On Line

In kinematics, the problem of motion reconstruction involves generation of a motion from the specification of distinct positions of a rigid body. In its most basic form, this problem involves determination of a screw displacement that would move a rigid body from one position to the next. Much, if not all of the previous work in this area, has been based on point geometry. In this paper, we develop a method for motion reconstruction based on line geometry. A geometric method is developed based on line geometry that can be considered a generalization of the classical Reuleaux method used in two-dimensional kinematics. In two-dimensional kinematics, the well-known method of finding the instant center of rotation from the directions of the velocities of two points of the moving body can be considered an instantaneous case of Reuleaux’s method. This paper will also present a three-dimensional generalization for the instant center method or the instantaneous case of Reuleaux’s method using line geometry.

A Three-Dimensional Generalization of Reuleaux’s Method Based on Line Geometry

2006 ◽  
Author(s):  
Jasem Baroon ◽  
Bahram Ravani
Keyword(s):  
Rigid Body ◽  
Least Squares ◽  
Least Squares Method ◽  
Three Dimensional ◽  
Line Geometry ◽  
Basic Form ◽  
Motion Reconstruction ◽  
Linear Solution ◽  
On Line

In kinematics, the problem of motion reconstruction involves generation of a motion from the specification of distinct positions of a rigid body. In its most basic form, this problem involves determination of a screw displacement that would move a rigid body from one position to the next. Much if not all of the previous work in this area has been based on point geometry. In this paper, we develop a method for motion reconstruction based on line geometry. An elegant geometric method is developed based on line geometry that can be considered as a generalization of the classical Reuleaux’s method used in 2D kinematics. The case of over determined system is also considered a linear solution is presented based on least squares method.

Expanding the theory: Nonverbal determination of referents in a joystick task

2001 ◽  
Vol 24 (2) ◽  
pp. 224-225
Author(s):  
Katherine A. Leighty ◽  
Sarah E. Cummins-Sebree ◽  
Dorothy M. Fragaszy
Keyword(s):  
Three Dimensional ◽  
Two Dimensional ◽  
Nonhuman Species

The arguments of Stoffregen & Bardy for studying perception based on the global array are intriguing. This theory can be examined in nonhuman species using nonverbal tasks. We examine how monkeys master a skill that incorporates a two-dimensional/three-dimensional interface. We feel this provides excellent support for Stoffregen & Bardy's theory.

The Volume of Motion: Introduction, Derivation, and an Application Comparing Various Spinal Fixation Devices

1993 ◽  
Vol 115 (1) ◽  
pp. 43-46 ◽  
Author(s):  
J. J. Crisco
Keyword(s):  
Rigid Body ◽  
Three Dimensional ◽  
Spinal Fixation ◽  
Dimensional Parameter ◽  
Directional Information ◽  
One Dimensional ◽  
Fixation Devices ◽  
Spinal Fixation Devices ◽  
Mathematical Derivation

Range of motion (ROM), the displacement between two limits, is one of the most common parameters used to describe joint kinematics. The ROM is a one-dimensional parameter, although the motion at many normal and pathological joints is three-dimensional. Certainly, the ROM yields vital information, but an overall measure of the three-dimensional mobility at a joint may also be useful. The volume of motion (VOM) is such a measure. The translational VOM is the volume defined by all possible ROMs of a point on a rigid body. The rotational VOM, although its interpretation is not as tangible as the translational VOM, is a measure of the three-dimensional rotational mobility of a rigid body. The magnitude of the VOM is proportional to mobility; the VOM is a scaler, which does not contain any directional information. Experimental determination of the VOM is not practical since it would require applying loads in an infinite number of directions. The mathematical derivation given here allows the VOM to be calculated, with the assumption of conservative elasticity, from the resultant displacements of three distinct load vectors of equal magnitude. An example of the VOM is presented in the comparison of the biomechanical stabilizing potential of various spinal fixation devices.

The method of caustics for the determination of normal loads acting on surfaces of elastic bodies

1980 ◽  
Vol 15 (1) ◽  
pp. 37-41 ◽  
Author(s):  
P S Theocaris ◽  
N I Ioakimidis
Keyword(s):  
Three Dimensional ◽  
Contact Problems ◽  
Two Dimensional ◽  
Concentrated Force ◽  
Elastic Bodies ◽  
Plate And Shell ◽  
Elasticity Problems ◽  
Three Dimensional Elasticity ◽  
Quantities Of Interest

The optical method of caustics constitutes an efficient experimental technique for the determination of quantities of interest in elasticity problems. Up to now, this method has been applied only to two-dimensional elasticity problems (including plate and shell problems). In this paper, the method of caustics is extended to the case of three-dimensional elasticity problems. The particular problems of a concentrated force and a uniformly distributed loading acting normally on a half-space (on a circular region) are treated in detail. Experimentally obtained caustics for the first of these problems were seen to be in satisfactory agreement with the corresponding theoretical forms. The treatment of various, more complicated, three-dimensional elasticity problems, including contact problems, by the method of caustics is also possible.

Electron Crystallographic Determination of the Structure of Bacteriorhodopsin

1990 ◽  
Vol 48 (1) ◽  
pp. 90-91
Author(s):  
R. Henderson ◽  
J.M. Baldwin ◽  
T.A. Ceska ◽  
E. Beckman ◽  
F. Zemlin ◽  
...  
Keyword(s):  
High Resolution ◽  
Proton Pump ◽  
Three Dimensional ◽  
Atomic Resolution ◽  
Two Dimensional ◽  
New Methods ◽  
Density Map ◽  
Diffraction Patterns

The light driven proton pump bacteriorhodopsin (bR) occurs naturally as two-dimensional crystals. A three-dimensional density map of the structure, at near atomic resolution, has been obtained by studying the crystals using electron cryo-microscopy to obtain diffraction patterns and high resolution micrographs (1).New methods have been developed for analysing micrographs from tilted specimens, incorporating the methods previously developed for untilted specimens that enable large areas to be analysed and corrected for distortions. Data from 72 images, from both tilted and untilted specimens, have been analysed to produce the phases of 2700 independent Fourier components of the structure. The amplitudes of these components have been accurately measured from 150 diffraction patterns. Together, these data represent about half of the full three-dimensional transform to 3.5 Å. The distribution of the data which is included in the map is shown in fig. 1. For specimen tilts up to around 20° the data is essentially complete. For higher tilts the data is more sparsely sampled, and is at present about half complete.

Attitude Angle Measurement Method Based on the Three-Dimensional Accelerometer

2013 ◽  
Vol 333-335 ◽  
pp. 152-156
Author(s):  
Yu Fa Tang ◽  
He Zhang ◽  
Li Hong
Keyword(s):  
Circuit Design ◽  
Inclination Angle ◽  
Attitude Determination ◽  
Three Dimensional ◽  
Angle Measurement ◽  
Two Dimensional ◽  
Theoretical Support ◽  
Attitude Angle ◽  
Hardware Circuit

On the basis of a study of measuring inclination angle with a two-dimensional accelerometer, a principle method using a three-dimensional accelerometer to measure attitude angle is analysed on the condition of micro-rotating. The method can reduce random systematic errors caused by uniaxial or biaxial output of the two-dimensional accelerometer. It can simultaneously measure both inclination angle and roll angle. So hardware selection, hardware circuit design and experiments are done: simulate the roll and tilt movement of the special objects and compare the solver results with the actual results. The principle method achieves preferable results, and provides a theoretical support for attitude determination of a particular industry as well.

Sign in / Sign up

Export Citation Format

Share Document