Geometrical Kinematic Analysis of a Planar Serial Manipulator Using the Barycentric Formula

Author(s):  
Chan. Lee ◽  
Ma Eum. Kim ◽  
Jeh Won. Lee
Author(s):  
Chan Lee ◽  
Jeh Won Lee ◽  
TaeWon Seo

The kinematics, instantaneous motion, and statics of a manipulator have recently been determined algebraically. In the past, such studies did not provide any intuition about the equation. Robot designers had to use a numerical method or trial-and-error solver with unintuitive equations. Alternatively, all algebraic processes have their own geometrical meaning. Geometric analysis provides intuition for designing the linkages of a robot. Screw theory and barycentric formulas are used to find meaningful geometric measures. The kinematics and statics of a manipulator are described by an axis screw and its reciprocal line screw. The barycenter of a triangle with edges and a perpendicular distance between the two screws are useful geometric measures for geometric analysis. This study provides a geometric interpretation of the kinematics and statics of a planar manipulator using a barycentric formula.


Author(s):  
L. -M. Peng ◽  
M. J. Whelan

In recent years there has been a trend in the structure determination of reconstructed surfaces to use high energy electron diffraction techniques, and to employ a kinematic approximation in analyzing the intensities of surface superlattice reflections. Experimentally this is motivated by the great success of the determination of the dimer adatom stacking fault (DAS) structure of the Si(111) 7 × 7 reconstructed surface.While in the case of transmission electron diffraction (TED) the validity of the kinematic approximation has been examined by using multislice calculations for Si and certain incident beam directions, far less has been done in the reflection high energy electron diffraction (RHEED) case. In this paper we aim to provide a thorough Bloch wave analysis of the various diffraction processes involved, and to set criteria on the validity for the kinematic analysis of the intensities of the surface superlattice reflections.The validity of the kinematic analysis, being common to both the TED and RHEED case, relies primarily on two underlying observations, namely (l)the surface superlattice scattering in the selvedge is kinematically dominating, and (2)the superlattice diffracted beams are uncoupled from the fundamental diffracted beams within the bulk.


2008 ◽  
Author(s):  
Connie E. Myerson ◽  
Eniko K. Toth ◽  
Joseph M. Wasserman ◽  
W.D. Dietrich ◽  
Edward J. Green

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