Automated Generation of Linkage Loop Equations for Planar 1-DoF Linkages, Demonstrated up to 8-Bar

Volume 5A: 38th Mechanisms and Robotics Conference ◽

10.1115/detc2014-35263 ◽

2014 ◽

Author(s):

Brian E. Parrish ◽

J. Michael McCarthy ◽

David Eppstein

Keyword(s):

Kinematic Analysis ◽

Common Edge ◽

Automated Generation ◽

Cycle Basis

In this paper we present an algorithm that automatically creates the linkage loop equations for planar 1-DoF linkages of any topology with rotating joints, demonstrated up to 8-bars. The algorithm derives the linkage loop equations from the linkage graph by establishing a cycle basis through a single common edge. Divergent and convergent loops are identified and used to establish the fixed angles of the ternary and higher links. Results demonstrate the automated generation of the linkage loop equations for the five distinct 6-bar mechanisms, Watt I-II and Stephenson I-III, as well as the seventy one distinct 8-bar mechanisms. The resulting loop equations enable the automatic derivation of the Dixon determinant for linkage kinematic analysis of the position of every possible assembly configuration. The loop equations also enable the automatic derivation of the Jacobian for singularity evaluation and tracking of a particular assembly configuration over the desired range of input angles. The methodology provides the foundation for the automated configuration analysis of every topology and every assembly configuration of 1-DoF linkages with rotating joints up to 8-bar. The methodology also provides a foundation for automated configuration analysis of 10-bar and higher linkages.

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Automated Generation of Linkage Loop Equations for Planar One Degree-of-Freedom Linkages, Demonstrated up to 8-Bar

Journal of Mechanisms and Robotics ◽

10.1115/1.4029306 ◽

2015 ◽

Vol 7 (1) ◽

Cited By ~ 5

Author(s):

Brian E. Parrish ◽

J. Michael McCarthy ◽

David Eppstein

Keyword(s):

Kinematic Analysis ◽

Degree Of Freedom ◽

Common Edge ◽

Adjacency Graph ◽

Automated Generation ◽

Cycle Basis ◽

Revolute Joints

In this paper, we present an algorithm that automatically creates the linkage loop equations for planar one degree of freedom, 1DOF, linkages of any topology with revolute joints, demonstrated up to 8 bar. The algorithm derives the linkage loop equations from the linkage adjacency graph by establishing a rooted cycle basis through a single common edge. Divergent and convergent loops are identified and used to establish the fixed angles of the ternary and higher links. Results demonstrate the automated generation of the linkage loop equations for the nine unique 6-bar linkages with ground-connected inputs that can be constructed from the five distinct 6-bar mechanisms, Watt I–II and Stephenson I–III. Results also automatically produced the loop equations for all 153 unique linkages with a ground-connected input that can be constructed from the 71 distinct 8-bar mechanisms. The resulting loop equations enable the automatic derivation of the Dixon determinant for linkage kinematic analysis of the position of every possible assembly configuration. The loop equations also enable the automatic derivation of the Jacobian for singularity evaluation and tracking of a particular assembly configuration over the desired range of input angles. The methodology provides the foundation for the automated configuration analysis of every topology and every assembly configuration of 1DOF linkages with revolute joints up to 8 bar. The methodology also provides a foundation for automated configuration analysis of 10-bar and higher linkages.

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A General Method for Kinematic Analysis of Epicyclic Bevel Gear Trains Applied to Robotic Wrist Mechanisms

Volume 4A: Dynamics, Vibration and Control ◽

10.1115/imece2013-62177 ◽

2013 ◽

Author(s):

Ilie Talpasanu

Keyword(s):

Kinematic Analysis ◽

Degrees Of Freedom ◽

Simple Procedure ◽

Bevel Gear ◽

Efficient Computation ◽

General Applicability ◽

Cycle Basis ◽

Angular Velocities ◽

Gear Trains ◽

Robotic Wrist

This paper presents a novel and simple technique for the kinematic analysis of bevel gear trains (BGT). The approach is based on edge-oriented graphs for efficient computation of BGT’s relative and absolute velocities of links using incidence matrices. The kinematic equations are generated in matrix form using a cycle basis from a cycle matroid. The set of independent equations is automatically obtained from matrix orthogonalities and not by taking derivatives. Equation coefficients are expressed as function of speed ratios and have minimal variables. Then the relationships between the output and input angular velocities can be determined. In addition, a simple procedure is demonstrated to check for mechanism singularities. The method presented here has general applicability and can be employed for spatial geared mechanisms with any number of gears and degrees of freedom as illustrated by numerical examples of robotic wrist mechanisms.

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A General Method for Kinematic Analysis of Robotic Wrist Mechanisms

Journal of Mechanisms and Robotics ◽

10.1115/1.4030466 ◽

2015 ◽

Vol 7 (3) ◽

Cited By ~ 1

Author(s):

Ilie Talpasanu

Keyword(s):

Kinematic Analysis ◽

Degrees Of Freedom ◽

Simple Procedure ◽

Efficient Computation ◽

General Applicability ◽

Cycle Basis ◽

Angular Velocities ◽

Gear Trains ◽

Cycle Matroid ◽

Robotic Wrist

Abstract The paper presents a novel and simple technique for the kinematic analysis of bevel gear trains (BGT). The approach is based on edge-oriented graphs for efficient computation of BGT’s absolute and relative velocities of links using incidence matrices. The kinematic equations are generated in matrix form using a cycle basis from a cycle matroid. The set of independent equations is automatically obtained from matrix orthogonalities and not by taking derivatives. Equation coefficients are expressed as function of speed ratios and have minimal variables. Then the relationships between the output and input angular velocities can be determined. In addition, a simple procedure is demonstrated to check for mechanism singularities. The method presented here has general applicability and can be employed for spatial geared mechanisms with any number of gears and degrees of freedom (DOF) as illustrated by numerical examples of robotic wrist mechanisms.

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Kinematic Analysis of Epicyclic Bevel Gear Trains With Matroid Method

Journal of Mechanical Design ◽

10.1115/1.4007144 ◽

2012 ◽

Vol 134 (11) ◽

Cited By ~ 8

Author(s):

Ilie Talpasanu ◽

P. A. Simionescu

Keyword(s):

Kinematic Analysis ◽

Degrees Of Freedom ◽

Time Derivative ◽

Oriented Graph ◽

Bevel Gear ◽

Efficient Computation ◽

Cycle Basis ◽

Angular Velocities ◽

Gear Trains ◽

Cycle Matroid

The paper presents a novel technique for the kinematic analysis of bevel gear trains using the incidence matrices of an edge-oriented graph of the mechanism. The kinematic equations are then obtained in matrix form using a cycle basis from a cycle matroid. These equations can be systematically generated, and allow for an efficient computation of the angular velocities of the gears and planet carriers of the mechanism without employing time derivative operations. As illustrated in the paper, the method is applicable to bevel gear trains of any number of gears or degrees of freedom.

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Kinematic Approximations in TED and RHEED Analysis of Reconstructed Surfaces

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100135587 ◽

1990 ◽

Vol 48 (2) ◽

pp. 396-397

Author(s):

L. -M. Peng ◽

M. J. Whelan

Keyword(s):

Electron Diffraction ◽

Kinematic Analysis ◽

Incident Beam ◽

High Energy ◽

Energy Electron ◽

Great Success ◽

High Energy Electron ◽

Kinematic Approximation ◽

Reconstructed Surfaces

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.

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