scholarly journals Four-Pose Synthesis of Angle-Symmetric 6R Linkages

2015 ◽  
Vol 7 (4) ◽  
Author(s):  
Gábor Hegedüs ◽  
Josef Schicho ◽  
Hans-Peter Schröcker
Keyword(s):  
Rotation Angle ◽  
Dual Quaternions ◽  
Revolute Joints ◽  
Factorization Theory ◽  
Theory Of Motion ◽  
Kinematic Loops ◽  
Parametric Families ◽  
Synthesis Approach ◽  
Relative Motions

We use the recently introduced factorization theory of motion polynomials over the dual quaternions and cubic interpolation on quadrics for the synthesis of closed kinematic loops with six revolute joints that visit four prescribed poses. The resulting 6R linkages are special in the sense that the relative motions of all links are rational. They exhibit certain elegant properties such as symmetry in the rotation angles and, at least in theory, full-cycle mobility. Our synthesis approach admits either no solution or two one-parametric families of solutions. We suggest strategies for picking good solutions from these families. They ensure a fair coupler motion and optimize other linkage characteristics such as total rotation angle or linkage size. A comprehensive synthesis example is provided.

scholarly journals An Algorithm for the Factorization of Split Quaternion Polynomials

2021 ◽  
Vol 31 (3) ◽  
Author(s):  
Daniel F. Scharler ◽  
Hans-Peter Schröcker
Keyword(s):  
Hyperbolic Plane ◽  
Dual Quaternion ◽  
Real Polynomial ◽  
Split Quaternion ◽  
Split Quaternions ◽  
Dual Quaternions ◽  
Factorization Theory ◽  
Real Polynomials ◽  
Theory Of Motion ◽  
Univariate Polynomials

AbstractWe present an algorithm to compute all factorizations into linear factors of univariate polynomials over the split quaternions, provided such a factorization exists. Failure of the algorithm is equivalent to non-factorizability for which we present also geometric interpretations in terms of rulings on the quadric of non-invertible split quaternions. However, suitable real polynomial multiples of split quaternion polynomials can still be factorized and we describe how to find these real polynomials. Split quaternion polynomials describe rational motions in the hyperbolic plane. Factorization with linear factors corresponds to the decomposition of the rational motion into hyperbolic rotations. Since multiplication with a real polynomial does not change the motion, this decomposition is always possible. Some of our ideas can be transferred to the factorization theory of motion polynomials. These are polynomials over the dual quaternions with real norm polynomial and they describe rational motions in Euclidean kinematics. We transfer techniques developed for split quaternions to compute new factorizations of certain dual quaternion polynomials.

Synthesis of Planar, Shape-Changing Rigid Body Mechanisms Approximating Closed Curves

2007 ◽  
Author(s):  
Justin A. Persinger ◽  
James P. Schmiedeler ◽  
Andrew P. Murray
Keyword(s):  
Numerical Optimization ◽  
Shape Change ◽  
Closed Curves ◽  
Single Degree Of Freedom ◽  
Revolute Joints ◽  
Planar Shape ◽  
A Chain ◽  
Planar Linkages ◽  
Arc Lengths ◽  
Synthesis Approach

This paper presents a procedure to synthesize planar linkages, composed of rigid links and revolute joints, that are capable of approximating a shape change defined by a set of closed curves possessing similar arc lengths. The synthesis approach is more rigorous and more broadly applicable to dramatic changes between larger numbers of shapes than existing techniques that employ graphical methods. Link geometry is determined through an existing procedure, and those links are then joined together in a chain using numerical optimization to minimize the error in approximating the shape change. Binary links are added to this chain via a search of the design space such that actuated links can be driven monotonically to exact the shape change. The focus is single-degree-of-freedom (DOF) mechanisms that approximate closed curves, but the methodology is similarly applicable to generating mechanisms approximating sets of open curves and multi-DOF systems. The procedure is applied to synthesize an example mechanism that changes between circular, elliptical, and teardrop shapes as inspired by an aerodynamic flow field modification application.

Synthesis of Planar Rigid-Body Mechanisms Approximating Shape Changes Defined by Closed Curves

2009 ◽  
Vol 131 (7) ◽  
Author(s):  
Justin A. Persinger ◽  
James P. Schmiedeler ◽  
Andrew P. Murray
Keyword(s):  
Numerical Optimization ◽  
Shape Change ◽  
Closed Curves ◽  
Single Degree Of Freedom ◽  
Revolute Joints ◽  
A Chain ◽  
Planar Linkages ◽  
Arc Lengths ◽  
Synthesis Approach ◽  
Shape Changes

This paper presents a procedure to synthesize planar linkages, composed of rigid links and revolute joints, that are capable of approximating a shape change defined by a set of closed curves possessing similar arc lengths. The synthesis approach is more rigorous and more broadly applicable to dramatic changes between larger numbers of shapes than existing techniques that employ graphical methods. It specifically addresses the challenges of approximating closed curves, but the methodology is equally applicable to open curves. Link geometry is determined through an existing procedure, and those links are then joined together in a chain using numerical optimization to minimize the error in approximating the shape change. Binary links are added to this chain via a search of the design space, forming a single-degree-of-freedom mechanism in which an actuated link can be driven monotonically to exact the shape change. The procedure is applied to synthesize an example mechanism that changes between circular, elliptical, and teardrop shapes as inspired by an aerodynamic flow field modification application.

Reconfiguration Analysis of Multimode Single-Loop Spatial Mechanisms Using Dual Quaternions

2017 ◽  
Vol 9 (5) ◽  
Author(s):  
Xianwen Kong
Keyword(s):  
Algebraic Geometry ◽  
Single Degree Of Freedom ◽  
Plane Symmetric ◽  
Dual Quaternions ◽  
Revolute Joints ◽  
Spatial Mechanisms ◽  
Reconfigurable Mechanisms ◽  
Motion Modes ◽  
Kinematic Loop ◽  
And Robotics

Although kinematic analysis of conventional mechanisms is a well-documented fundamental issue in mechanisms and robotics, the emerging reconfigurable mechanisms and robots pose new challenges in kinematics. One of the challenges is the reconfiguration analysis of multimode mechanisms, which refers to finding all the motion modes and the transition configurations of the multimode mechanisms. Recent advances in mathematics, especially algebraic geometry and numerical algebraic geometry, make it possible to develop an efficient method for the reconfiguration analysis of reconfigurable mechanisms and robots. This paper first presents a method for formulating a set of kinematic loop equations for mechanisms using dual quaternions. Using this approach, a set of kinematic loop equations of spatial mechanisms is composed of six polynomial equations. Then the reconfiguration analysis of a novel multimode single-degree-of-freedom (1DOF) 7R spatial mechanism is dealt with by solving the set of loop equations using tools from algebraic geometry. It is found that the 7R multimode mechanism has three motion modes, including a planar 4R mode, an orthogonal Bricard 6R mode, and a plane symmetric 6R mode. Three (or one) R (revolute) joints of the 7R multimode mechanism lose their DOF in its 4R (or 6R) motion modes. Unlike the 7R multimode mechanisms in the literature, the 7R multimode mechanism presented in this paper does not have a 7R mode in which all the seven R joints can move simultaneously.

Structure and migration of planar defects in crystals observed in atomic scale

1978 ◽  
Vol 36 (1) ◽  
pp. 284-285 ◽  
Author(s):  
H. Hashimoto ◽  
Y. Sugimoto ◽  
Y. Takai ◽  
H. Endoh
Keyword(s):  
Electron Microscope ◽  
Rotation Angle ◽  
Crystal Surface ◽  
Electron Gun ◽  
Atomic Scale ◽  
Present Observation ◽  
Twist Boundary ◽  
Optical Magnification ◽  
Zinc Crystal ◽  
And Migration

As was demonstrated by the present authors that atomic structure of simple crystal can be photographed by the conventional 100 kV electron microscope adjusted at “aberration free focus (AFF)” condition. In order to operate the microscope at AFF condition effectively, highly stabilized electron beams with small energy spread and small beam divergence are necessary. In the present observation, a 120 kV electron microscope with LaB6 electron gun was used. The most of the images were taken with the direct electron optical magnification of 1.3 million times and then magnified photographically.1. Twist boundary of ZnSFig. 1 is the image of wurtzite single crystal with twist boundary grown on the surface of zinc crystal by the reaction of sulphur vapour of 1540 Torr at 500°C. Crystal surface is parallel to (00.1) plane and electron beam is incident along the axis normal to the crystal surface. In the twist boundary there is a dislocation net work between two perfect crystals with a certain rotation angle.

Musculoskeletal disorder risk associated with auto rotation angle during an assembly task

2009 ◽  
Author(s):  
Sue A. Ferguson ◽  
William S. Marras ◽  
W. Gary Allread ◽  
Gregory G. Knapik ◽  
Kimberly A. Vandlen ◽  
...  
Keyword(s):  
Musculoskeletal Disorder ◽  
Rotation Angle ◽  
Assembly Task ◽  
Disorder Risk

Structure and Dynamics of Spherical and Rodlike Alkyl Ethoxylate Surfactant Micelles Investigated Using NMR Relaxation and Atomistic Molecular Dynamics Simulations

2019 ◽  
Author(s):  
Allison Edwards ◽  
Abdolreza Javidialesaadi ◽  
Katie Weigandt ◽  
George Stan ◽  
Charles Eads
Keyword(s):  
Molecular Dynamics ◽  
Molecular Dynamics Simulations ◽  
Nmr Relaxation ◽  
Cross Relaxation ◽  
Relaxation Rates ◽  
Surfactant Micelles ◽  
Cylindrical Micelles ◽  
Spherical Micelles ◽  
Dynamics Simulations ◽  
Relative Motions

We study molecular arrangements and dynamics in alkyl ethoxylate nonionic surfactant micelles by combining high field (600 and 700 MHz) NMR relaxation measurements with large-scale atomistic molecular dynamics simulations. For spherical micelles, but not for cylindrical micelles, cross relaxation rates are positive only for surfactant alkyl tail atoms connected to the hydrophilic head group. All cross relaxation rates are negative for cylindrical micelles. This effect is reproducible either by changing composition (ratios of the nonionic surfactants) or changing temperature of a single surfactant in order to change the micelle shape. We validate the micelle shape by SANS and use the results as a guide for our simulations. We calculate parameters that determine relaxation rates directly from simulated trajectories, without introducing specific functional forms. Results indicate that relative motions of nearby atoms are liquid-like, in agreement with 13C T1 measurements, though constrained by micelle morphology. Relative motions of distant atoms have slower components because the relative changes in distances and angles are smaller when the moving atoms are further apart. The slow, long-range motions appear to be responsible for the predominantly negative cross relaxation rates observed in NOESY spectra. The densities of atoms from positions 1 and 2 in the boundary region are lower in spherical micelles compared to cylindrical micelles. Correspondingly, motions in this region are less constrained by micelle morphology in the spherical compared to the cylindrical cases. The two effects of morphology lead to the unusual occurrence of positive cross relaxation involving positions 1 and 2 for spheres.

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