Realization of an Arbitrary Planar Stiffness With a Simple Symmetric Parallel Mechanism

2011 ◽  
Vol 3 (4) ◽  
Author(s):  
Shuguang Huang ◽  
Joseph M. Schimmels
Keyword(s):  
Stiffness Matrix ◽  
Parallel Mechanism ◽  
The Other ◽  
New Method ◽  
Compliant Behavior ◽  
Elastic Mechanism ◽  
Symmetric Geometry ◽  
Synthesis Procedure

This paper presents a new method for the realization of a planar compliant behavior with an elastic mechanism. The mechanisms considered are parallel with symmetric geometry. We show that any planar stiffness matrix can be realized using a parallel mechanism with four line springs connected symmetrically. Among the four springs, two are identical parallel springs equidistant from the stiffness center, and the other two identical springs intersect at the stiffness center. A synthesis procedure based on geometry is presented and mechanism compactness is discussed.

Realization of a Planar Stiffness With a Simple Symmetric Parallel Mechanism

2010 ◽  
Author(s):  
Shuguang Huang ◽  
Joseph M. Schimmels
Keyword(s):  
Stiffness Matrix ◽  
Parallel Mechanism ◽  
The Other ◽  
New Method ◽  
Parallel Mechanisms ◽  
Compliant Behavior ◽  
Elastic Mechanism ◽  
Symmetric Geometry ◽  
Synthesis Procedure

This paper presents a new method for the realization of a planar compliant behavior with an elastic mechanism. The mechanisms considered are parallel mechanisms with symmetric geometry. We show that any planar stiffness matrix can be realized using a parallel mechanism with four line springs connected symmetrically. Among the four springs, two are identical parallel springs equidistant from the stiffness center, and the other two identical springs intersect at the stiffness center. A synthesis procedure is presented.

Spatial Compliances Achieved With Serial Elastic Mechanisms

2000 ◽  
Author(s):  
Shuguang Huang ◽  
Joseph M. Schimmels
Keyword(s):  
Rotational Motion ◽  
Stiffness Matrix ◽  
Parallel Mechanism ◽  
Elastic System ◽  
Compliance Matrix ◽  
Elastic Joint ◽  
Compliant Behavior ◽  
Elastic Mechanism ◽  
Spatial Compliance ◽  
Serial Mechanism

Abstract Previously, the structure of a spatial stiffness matrix and its realization using a parallel elastic system have been addressed. This paper extends those results to the analysis and realization of a spatial compliance matrix using a serial mechanism. We show that, a spatial compliance matrix can be decomposed into a set of rank-1 primitive matrices, each of which can be realized with an elastic joint in a serial mechanism. To realize a general spatial compliance, the serial mechanism must contain joints that couple the translational and rotational motion along/about an axis. The structure of a spatial compliance matrix can be uniquely interpreted by a 6-joint serial elastic mechanism whose geometry is obtained from the eigenscrew decomposition of the compliance matrix. The results obtained from the analysis of spatial compliant behavior and its realization in a serial mechanism are compared with those obtained for spatial stiffness behavior and its realization in a parallel mechanism.

Planar Compliance Realization with Two 3-Joint Serial Manipulators Connected in Parallel

2021 ◽  
pp. 1-18
Author(s):  
Shuguang Huang ◽  
Joseph Schimmels
Keyword(s):  
Stiffness Matrix ◽  
Parallel Mechanism ◽  
Geometric Construction ◽  
Serial Manipulators ◽  
Compliant Behavior ◽  
New Synthesis ◽  
Synthesis Procedure ◽  
Serial Mechanism

Abstract In this paper, the realization of any specified planar compliance with two 3R serial elastic mechanisms is addressed. Using the concepts of dual elastic mechanisms, it is shown that the realization of a compliant behavior with 2 serial mechanisms connected in parallel is equivalent to its realization with a 6-spring fully parallel mechanism. Since the spring axes of a 6-spring parallel mechanism indicate the geometry of a dual 3R serial mechanism, a new synthesis procedure for the realization of a stiffness matrix with a 6-spring parallel mechanism is first developed. Then, this result is extended to a geometric construction-based synthesis procedure for two 3-joint serial mechanisms.

Realization of an Arbitrary Elastic Behavior With an Elastic Mechanism Having Concurrent Axes

2000 ◽  
Author(s):  
Shuguang Huang ◽  
Joseph M. Schimmels
Keyword(s):  
Stiffness Matrix ◽  
Parallel Mechanism ◽  
Elastic Behavior ◽  
Unique Point ◽  
Compliance Matrix ◽  
Elastic Mechanism ◽  
Serial Mechanism

Abstract In this paper, synthesis of an arbitrary elastic behavior with an elastic mechanism is addressed. The mechanisms considered are parallel and serial mechanisms with concurrent axes. We show that any stiffness matrix can be realized through a parallel mechanism with all spring axes intersecting at a unique point. This point is shown to be the center of stiffness. We also show that any compliance matrix can be realized through a serial mechanism with all joint axes intersecting at a unique point. This point is shown to be the center of compliance. Synthesis procedures for mechanisms with these properties are provided.

The Duality in Spatial Stiffness and Compliance as Realized in Parallel and Serial Elastic Mechanisms

2000 ◽  
Vol 124 (1) ◽  
pp. 76-84 ◽  
Author(s):  
Shuguang Huang ◽  
Joseph M. Schimmels
Keyword(s):  
Stiffness Matrix ◽  
Elastic System ◽  
Positive Definite Matrix ◽  
Elastic Behavior ◽  
Compliance Matrix ◽  
Compliant Behavior ◽  
Elastic Mechanism ◽  
Compliance Matrices ◽  
Spatial Compliance ◽  
Serial Mechanism

Spatial elastic behavior is characterized by a 6×6 positive definite matrix, the spatial stiffness matrix, or its inverse, the spatial compliance matrix. Previously, the structure of a spatial stiffness matrix and its realization using a parallel elastic system have been addressed. This paper extends those results to the analysis and realization of a spatial compliance matrix using a serial mechanism and identifies the duality in spatial stiffness and compliance associated with parallel and serial elastic mechanisms. We show that, a spatial compliance matrix can be decomposed into a set of rank-1 compliance matrices, each of which can be realized with an elastic joint in a serial mechanism. To realize a general spatial compliance, the serial mechanism must contain joints that couple the translational and rotational motion along/about an axis. The structure of a spatial compliance matrix can be uniquely interpreted by a 6-joint serial elastic mechanism whose geometry is obtained from the eigenscrew decomposition of the compliance matrix. The results obtained from the analysis of spatial compliant behavior and its realization in a serial mechanism are compared with those obtained for spatial stiffness behavior and its realization in a parallel mechanism.

scholarly journals On Newcomb's method of investigating periodicities and its application to Brückner's weather cycle

1914 ◽  
Vol 90 (619) ◽  
pp. 349-355
Keyword(s):  
Thermal Radiation ◽  
The Other ◽  
New Method ◽  
Critical Examination ◽  
Numerical Work ◽  
Average Value ◽  
Other Hand ◽  
Relationship Of ◽  
The Relationship ◽  
Great Simplicity

During the last few years of his life Prof. Simon Newcomb was keenly interested in the problem of periodicities, and devised a new method for their investigation. This method is explained, and to some extent applied, in a paper entitled "A Search for Fluctuations in the Sun's Thermal Radiation through their Influence on Terrestrial Temperature." The importance of the question justifies a critical examination of the relationship of the older methods to that of Newcomb, and though I do not agree with his contention that his process gives us more than can be obtained from Fourier's analysis, it has the advantage of great simplicity in its numerical work, and should prove useful in a certain, though I am afraid, very limited field. Let f ( t ) represent a function of a variable which we may take to be the time, and let the average value of the function be zero. Newcomb examines the sum of the series f ( t 1 ) f ( t 1 + τ) + f ( t 2 ) f ( t 2 + τ) + f ( t 3 ) f ( t 3 + τ) + ..., where t 1 , t 2 , etc., are definite values of the variable which are taken to lie at equal distances from each other. If the function be periodic so as to repeat itself after an interval τ, the products are all squares and each term is positive. If, on the other hand, the periodic time be 2τ, each product will be negative and the sum itself therefore negative. It is easy to see that if τ be varied continuously the sum of the series passes through maxima and minima, and the maxima will indicated the periodic time, or any of its multiples.

The Parallel Mechanism and Variable Acceleration Control Method

2013 ◽  
Vol 579-580 ◽  
pp. 659-664
Author(s):  
Xiang Bo Ouyang ◽  
Ke Tian Li ◽  
Hong Jian Xia ◽  
Su Juan Wang ◽  
Huan Wei Zhou ◽  
...  
Keyword(s):  
Parallel Mechanism ◽  
Control Method ◽  
The Other ◽  
Connecting Rod ◽  
Motion Platform ◽  
The Third ◽  
Symmetric Structure ◽  
Slide Block ◽  
Operation Process ◽  
Moving Platform

t presents the parallel mechanism and variable acceleration control method, which is composed of slider, connecting rod, moving platform and linear guide etc. The motion platform is supported by three connecting rods through hinging, the other end of the connecting rods are respectively hinged with two sliders. Among them two pairs of connecting rod, two sliders and the moving platform formed a symmetric structure that is the so called Parallel Mechanism. The third connecting rod is parallel to one of two connecting rods, so that the two parallel connecting rods, slide block and the moving platform formed a parallelogram structure, it makes that the moving platform is always parallel to liner guiderail in the process of movement. By controlling the two sliders moving in the way of variable acceleration, it can make the trajectory curve, speed curve and acceleration curve of the moving platform are continuous, smooth, so impact and vibration of the moving platform is limited in the operation process.

A New Method Tracing Load-Deflection Equilibrium Path of a Doubly Nonlinear Truss

2012 ◽  
Vol 166-169 ◽  
pp. 68-72
Author(s):  
Shu Tang Liu ◽  
Qi Liang Long
Keyword(s):  
Matrix Equation ◽  
Stiffness Matrix ◽  
Large Scale ◽  
New Method ◽  
Truss Structure ◽  
Equilibrium Path ◽  
Nodal Coordinates ◽  
Doubly Nonlinear ◽  
Global Stiffness Matrix

A new method tracing the load-deflection equilibrium path of a truss with doubly nonlinearity is proposed. The total global stiffness matrix equation has been formulated in terms of nodal coordinates, iteration formulations has been written through adopting a single control coordinate, so that an new method tracing the load-deflection equilibrium path has been proposed. Analysis results of Star dome truss and Schwedeler dome truss have shown that the proposed method is stable numerically, quick in convergence, high in degree of accuracy and easy in use. The proposed method can be used for large-scale truss structure.

Locomotory Diseases Influence on Body Equilibrium and Balance

2014 ◽  
Vol 555 ◽  
pp. 652-658 ◽  
Author(s):  
Barbu Cristian Braun ◽  
Ileana Constanta Rosca
Keyword(s):  
Body Mass ◽  
Human Subjects ◽  
Force Plate ◽  
The Body ◽  
The Other ◽  
New Method ◽  
First Person ◽  
Mass Center ◽  
Stability Problems ◽  
Research Stage

The paper describes a new method of body equilibrium evaluation applied for different human subjects, the principal aim being to demonstrate to what extent any locomotory diseases could influence the body stability and equilibrium. The research refers to identify some persons with different locomotory diseases and to find both the influence on equilibrium and stability and if possible to improve them. Our research stage, synthesized in this paper, explains the body equilibrium evaluation in orthostatic posture done for different subjects, aged between 20 and 40 years. A number of 10 relevant persons were considered to be evaluated, 2 of them having some locomotory diseases. The first person presents any neuro-motor stability problems in case of long standing case. The other person has both Achilles tendons torn and operated. All subjects were tested in orthostatic posture, in 3 distinct positions, using a Kistler force plate. The experiments referred to the body mass center (COM) displacement in sagittal and lateral planes, representing an interesting characteristic for its equilibrium. It was shown that the person with diseases affecting stability presented a loss of equilibrium when standing for 10-20 seconds, i.e. higher COM displacements in both planes reported to the other tested subjects.

A modified Runge-Kutta method

SIMULATION ◽  
1968 ◽  
Vol 10 (5) ◽  
pp. 221-223 ◽  
Author(s):  
A.S. Chai
Keyword(s):  
Error Estimate ◽  
Linear Combination ◽  
Experimental Results ◽  
The Other ◽  
New Method ◽  
Kutta Method ◽  
Starting Values ◽  
Runge Kutta Method ◽  
Runge Kutta ◽  
A Minor

It is possible to replace k2 in a 4th-order Runge-Kutta for mula (also Nth-order 3 ≤ N ≤ 5) by a linear combination of k1 and the ki's in the last step, using the same procedure for computing the other ki's and y as in the standard R-K method. The advantages of the new method are: It re quires one less derivative evaluation, provides an error estimate at each step, gives more accurate results, and needs a minor change to switch to the RK to obtain the starting values. Experimental results are shown in verification of the for mula.

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