An Inverse Force Analysis of a Spatial Three-Spring System

1994 ◽  
pp. 261-270 ◽  
Author(s):  
P. Dietmaier
Keyword(s):  
Force Analysis ◽  
Spring System ◽  
Inverse Force

An Inverse Force Analysis of a Planar Two-Spring System

1994 ◽  
Author(s):  
Thomas M. Pigoski ◽  
Joseph Duffy
Keyword(s):  
The Other ◽  
Spring Stiffness ◽  
Force Analysis ◽  
Degree Polynomial ◽  
Real Solutions ◽  
Variable Elimination ◽  
Spring System ◽  
The Common ◽  
Resultant Length ◽  
Inverse Force

Abstract A closed-form inverse force analysis was performed on a planar two-spring system. The two springs were grounded to pivots at one end and attached to a common pivot at the other. A known force was applied to the common pivot of the system, and it was required to determine all of the assembly configurations. By variable elimination, a sixth degree polynomial in the resultant length of one spring was derived, and from this, six real solutions of the point of application of force were obtained. Following this, the applied force was incremented along a line and the six paths of the moving pivot were tracked starting from the zero-load configurations. An analysis of these results showed stability phenomena indicating the workspace of this system contained regions of negative spring stiffness and points of catastrophe.

An Inverse Force Analysis of a Tetrahedral Three-Spring System

1995 ◽  
Vol 117 (2A) ◽  
pp. 286-291 ◽  
Author(s):  
P. Dietmaier
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
The Other ◽  
Force Analysis ◽  
Equilibrium Configurations ◽  
Spring System ◽  
The Common ◽  
The Stability ◽  
Inverse Force

A tetrahedral three-spring system under a single load has been analyzed and a closed-form solution for the equilibrium positions is given. Each of the three springs is attached at one end to a fixed pivot in space while the other three ends are linked by a common pivot. The springs are assumed to behave in a linearly elastic way. The aim of the paper at hand was to find out what the maximum number of equilibrium positions of such a system might be, and how to compute all possible equilibrium configurations if a given force is applied to the common pivot. First a symmetric and unloaded system was studied. For such a system it was shown that there may exist a maximum of 22 equilibrium configurations which may all be real. Second the general, loaded system was analyzed, revealing again a maximum of 22 real equilibrium configurations. Finally, the stability of this three-spring system was investigated. A numerical example illustrates the theoretical findings.

An Inverse Force Analysis of a Planar Two-Spring System

1995 ◽  
Vol 117 (4) ◽  
pp. 548-553 ◽  
Author(s):  
T. M. Pigoski ◽  
J. Duffy
Keyword(s):  
The Other ◽  
Spring Stiffness ◽  
Force Analysis ◽  
Degree Polynomial ◽  
Real Solutions ◽  
Variable Elimination ◽  
Spring System ◽  
The Common ◽  
Resultant Length ◽  
Inverse Force

A closed-form inverse force analysis was performed on a planar two-spring system. The two springs were grounded to pivots at one end and attached to a common pivot at the other. A known force was applied to the common pivot of the system, and it was required to determine all of the assembly configurations. By variable elimination, a sixth degree polynomial in the resultant length of one spring was derived, and from this, six real solutions of the point of application of force were obtained. Following this, the applied force was incremented along a line and the six paths of the moving pivot were tracked starting from the zero-load configurations. An analysis of these results showed stability phenomena indicating the workspace of this system contained regions of negative spring stiffness and points of catastrophe.

Inverse Force Analysis of General Planar Three-Spring System Using Continuation Method

1998 ◽  
Author(s):  
An-Xin Liu ◽  
Bao-Qian Shi ◽  
Ming Zhang ◽  
Ting-Li Yang
Keyword(s):  
Continuation Method ◽  
Force Balance ◽  
Polynomial Form ◽  
Static Equilibrium ◽  
Force Analysis ◽  
Balance Equations ◽  
Spring System ◽  
Inverse Force

Abstract The inverse force analysis of planar three-spring system is studied in this paper. First, the force balance equations and moment balance equations, together with the loop equations, are reduced into polynomial form. Then continuation method is used to find all static equilibrium positions of the system.

A new method for reverse force analysis of a spatial three-spring system

2001 ◽  
Vol 36 (5) ◽  
pp. 623-632 ◽  
Author(s):  
Limin Fan ◽  
Qizheng Liao ◽  
Chonggao Liang
Keyword(s):  
New Method ◽  
Force Analysis ◽  
Spring System

A New Algebraic Solution to Inverse Static Force Analysis of a Special Planar Three-Spring System

2016 ◽  
Author(s):  
Ying Zhang ◽  
Qizheng Liao ◽  
Shimin Wei ◽  
Feng Wei ◽  
Duanling Li
Keyword(s):  
Polynomial Equation ◽  
Algebraic Solution ◽  
Static Force ◽  
Force Analysis ◽  
Elimination Algorithm ◽  
Equilibrium Configurations ◽  
Spring System ◽  
Univariate Polynomial ◽  
Variable Substitution ◽  
Resultant Matrix

In this paper, we present a new algebraic elimination algorithm for the inverse static force analysis of a special planar three-spring system. The system consists of three linear springs joined to the ground at the two fixed pivots and connected to the two moving pivots at the platform. When exerted by specified static force, the goal of inverse static analysis is to determine all the equilibrium configurations. First of all, a system of seven polynomial equations in seven variables is established based on the geometric constraint and static force balancing. Then, four basic constraint equations in four variables are obtained by variable substitution. Next, a 20 by 20 resultant matrix is reduced by means of three consecutive Sylvester elimination process. Finally, a 54th-degree univariate polynomial equation is directly derived without extraneous roots in the computer algebra system Mathematica 9.0. At last, a numerical example is given to verify the elimination procedure.

A reverse static force analysis of a special planar three-spring system

1997 ◽  
Vol 32 (5) ◽  
pp. 609-615 ◽  
Author(s):  
L. Sun ◽  
C.G. Liang ◽  
Q.Z. Liao
Keyword(s):  
Static Force ◽  
Force Analysis ◽  
Spring System

The Inverse Force Analysis of a Four-Bar Mechanism With Compliant Input and Output Links

1996 ◽  
Author(s):  
J. P. Yin ◽  
G. K. Matthew ◽  
J. Duffy
Keyword(s):  
Closed Form ◽  
Angular Displacement ◽  
Force Analysis ◽  
Output Link ◽  
Degree Polynomial ◽  
Numerical Result ◽  
Input And Output ◽  
Half Angle ◽  
Inverse Force

Abstract A closed-form inverse force analysis was performed for a planar four-bar mechanism with a rigid coupler and frame but with compliance in the form of linear springs in the input and output links. A known force was applied to the coupler link on a line fixed in the plane containing the frame. A sixteenth degree polynomial in the tan-half-angle of the angular displacement of the output link was derived using algebraic elimination. A numerical result is presented which verifies the solutions.

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