Inverse analysis of a planar two-spring system

Hines, R.; Duffy, Joseph; Primrose, E. J. F.

doi:10.1002/(sici)1097-4563(199610)13:10<679::aid-rob4>3.0.co;2-s

Cited by 2 publications

(1 citation statement)

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“…[3][4][5][6][7][8][9][10][11][12][13][14][15][16] The research on the inverse static force analysis of planar compliant systems has been well studied. [3][4][5][6][7][8][9][10][11][12] The inverse force analysis of the planar two-spring system acting in parallel and connected to a common pivot has been performed by Pigoski and Duffy, 3 Hines et al, 4 Han et al, 5 and Fan and Liao, 6 while for the planar two-spring system acting 1 in parallel but not connected to a common pivot, Han et al 7 studied this system. Sun et al 8,9 analyzed the inverse force problem of the special planar threespring system and Liu et al 10 studied the inverse force analysis of the general planar three-spring system.…”

Section: Introductionmentioning

confidence: 99%

A new closed-form solution to inverse static force analysis of a spatial three-spring system

Zhang

Liao

et al. 2014

Proceedings of the Institution of Mechanical Engineers, Part C:

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In this paper, a new closed-form solution to the inverse static force analysis of a spatial three-spring system is presented. The system is formed by three springs each of which connects the ground at one end and joins a common point at the other. When a known force is applied to the common point of the system, the goal of inverse static analysis is to determine all the equilibrium configurations. A system of three polynomial equations in three variables is derived based on the geometric constraint and static force balancing. A 20 by 20 Dixon resultant matrices firstly derived from these three polynomials and then reduced to an 18 by 18 matrix. A 46th-degree univariate polynomial equation is yielded from the above 18 by 18 matrix. By further analysis, we found that 24 roots were degenerated and only the remaining 22 roots are the ones for the three-spring system. The result agrees with previous results. At last, two numerical examples are given to verify the elimination procedure. The presented algebraic elimination solution reveals some intrinsic geometry nature of this challenging problem.

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Section: Introductionmentioning

confidence: 99%

A new closed-form solution to inverse static force analysis of a spatial three-spring system

Zhang

Liao

et al. 2014

Proceedings of the Institution of Mechanical Engineers, Part C:

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Inverse Static Analysis of a Planar System With Flexural Pivots

Carricato

Parenti‐Castelli

Duffy

2000

Journal of Mechanical Design

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This article presents the inverse static analysis of a two degrees of freedom planar mechanism with flexural pivots. Such analysis aims to detect the entire set of equilibrium configurations of the system once the external load is assigned. The presence of flexural pivots represents a novelty, although it remarkably complicates the problem since it causes the two state variables to appear in the solving equations as arguments of both trigonometric and linear functions. The proposed procedure eliminates one variable and leads to two equations in one unknown only. The union of the root sets of such equations constitutes the global set of solutions of the problem. Particular attention is paid to the analysis of the reliability of the final equations: critical situations, in which the solving equations may hide solutions or yield false ones, are studied. Finally, a numerical example is provided and, in the Appendix, a special design that offers computational advantages is proposed.

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Inverse analysis of a planar two-spring system

Cited by 2 publications

References 4 publications

A new closed-form solution to inverse static force analysis of a spatial three-spring system

A new closed-form solution to inverse static force analysis of a spatial three-spring system

Inverse Static Analysis of a Planar System With Flexural Pivots

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