1998
DOI: 10.1177/027836499801700108
|View full text |Cite
|
Sign up to set email alerts
|

Catastrophe Analysis of the Planar Two-Spring Mechanism

Abstract: A stability analysis is performed for the planar two-spring system using catastrophe theory. Basic elements of catastrophe theory are outlined and applied to the two-spring system to give catastrophe locus plots showing where a change in stability occurs. The method used for the two-spring yields a stability analysis without having to solve the inverse analysis. The inverse analysis for the two-spring system is used to illustrate system equilibrium positions before, during, and after a change in stability.

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
2
1
1

Citation Types

0
7
0

Year Published

2002
2002
2020
2020

Publication Types

Select...
6

Relationship

0
6

Authors

Journals

citations
Cited by 9 publications
(7 citation statements)
references
References 9 publications
0
7
0
Order By: Relevance
“…The work of Marsh, Duffy et al [58][59][60] should also be mentioned, though it is not dealt with further in this paper. It concerns parallel compliant mechanisms, where the use of springs gives rise to a potential function and static configurations correspond to local minima.…”
Section: Introductionmentioning
confidence: 99%
“…The work of Marsh, Duffy et al [58][59][60] should also be mentioned, though it is not dealt with further in this paper. It concerns parallel compliant mechanisms, where the use of springs gives rise to a potential function and static configurations correspond to local minima.…”
Section: Introductionmentioning
confidence: 99%
“…At both critical points, a discontinuous behavior of the mechanism is experienced under a continuous change in the parameters, which is known as a catastrophe, a phenomenon often observed in mechanisms with springs. 13,18 Figure 8 also shows that the critical point C 1 is transformed into two fold points when L 2 is slightly increased or decreased. Figure 9 shows a 3-D view of the solution continuity when the design parameter L 2 is considered.…”
Section: Solution Continuitymentioning
confidence: 91%
“…known as a catastrophe, a phenomenon often observed in mechanisms with springs [12,17]. Figure 8b shows that when L 2 is slightly increased, the first critical point C 1 is transformed into a fold point.…”
Section: Solution Continuitymentioning
confidence: 93%
“…These effects are essentialy dangerous for parallel manipulators wich impose numerious passive joints. Some aspects of multiple-equilibrium problem for robotic manipulators have been examined in the works [63,64] who applied the Catastrophe theory for the stability analysis of the planar parallel manipulators with several flexural elements under external loading. However, they did not propose a general approach for stability analysis of the manipulator configurations.…”
Section: Stiffness Matrix For the Loaded Manipulatormentioning
confidence: 99%