Catastrophe Analysis of the Planar Two-Spring Mechanism

Hines, R.; Marsh, D.; Duffy, Joseph

doi:10.1177/027836499801700108

Cited by 9 publications

(7 citation statements)

References 9 publications

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“…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%

Singularity-theoretic methods in robot kinematics

Donelan

2007

Robotica

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SUMMARYThe significance of singularities in the design and control of robot manipulators is well known, and there is an extensive literature on the determination and analysis of singularities for a wide variety of serial and parallel manipulators—indeed such an analysis is an essential part of manipulator design. Singularity theory provides methodologies for a deeper analysis with the aim of classifying singularities, providing local models and local and global invariants. This paper surveys applications of singularity-theoretic methods in robot kinematics and presents some new results.

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Section: Introductionmentioning

confidence: 99%

Singularity-theoretic methods in robot kinematics

Donelan

2007

Robotica

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“…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%

Kinetostatic analysis and solution classification of a class of planar tensegrity mechanisms

Wenger¹,

Chablat²

2018

Robotica

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Tensegrity mechanisms are composed of rigid and tensile parts that are in equilibrium. They are interesting alternative designs for some applications, such as modelling musculo-skeleton systems. Tensegrity mechanisms are more difficult to analyze than classical mechanisms as the static equilibrium conditions that must be satisfied generally result in complex equations. A class of planar one-degree-of-freedom tensegrity mechanisms with three linear springs is analyzed in detail for the sake of systematic solution classifications. The kinetostatic equations are derived and solved under several loading and geometric conditions. It is shown that these mechanisms exhibit up to six equilibrium configurations, of which one or two are stable, depending on the geometric and loading conditions. Discriminant varieties and cylindrical algebraic decomposition combined with Groebner base elimination are used to classify solutions as a function of the geometric, loading and actuator input parameters.

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“…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%

Stiffness modeling for perfect and non-perfect parallel manipulators under internal and external loadings

Klimchik

Chablat

Pashkevich

2014

Mechanism and Machine Theory

120

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International audienceThe paper presents an advanced stiffness modeling technique for perfect and non-perfect parallel manipulators under internal and external loadings. Particular attention is paid to the manipulators composed of non-perfect serial chains, whose geometrical parameters differ from the nominal ones and do not allow to assemble manipulator without internal stresses that considerably affect the stiffness properties and also change the end-effector location. In contrast to other works, several types of loadings are considered simultaneously: an external force applied to the end-effector, internal loadings generated by the assembling of non-perfect serial chains and external loadings applied to the intermediate points (auxiliary loading due to the gravity forces and relevant compensator mechanisms, etc.). For this type of manipulators, a non-linear stiffness modeling technique is proposed that allows to take into account inaccuracy in the chains and to aggregate their stiffness models for the case of both small and large deflections. Advantages of the developed technique and its ability to compute and compensate the compliance errors caused by the considered factors are illustrated by an example that deals with parallel manipulators of the Orthoglide family

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Catastrophe Analysis of the Planar Two-Spring Mechanism

Cited by 9 publications

References 9 publications

Singularity-theoretic methods in robot kinematics

Singularity-theoretic methods in robot kinematics

Kinetostatic analysis and solution classification of a class of planar tensegrity mechanisms

Stiffness modeling for perfect and non-perfect parallel manipulators under internal and external loadings

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