Kinematic Analysis of a Planar Tensegrity Mechanism with Pre-Stressed Springs

Crane, Carl D.; Bayat, Jahan; Vikas, Vishesh; Roberts, Rodney G.

doi:10.1007/978-1-4020-8600-7_44

Cited by 19 publications

(27 citation statements)

References 2 publications

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“…The inverse static model that expresses ρ as a function of y is difficult to obtain if nonzero free length of the springs are considered. As noticed previously in [4], the use of nonzero free length springs in a tensegrity mechanism significantly increases its analysis complexity. In our situation, no analytical expression could be found.…”

Section: Modeling and Analysis Criteriamentioning

confidence: 89%

Influence of Spring Characteristics on the Behavior of Tensegrity Mechanisms

Boehler

Vedrines

Abdelaziz

et al. 2014

Advances in Robot Kinematics

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There is today a growing interest for tensegrity mechanisms. Their analysis is however challenging because of their self-stress state. The most popular tensegrity mechanisms use linear springs as tensioned elements. Their synthesis for given user requirements is an open issue. In this article, we propose as a first step to better understand the influence of the spring characteristics, that constitute important design parameters. The influence of spring free length is in particular assessed, considering two planar tensegrity mechanisms. Impact of the spring selection on the workspace, the stiffness and the actuation requirements is observed. The simulation results outline that using nonzero free length springs can be of interest, and conclusions are given on further steps towards a synthesis method.

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Section: Modeling and Analysis Criteriamentioning

confidence: 89%

Influence of Spring Characteristics on the Behavior of Tensegrity Mechanisms

Boehler

Vedrines

Abdelaziz

et al. 2014

Advances in Robot Kinematics

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show abstract

“…for the calculation of the discriminant varieties but the computation time of the cylindrical algebraic decomposition increases and graphical representations are more challenging. Using springs with non-zero free lengths make the equations much more complex and might render symbolic calculations intractable, as shown in [11] and already observed in former works [8,9]. Practically, however, equivalent zero-free lengths springs can be designed without much effort.…”

Section: Solution Continuitymentioning

confidence: 98%

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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“…The equation of these curves can be obtained by deriving the discriminant of the characteristic polynomial (6). By doing so, a polynomial of degree 16 in x and y is obtained.…”

Section: Workpace Analysismentioning

confidence: 99%

“…Tensegrity is known in architecture and art for more than a century [2] and is suitable for modeling living organisms [4]. Tensegrity mechanisms have been more recently studied for their promising properties in robotics such as low inertia, natural compliance and deployability [5], [6], [7]. A tensegrity mechanism is obtained when one or several elements are actuated.…”

Section: Introductionmentioning

confidence: 99%

Kinematic Analysis of Planar Tensegrity 2-X Manipulators

Furet

Max

Wenger

2018

Advances in Robot Kinematics 2018

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Abstract. This paper analyzes the kinematics of planar tensegrity manipulators made of two Snelson's X-shape mechanisms in series. The variable instantaneous center of rotation of each mechanism renders the kinematic analysis of the resulting manipulator more challenging. A general formulation of the direct kinematics is set. A method is proposed to solve the inverse kinematic problem in a symbolic way and up to four inverse kinematic solutions are found. The singularities of the manipulator are shown to divide the joint space into two singularity-free components, showing for the first time a planar positioning manipulator that can be cuspidal. The workspace is determined and plotted for different values of the geometric parameters.

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Kinematic Analysis of a Planar Tensegrity Mechanism with Pre-Stressed Springs

Cited by 19 publications

References 2 publications

Influence of Spring Characteristics on the Behavior of Tensegrity Mechanisms

Influence of Spring Characteristics on the Behavior of Tensegrity Mechanisms

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

Kinematic Analysis of Planar Tensegrity 2-X Manipulators

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