Research Papers

Probabilistic Elastic Element Design for Robust Natural Dynamics of Structure-Controlled Variable Stiffness Actuators

[+] Author and Article Information
Florian Stuhlenmiller

Mechatronic Systems in Mechanical Engineering,
TU Darmstadt,
Darmstadt 64287, Germany
e-mail: stuhlenmiller@ims.tu-darmstadt.de

Jochen Schuy, Philipp Beckerle

Mechatronic Systems in Mechanical Engineering,
TU Darmstadt,
Darmstadt 64287, Germany

Manuscript received May 8, 2017; final manuscript received November 15, 2017; published online December 22, 2017. Assoc. Editor: Philippe Wenger.

J. Mechanisms Robotics 10(1), 011009 (Dec 22, 2017) (9 pages) Paper No: JMR-17-1138; doi: 10.1115/1.4038648 History: Received May 08, 2017; Revised November 15, 2017

This paper proposes a probabilistic approach for the design of elastic elements to be used in structure-controlled variable stiffness actuators (VSA) for robotic applications. Considering the natural dynamics of the elastic actuation system, requirements are defined and material selection as well as geometry calculation are performed using lumped parameter models. Monte Carlo simulations are integrated in the design procedure to ensure a robust implementation of the required dynamical characteristics. Thereby, effects of uncertainties that might be caused by manufacturing or deviations of material properties are taken into account. To validate the suitability of the overall approach and the particular methods, a torsional elastic element is implemented and experimentally evaluated. The evaluation shows a fulfillment of the key requirements, i.e., specific natural dynamic behavior, that is only achieved due to considering uncertainties. Further, the transferability of the approach to other structure-controlled elastic actuators is discussed and implications are given. Only the governing equations of stiffness properties in certain load situation need to be adapted, e.g., from torsion to bending. Due to the simple transfer, the proposed probabilistic and model-based approach is promising for application to various actuator concepts with structure-controlled variable stiffness.

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Fig. 1

Schematic concept (left) and photography (right) of the VTS-prototype

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Fig. 2

Design procedure for the elastic mechanism

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Fig. 3

Examined cross sections

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Fig. 4

Location of contact forces depending on polygonal cross section shapes

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Fig. 5

Model of the elastic element with quadratic cross section

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Fig. 6

Distribution (gray) and mean value (black) of the natural frequency for b = 17.4 mm

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Fig. 7

Distribution (gray) and mean value (black) of the natural frequency for badj = 16 mm

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Fig. 8

Demounted views of the test rig implementing the VTS concept: Left - Elastic element in slitted aluminum tube. Right - Elastic element with brass slider. In both cases, the upper part of the picture shows the stiffness adjustment mechanism while the lower left part shows the motor that moves the link. The relocatable counter bearing is realized by the slitted tube and the slider.

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Fig. 9

Frequency-length characteristic: experimentally evaluated (black) and analytical (gray)

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Fig. 10

Stiffness-length characteristic: experimentally evaluated (black) and analytical (gray)

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Fig. 11

Damping-length characteristic: experimentally evaluated



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