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Research Papers

Efficient Collision Detection Method for Flexure Mechanisms Comprising Deflected Leafsprings

[+] Author and Article Information
M. Naves

Chair of Precision Engineering,
University of Twente,
P.O. Box: 217,
Enschede 7500 AE, The Netherlands
e-mail: m.naves@utwente.nl

R. G. K. M. Aarts

Chair of Structural Dynamics,
Acoustics & Control,
University of Twente,
P.O. Box: 217,
Enschede 7500 AE, The Netherlands
e-mail: r.g.k.m.aarts@utwente.nl

D. M. Brouwer

Chair of Precision Engineering,
University of Twente,
P.O. Box: 217,
Enschede 7500 AE, The Netherlands
e-mail: d.m.brouwer@utwente.nl

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANISMS AND ROBOTICS. Manuscript received February 20, 2018; final manuscript received September 10, 2018; published online October 1, 2018. Assoc. Editor: James J. Joo.

J. Mechanisms Robotics 10(6), 061012 (Oct 01, 2018) (7 pages) Paper No: JMR-18-1047; doi: 10.1115/1.4041484 History: Received February 20, 2018; Revised September 10, 2018

When designing and optimizing spatial flexure mechanisms, it is hard to predict collision due to 3D motion and large deformations, which compromises the utilization of spatial freedom. A computationally efficient collision test is desirable to assure that feasible mechanism designs are found when algorithmically optimizing the shape of elastic mechanisms, which are prone to collision. In this paper, a method is presented to test for collision specifically suited for flexure mechanisms by taking advantage of the typical slender aspect ratio and shape of the elastic members. Hereby, an efficient collision test is obtained that allows for the computation of a quantitative value for the severeness of collision. This value can then be used to efficiently converge to collision free solutions without excluding good mechanism designs leading to improved mechanisms, which utilize the maximum spatial design freedom.

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References

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Figures

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Fig. 1

Geometrical reduction of two leafsprings: (a) original geometry and (b) simplified geometry consisting of six flat surfaces

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Fig. 2

Schematic representation of bounding box alignment for two flat surfaces: (a) bounding boxes aligned with global axis (x, y, z) and (b) oriented bounding boxes aligned with local axis (x¯, y¯, z¯)

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Fig. 3

Schematic illustration of the directional vectors of surfaces A and B. Note: vector An is hidden behind surface A.

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Fig. 4

Scalar projection of vertices B0, B1, B2, and B3 on line A0A1↔

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Fig. 5

Line of intersection between surface A and B with Ap and Bp perpendicular to the line of intersection

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Fig. 6

Intersecting points between the line of intersection and the outer ribs of surface A

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Fig. 7

Relative position of the intersecting points with line of intersection

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Fig. 8

Parameterized model of the cylindrical torsion spring with height h (in mm) and total rotation angle of the undeformed curved leafsprings n (in deg). The width b and thickness t of the leafsprings are fixed to 10 mm and 2 mm, respectively.

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Fig. 9

Deflected state of a torsion spring with each leafspring modeled with 12 flexible beam elements. The deflected state is given for design parameter settings n=360 deg and h=50 mm which just avoids collision at (a) −90 deg deflection and (b) +90 deg deflection.

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Fig. 10

Summed penetration depth as function of design parameters n and h

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