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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Gunnink, K. , Aarts, R. , and Brouwer, D. , 2013, “ Performance Optimization of Large Stroke Flexure Hinges for High Stiffness and Eigenfrequency,” 28th Annual Meeting of the American Society for Precision Engineering (ASPE), Saint Paul, MN, pp. 20–25.
Naves, M. , Brouwer, D. , and Aarts, R. , 2017, “ Building Block-Based Spatial Topology Synthesis Method for Large-Stroke Flexure Hinges,” ASME J. Mech. Rob., 9(4), p. 041006. [CrossRef]
Henein, S. , Spanoudakis, P. , Droz, S. , Myklebust, L. , and Onillon, E. , 2003, “ Flexure Pivot for Aerospace Mechanisms,” Tenth European Space Mechanisms and Tribology Symposium, pp. 285–288.
Wiersma, D. , Boer, S. , Aarts, R. , and Brouwer, D. , 2014, “ Design and Performance Optimization of Large Stroke Spatial Flexures,” ASME J. Comput. Nonlinear Dyn., 9(1), p. 11016.
Farhadi Machekposhti, D. , Tolou, N. , and Herder, J. L. , 2015, “ A Review on Compliant Joints and Rigid-Body Constant Velocity Universal Joints Toward the Design of Compliant Homokinetic Couplings,” ASME J. Mech. Des., 137(3), p. 032301. [CrossRef]
Naves, M. , Aarts, R. , and Brouwer, D. , 2017, “ Large Stroke High Support Stiffness Flexure Based Universal Joint,” 32nd Annual Meeting of the American Society for Precision Engineering, Charlotte NC, Oct.
Trease, B. P. , Moon, Y.-M. , and Kota, S. , 2005, “ Design of Large-Displacement Compliant Joints,” ASME J. Mech. Des., 127(4), p. 788. [CrossRef]
Naves, M. , Aarts, R. , and Brouwer, D. , 2017, “ Large Stroke Three Degree-of-Freedom Spherical Flexure Joint,” EUSPEN 17th International Design Engineering Technical Conference, Hannover, Germany, May 29–June 2.
Moon, Y. , and Kota, S. , 2002, “ Design of Compliant Parallel Kinematic Machines,” ASME Paper No. DETC2002/MECH-34204.
Haftka, R. , and Gürdal, Z. , 2012, Elements of Structural Optimization, 3rd ed., Vol. 11, Springer Science & Business Media, Dordrecht, The Netherlands.
Weller, R. , 2013, New Geometric Data Structures for Collision Detection and Haptics, Springer International Publishing, Dordrecht, The Netherlands.
Ericson, C. , 2004, Real-Time Collision Detection, CRC Press, San Francisco, CA.
Hubbard, P. M. , 1996, “ Approximating Polyhedra With Spheres for Time-Critical Collision Detection,” ACM Trans. Graph., 15(3), pp. 179–210. [CrossRef]
Teschner, M. , Kimmerle, S. , Heidelberger, B. , Zachmann, G. , Raghupathi, L. , Fuhrmann, A. , Cani, M.-P. , Faure, F. , Magnenat-Thalmann, N. , Strasser, W. , and Volino, P. , 2005, “ Collision Detection for Deformable Objects,” Computer Graphics Forum, Vol. 24, Blackwell Publishing, Oxford, UK, pp. 61–81.
Moore, M. , and Wilhelms, J. , 1988, “ Collision Detection and Response for Computer Animation,” Comput. Graph., 22(4), pp. 289–298. [CrossRef]
van den Bergen, G. , 2001, “ Proximity Queries and Penetration Depth Computation on 3d Game Objects,” Game Developers Conference, San Francisco, CA, Mar. 14.
Ye, X. , Huang, L. , Wang, L. , and Xing, H. , 2015, “ An Improved Algorithm for Triangle to Triangle Intersection Test,” IEEE International Conference on Information and Automation, Lijiang, China, Aug. 8–10, pp. 2689–2694.
Guigue, P. , and Devillers, O. , 2003, “ Fast and Robust Triangle-Triangle Overlap Test Using Orientation Predicates,” J. Graph. Tools, 8(1), pp. 25–32.
Möller, T. , 2012, “ A Fast Triangle-Triangle Intersection Test,” J. Graph. Tools, 2(2), pp. 25–30. [CrossRef]
Nijenhuis, M. , and Brouwer, D. , 2016, “ A Closed-Form Model for the Support Stiffness of Spatial Flexure Strips With Limited Twist,” ASME Paper No. DETC2016-59979.
Gottschalk, S. , Lin, M. , and Manocha, D. , 1996, “ OBBTree: A Hierarchical Structure for Rapid Interference Detection,” 23rd Annual Conference on Computer Graphics and Interactive Techniques (SIGGRAPH '96), New Orleans, LA, Aug. 4–9, pp. 171–180.
Gellert, W. , Gottwald, S. , Hellwich, M. , Kastner, H. , and Kustner, H. , 1989, “ Analytic Geometry of Space,” The VNR Concise Encyclopedia of Mathematics, K. Hirsch and H. Reichardt , eds., Van Nostrand Reinhold, New York, Chap. 24, pp. 530–545.
Schwarze, J. , 1990, “ Intersection of Two Lines in Three-Space,” Graphics Gems I, A. Glassner , ed., Academic Press, London, UK, Chap. 5, pp. 296–341.
Jonker, J. , and Meijaard, J. , 1990, “ SPACAR—Computer Program for Dynamic Analysis of Flexible Spatial Mechanisms and Manipulators,” Multibody Systems Handbook, Springer, Berlin, pp. 123–143.
Meijaard, J. , 2013, “ Fluid-Conveying Flexible Pipes Modeled by Large-Deflection Finite Elements in Multibody Systems,” ASME J. Comput. Nonlinear Dyn., 9(1), p. 11008. [CrossRef]


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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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