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Research Papers

A Metric to Evaluate and Synthesize Distributed Compliant Mechanisms

[+] Author and Article Information
Girish Krishnan

Department of Mechanical Engineering,
University of Michigan,
Ann Arbor, MI 48109 
e-mail: gikrishn@umich.edu

Charles Kim

Department of Mechanical Engineering,
Bucknell University,
Lewisburg, PA 17837 
e-mail: charles.kim@bucknell.edu

Sridhar Kota

Department of Mechanical Engineering,
University of Michigan,
Ann Arbor, MI 48109 
e-mail: kota@umich.edu

Contributed by the Design Automation Committee of ASME for publication in the Journal of Mechanical Design. Manuscript received November 29, 2011; final manuscript received September 23, 2012; published online November 21, 2012. Assoc. Editor: Shinji Nishiwaki.

J. Mech. Des 135(1), 011004 (Nov 21, 2012) (9 pages) Paper No: MD-11-1481; doi: 10.1115/1.4007926 History: Received November 29, 2011; Revised September 23, 2012

Compliant mechanisms with evenly distributed stresses have better load-bearing ability and larger range of motion than mechanisms with compliance and stresses lumped at flexural hinges. In this paper, we present a metric to quantify how uniformly the strain energy of deformation and thus the stresses are distributed throughout the mechanism topology. The resulting metric is used to optimize cross-sections of conceptual compliant topologies leading to designs with maximal stress distribution. This optimization framework is demonstrated for both single-port mechanisms and single-input single-output mechanisms. It is observed that the optimized designs have lower stresses than their nonoptimized counterparts, which implies an ability for single-port mechanisms to store larger strain energy, and single-input single-output mechanisms to perform larger output work before failure.

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References

Smith, S. T., 2000, Flexure: Elements of Elastic Mechanisms, Gordon and Breach Science Publishers, Amsterdam.
Howell, L. L., 2001, Compliant Mechanisms, John-Wiley, New York.
Slocum, A. H., 1992, Precision Machine Design, Prentice-Hall, Englewood Cliffs, New Jersey.
Yin, L., and Ananthasuresh, G. K., 1994, “Design of Distributed Compliant Mechanisms,” Mech. Based Des. Struct. Mach., 31, pp. 151–179. [CrossRef]
Ananthasuresh, G. K., 1994, “A New Design Paradigm in Microelectromechanical Systems and Investigations on Compliant Mechanisms,” Ph.D. thesis, University of Michigan, Ann Arbor, MI.
Frecker, M. I., Ananthasuresh, G. K., Nishiwaki, S., Kikuchi, N., and Kota, S., 1997, “Topological Synthesis of Compliant Mechanisms Using Multi-Criteria Optimization,” J. Mech. Des., 119(2), pp. 238–245. [CrossRef]
Saxena, A., and Ananthasuresh, G. K., 2000, “On an Optimal Property of Compliant Topologies,” Struct. Multidiscip. Optim., 19, pp 36–49. [CrossRef]
Sigmund, O., and P., M. B., 2003, Topology Optimization: Theory, Methods and Applications, Springer-Verlag, Berlin.
Saxena, A., and Ananthasuresh, G. K., 2003, “A Computational Approach to the Number of Synthesis of Linkages,” J. Mech. Des., 125(1), pp. 110–118. [CrossRef]
Canfield, S. L., Chlarson, D. L., Shibakov, A., Richardson, J. D., and Saxena, A., 2007, “Multi-Objective Optimization of Compliant Mechanisms Including Failure Theories,” Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, September, Las Vegas, NV.
Canfield, S. L., Shibakov, A., and Richardson, J. D., 2009, “Design Space Analysis of Distributed Compliance in Segmented Beam Templates of Compliant Mechanisms,” Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, September, San Diego, CA.
Kota, S., Joo, J., Li, Z., Rodgers, S. M., and Sniegowski, J., 2001, “Design of Compliant Mechanisms: Applications to MEMS,” Analog Integrated Circuits and Signal Processing, pp. 7–15.
Kim, C. J., Moon, Y. M., and Kota, S., 2008, “A Building Block Approach to the Conceptual Synthesis of Compliant Mechanisms Utilizing Compliance and Stiffness Ellipsoids,” J. Mech. Des., 130(2), p. 022308. [CrossRef]
Krishnan, G., Kim, C., and Kota, S., 2011, “An Intrinsic Geometric Framework for the Building Block Synthesis of Single Point Compliant Mechanisms,” J. Mech. Rob., 3(1), p. 011001. [CrossRef]
Kim, C. J., Kota, S., and Moon, Y. M., 2006, “An Instant Center Approach Toward the Conceptual Design of Compliant Mechanisms,” J. Mech. Des., 128(3), pp. 542–550. [CrossRef]
Krishnan, G., Kim, C., and Kota, S., 2010, “Load-Transmitter Constraint Sets: Part I—An Effective Tool to Visualize Load Flow in Compliant Mechanisms and Structures,” Proceedings of 2010 ASME International Design Engineering Technical Conferences and, Computers and Information in Engineering Conferences, August, Montreal, CA.
Hetrick, J. A., and Kota, S., 1999, “An Energy Formulation for Parametric Size and Shape Optimization of Compliant Mechanisms,” J. Mech. Des., 121(2), pp. 229–234. [CrossRef]
Michell, A. G. M., 1904, “The Limits of Economy of Material in Frame-Structures,” Philosophical Magazine Series, Vol. 6.
Vogel, S., 2003, Comparative Biomechanics, Princeton University Press, Princeton, New Jersey.
Sivanagendra, P., and Ananthasuresh, G., 2009, “Size Optimization of a Cantilever Beam Under Deformation-Dependent Loads With Application to Wheat Stalks,” Struct. Multidiscip Optim., 39(3), pp. 327–336. [CrossRef]
Awtar, S., and Slocum, A. H., 2007, “Constraint-Based Design of Parallel Kinematic XY Flexure Mechanisms,” ASME J. Mech. Des., 129(8), pp. 816–830. [CrossRef]
Cappelleri, D. J., Krishnan, G., Kim, C., Kumar, V., and Kota, S., 2010, “Toward the Design of a Decoupled, Two-Dimensional, Vision-Based MU N Force Sensor,” J. Mech. Rob., 2(2), p. 021010. [CrossRef]
Lu, K.-J., and Kota, S., 2005, “An Effective Method of Synthesizing Compliant Adaptive Structures Using Load Path Representation,” J. Intell. Mater. Syst. Struct., 16(4), pp. 307–317. [CrossRef]
Lu, K.-J., 2004, “Synthesis of Shape-Morphing Compliant Mechanisms,” Ph.D. thesis, University of Michigan, Ann Arbor, MI.
2007, PaperPro website: www.paperpro.com
Kalapay, D., and Kim, C., 2008, “Design of a Compliant Energy Storage Impulse Mechanism for a Desktop Stapler,” Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, September, Brooklyn, NY.

Figures

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Fig. 1

Michell structure is the stiffest structure that supports the applied load with minimum volume. All the bars in the truss framework have the same stress.

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Fig. 2

Examples in nature with uniform stress distribution: (a) A sea-anemone subjected to water currents [19], (b) a tree branch subjected to wind loads, (c) bending stress distribution at any given cross-section, and (d) determining the thickness of the beam with distance from the free end that uniformly distributes stresses along its length

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Fig. 3

Comparison of three beams: (a) flexure with lumped compliance, (b) beam with uniform cross section, (c) tapered beam with uniform stress distribution, all having the same stiffness, and (d) comparison of the stress distribution throughout their length

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Fig. 6

Cross-section refinement for a fixed-guided beam: (a) Initial beam with uniform cross-section, (b) optimized cross-section, and (c) optimized beam used in a double parallelogram flexure

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Fig. 7

topology with deformed profile, and (c) stress distribution along the elements in the initial and optimized topology

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Fig. 8

Evaluation of output work through transferred forces: (a) Input force producing input and output displacements, (b) transferred force applied in the opposite direction at the output restricts its displacement, and (c) output force versus displacement curve

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Fig. 9

A beam with distributed load w N/m acting along its length

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Fig. 10

Size optimization of a compliant gripper [24]: (a) Intial topology with uniform cross-section thickness, (b) optimized design with the cross-section alone allowed to vary, and (c) optimized design when cross-section thickness and undeformed beam curvatures are allowed to vary. The three designs have the same stiffness and amplification factor.

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Fig. 11

Comparison of the optimized gripper designs from Fig. 10 in terms of (a) stress, (b) mechanical efficiency, and (c) total material volume

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Fig. 12

An energy storage mechanism for a compliant stapler gun: (a) Problem specification with the initial design, (b) optimized design for high mechanical efficiency η and its deformed profile, (c) optimized design for maximum strain energy distribution np and its deformed profile, and (d) optimized design for maximum performance metric npm and its deformed profile

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