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Research Papers: Design of Mechanisms and Robotic Systems

Estimating Optimized Stress Bounds in Early Stage Design of Compliant Mechanisms

[+] Author and Article Information
Sree Kalyan Patiballa

Department of Industrial and
Enterprise Systems Engineering,
University of Illinois Urbana-Champaign,
Urbana, IL 61853
e-mail: patibal2@illinois.edu

Girish Krishnan

Mem. ASME
Department of Industrial and
Enterprise Systems Engineering,
University of Illinois Urbana-Champaign,
Urbana, IL 61853
e-mail: gkrishna@illinois.edu

1Corresponding author.

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received October 19, 2016; final manuscript received March 16, 2017; published online April 12, 2017. Assoc. Editor: Massimo Callegari.

J. Mech. Des 139(6), 062302 (Apr 12, 2017) (12 pages) Paper No: MD-16-1711; doi: 10.1115/1.4036305 History: Received October 19, 2016; Revised March 16, 2017

Design synthesis of distributed compliant mechanisms is often a two-stage process involving (a) conceptual topology synthesis and a subsequent (b) refinement stage to meet strength and manufacturing specifications. The usefulness of a solution is ascertained only after the sequential completion of these two steps that are, in general, computationally intensive. This paper presents a strategy to rapidly estimate final operating stresses even before the actual refinement process. This strategy is based on the uniform stress distribution metric, and a functional characterization of the different members that constitute the compliant mechanism topology. Furthermore, this paper uses the underlying mechanics of stress bound estimation to propose two rule of thumb guidelines for insightful selection of topologies and systematically modifying them for an application. The selection of the best conceptual solution in the early stage design avoids refinement of topologies that inherently may not meet the stress constraints. This paper presents two examples that illustrate these guidelines through the selection and refinement of topologies for a planar compliant gripper application.

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Figures

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Fig. 1

Contrasting the deformation nature of (a) lumped and (b) distributed compliant mechanisms [8]

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Fig. 2

Synthesis process of distributed compliant mechanisms: (a) problem specification, (b) conceptual design, (c) refinement to reduce stress, and (d) resize cross section to meet stiffness

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Fig. 3

(a) and (b) Plotting the transferred load flow in symmetric half of a gripper topology and identifying constraints and transmitters and (c) optimized cross section for even stress distribution

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Fig. 4

Dependence of metric on number of divisions for the free and guided boundary condition

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Fig. 5

Stress distributions of mechanism 1: the compliant four bar

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Fig. 6

Stress distributions of mechanism 2

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Fig. 7

Stress distributions of mechanism 3

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Fig. 8

Initial topologies of the three displacement amplifying compliant mechanisms (DaCMs): (a) mechanism A with a two-series load path, (b) mechanism B with a three-series load path, and (c) mechanism C with asymmetric parallel load path

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Fig. 9

Optimized topologies of (a) mechanism A, (b) mechanism B, and (c) mechanism C

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Fig. 10

Lower and upper stress bounds as a function of the geometric advantage (GA)

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Fig. 11

Optimized maximum stress and average predicted stresses as a function of the geometric advantage (GA)

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Fig. 12

Stiffness versus in-plane thickness

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Fig. 13

Initial and final stress distributions of mechanism D

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Fig. 14

Conceptual designs of the gripper mechanism: (a) mechanism 1 and (b) mechanism 2

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Fig. 15

Stiffness versus in-plane thickness for ABS plastic material

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Fig. 16

Stages in the design of the ABS gripper: (a) initial topology indicating the geometry variables, (b) geometry obtained by maximizing member volume from Eq. (12), (c) optimized cross sections to maximally distribute stress obtained from Eq. (2), and (d) fabricated gripper in the closed configuration

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Fig. 17

Stages in the design of the PDMS gripper: (a) initial geometry obtained by maximizing member volume from Eq. (12) and (b) optimized cross sections to maximally distribute stress obtained from Eq. (2)

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Fig. 18

Classes of compliant mechanisms where the proposed optimized stress bounds may not be valid: (a) mechanisms with nonuniform cross sections, (b) mechanisms with disproportionately long/short beam segments, and (c) mechanisms that undergo large deformation where the maximum stress significantly deviates from the linear case

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