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Research Papers

Systematic Synthesis of Large Displacement Contact-Aided Monolithic Compliant Mechanisms

[+] Author and Article Information
B. V. S. Nagendra Reddy, Sujitkumar V. Naik

Anupam Saxena1

Department of Mechanical Engineering, Indian Institute of Technology Kanpur, Kanpur – 208016, Indiaanupams@iitk.ac.in

Few of the existing boundary conditions can be removed if the corresponding nodes are absent in a candidate design. However, introducing additional boundary conditions is not implemented as a part of the current topology design procedure.

home.iitk.ac.in/∼anupams

1

Present address: IGM, RWTH-Aachen University, Germany.

J. Mech. Des 134(1), 011007 (Jan 04, 2012) (12 pages) doi:10.1115/1.4005326 History: Received May 05, 2011; Revised September 30, 2011; Published January 04, 2012; Online January 04, 2012

A single-piece contact-aided compliant mechanism (CCM) deforms to use one or many contact interactions to deliver the prescribed intricate input–output functionality. We present an automated synthesis procedure to design CCMs to trace large, non-smooth paths. Such paths can be traced by rigid-body or partially compliant mechanisms as well but the complexity, bulkiness and the presence of hinges is a disadvantage in terms of increased friction, backlash, need for lubrication, noise, and vibrations. In designing CCMs, both curved frame and two-dimensional finite elements are employed to represent the continuum and simulate the formation of contact sites. A contact site is one that allows relative rotation/sliding of a deforming member with respect to the neighboring one it is in contact with. The proposed design algorithm uses commercial software for large displacement contact analysis. The overall procedure automatically determines the CCM topology, feature shapes and sizes, and therefore the number (e.g., single or multiple) and nature (e.g., stiction or sliding) of contact sites. It systematically favors the continuum designs with lower function values when the synthesis problem is posed using a minimization objective. Synthesis of CCMs is exemplified for path generation applications though the proposed method can be employed for any generic kinematic task.

Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 1

Base mesh representing the design region. Member i can either be absent or if present will have the deformation characteristics of an initially curved frame element. Node (or junction) j can also get positioned appropriately within a user specified region (dashed lines) around it. Any two neighboring members can come in contact to form a contact site and abruptly alter the characteristics of the deforming continuum.

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Figure 2

Contact formulation between two deforming bodies Ω1 and Ω2

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Figure 3

A generic candidate CCM design to show how different initially curved members (with different in plane widths) can come in contact. ei : element numbers sharing a common junction k, i, j: two members proximal to each other without a common junction. F is the actuation load.

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Figure 4

(a) Nomenclature of contact faces of members sharing a common node. Inset: the common junction k in Fig. 3. (b) Local node and element numbering when a member is discretized into smaller curved frame elements.

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Figure 5

Illustration to identify the nearest potential contact surfaces around a junction

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Figure 6

(a) Proximal members i and j in Fig. 3 within which interaction is predicted and (b) identification of contact surfaces between two non-intersecting members, i and j.

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Figure 7

Illustration for removal of unnecessary interactions

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Figure 8

Modeling of a well connected junction as an octagon

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Figure 9

Contact modeling between two members (elements) sharing a common node, with element, node and surface labels. Frame members are modeled as quadrilateral elements.

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Figure 10

Prescribed/obtained paths modeled as linear piece-wise closed planar curves

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Figure 11

Example 1 with initially curved frame elements (a) Design specifications, (b) Solution after 320 evaluations, (c)–(e) various deformed configurations of the solution in (b), (f) comparison of actual and specified path

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Figure 12

Example 2 (a) Design specifications, (b) Solution after 280 evaluations, (c)–(e) various deformed configurations, (f) comparison between the specified and obtained paths

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Figure 13

Example 3: Synthesis Problem 1 re-solved by modeling curved members with two dimensional quadrilateral elements (a) Specifications, (b) Solution, (c)–(e) some deformed configurations, (f) comparison of actual and specified paths, (g) von Mises stress values for the final deformed CCM in (b) and (h) final deformed configuration with stress contours

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Figure 14

Example 4: Problem 2 re-solved. Curved members are modeled using two dimensional elements (a) Design specifications, (b) Solution after 3400 evaluations, (c)–(e) intermediate deformed states, (f) actual and specified paths, (g) and (h) von Mises stress values for the final deformed configuration. Stress contours are also shown.

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Figure 15

Example 5: Curved members modeled as two dimensional quadrilateral elements (a) Design specifications, (b) Solution (2500 evaluations), (c)–(e) intermediate deformed profile of the CCM in (b), (f) actual and specified paths, (g) von Mises stress values in the final deformed state and (h) stress contours at that state

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Figure 16

Example 6 (a) Design specifications, (b) CCM Solution (1600 evaluations), (c)–(e) some deformed states, (f) comparison of paths, (g) and (h) deformed configurations with stress contours

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Figure 17

Fabricated prototype of the solution in Fig.  1616 displaced configurations of the prototype. (c) Comparison of the specified (red) and experimentally obtained (black) path).

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Figure 18

(a)–(d) Comparison of the output paths for the CCMs in Figs.  13141516. The CCMs are analyzed using CPS4R and CPS4I element types. Solid lines: specified output path. Dashed red lines: Paths obtained with CPS4R elements. Blue dotted lines: CCM response with CPS4I elements.

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Figure 19

(left–right) Changes in the output paths for the CCMs in Figs.  141516 respectively with different friction coefficients. KEY: solid black line: Prescribed path. Dashed blue line: coefficient of friction μ = 0, dotted red line: μ = 0.2, dashed- dotted green line: μ = 1.

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